1.2.1: Exercises
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1. List out the elements of the set “The letters of the word Mississipi”
2. List out the elements of the set “Months of the year”
3. Write a verbal description of the set \(\{3,6,9\}\)
4. Write a verbal description of the set \(\{a, i, e, 0, u\}\)
5. Is \(\{1,3,5\}\) a subset of the set of odd integers?
6. Is \(\{A, B, C\}\)a subset of the set of letters of the alphabet?
For problems 7-12, consider the sets below, and indicate if each statement is true or false.
\(A=\{1,2,3,4,5\} \quad B=\{1,3,5\} \quad C=\{4,6\} \quad U=\{\text { numbers from } 0 \text { to } 10\}\)
7. \(3 \in B\)
8. \(5 \in C\)
9. \(B \subset A\)
10. \(C \subset A\)
11. \(C \subset B\)
12. \(C \subset U\)
Using the sets from above, and treating \(U\) as the Universal set, find each of the following:
13. \(A \cup B\)
14. \(A \cup C\)
15. \(A \cap C\)
16. \(B \cap C\)
17. \(A^{c}\)
18. \(B^{c}\)
Let \(D=\{b, a, c, k\}, \quad E=\{t, a, s, k\}, \quad F=\{b, a, t, h\}\). Using these sets, find the following:
19. \(D^{c} \cap E\)
20. \(F^{c} \cap D\)
21. \((D \cap E) \cup F\)
22. \(D \cap(E \cup P)\)
23. \((F \cap E)^{c} \cap D\)
24. \((D \cup E)^{c} \cap F\)
Create a Venn diagram to illustrate each of the following:
25. \((F \cap E) \cup D\)
26. \((D \cup E)^{c} \cap F\)
27. \(\left(F^{c} \cap E^{\prime}\right) \cap D\)
28. \((D \cup E) \cup F\)
Write an expression for the shaded region.
29.
30.
31.
32.
Let \(A=\{1,2,3,4,5\} \quad B=\{1,3,5\} \quad C=\{4,6\}\). Find the cardinality of the given set.
33. \(\mathrm{n}(A)\)
34. \(\mathrm{n}(B)\)
35. \(\mathrm{n}(A \cup C)\)
36. \(\mathrm{n}(A \cap C)\)
The Venn diagram here shows the cardinality of each set. Use this in 37-40 to find the cardinality of given set.
37. \(\mathrm{n}(A \cap C)\)
38. \(\mathrm{n}(B \cup C)\)
39. \(\mathrm{n}\left(A \cap B \cap C^{2}\right)\)
40. \(\mathrm{n}\left(A \cap B^{c} \cap C\right)\)
41. If \(n(G)=20, n(H)=30, n(G \cap H)=5,\) find \(n(G \cup H)\)
42. If \(n(G)=5, n(H)=8, n(G \cap H)=4,\) find \(n(G \cup H)\)
43. A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.
\(\begin{array}{ll} \text{52 only use Netflix} & \text{62 only use Redbox} \\ \text{24 only use a video store} & \text{16 use only a video store and Redbox} \\ \text{48 use only Netflix and Redbox} & \text{30 use only a video store and Netflix} \\ \text{10 use all three} & \text{25 use none of these} \end{array}\)
44. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?
\(\begin{array}{ll} \text{5 only said color} & \text{8 only said size} \\ \text{16 only said brand} & \text{20 said only color and size} \\ \text{42 said only color and brand} & \text{53 said only size and brand} \\ \text{102 said all three} & \text{20 said none of these} \end{array}\)
45. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars .
\(\begin{array}{ll} \text{18 had seen The Matrix (M)} & \text{24 had seen Star Wars (SW)} \\ \text{20 had seen Lord of the Rings (LotR)} & \text{10 had seen M and SW} \\ \text{14 had seen LotR and SW } & \text{12 had seen M and LotR} \\ \text{6 had seen all three} & \text{} \end{array}\)
46. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don’t use any alternate transportation.
\(\begin{array}{ll} \text{30% use the bus} & \text{20% ride a bicycle} \\ \text{25% walk} & \text{5% use the bus and ride a bicycle} \\ \text{10% ride a bicycle and walk} & \text{12% use the bus and walk} \\ \text{2% use all three} & \text{} \end{array}\)


Chapter 5: Revenue
Trouble at Tesco
On November 9, 2014, it was reported that several legal firms were considering launching a class action suit against British grocery giant Tesco PLC. The claims were related to revelations made by the company in September that its profits for the first half of the year were overstated by £ 263 million. In October, the United Kingdom's Serious Fraud Office announced that it was launching its own investigation into the accounting practices at Tesco. This followed the company's suspension of eight senior executives along with the resignation of the CEO.
The issue at Tesco stemmed primarily from a misstatement of a revenue category described as "commercial income." Although the company's primary business is selling groceries to consumers, it also earns a significant amount from suppliers. Manufacturers and suppliers understand that in a grocery store, the location of the product on the shelves can have a significant effect on the level of sales generated. Many of these suppliers will offer rebates or other payments to Tesco in exchange for preferential placement of their products on the shelves. These rebates will often be calculated on a sliding scale, increasing as the level of sales increases.
In Tesco's interim financial statements, many of these rebates would need to be estimated, as the sales level for the entire year would not yet be known. Tesco's auditor, PwC, indicated in its 2014 audit report that the determination of commercial income was an area of audit risk due to the judgment required and possibility of manipulation. Tesco had been experiencing decreasing market share in 2014, and this may have provided an incentive for some degree of earnings management. Some analysts suggested that Tesco might have booked promotional rebates based on historic results rather than current activity.
Problems with revenue recognition have been a source of many accounting errors and frauds over the years. Given the complex nature of some types of business transactions and contracts, the criteria for recognition of revenue may not always be clear. When significant levels of judgment are required to determine the point at which revenue should be recognized, the opportunity for misstatement grows. Given that many of the complex issues surrounding revenue recognition are not always well understood by financial-statement readers, managers may sometimes give in to the temptation to "work" the numbers a little bit.
This chapter will explore some of the issues and judgments required with respect to revenue recognition and some of the problems that companies like Tesco may face.
(Source: Marriage, 2014)
After completing this chapter, you should be able to:
- Describe the criteria for recognizing revenue and determine if a company has earned revenue in a business transaction.
- Discuss the problem of measurement uncertainty and alternative accounting treatments for these situations.
- Prepare journal entries for a number of different types of sales transactions.
- Apply revenue recognition concepts to the determination of profit from long-term construction contracts.
- Prepare journal entries for long-term construction contracts.
- Apply revenue recognition concepts to unprofitable long-term construction contracts.
- Describe presentation and disclosure requirements for revenue-related accounts.
- Discuss the earnings approach to revenue recognition and compare it to current IFRS requirements.
Introduction
Revenue is the essence of any business. Without revenue, a business cannot exist. The basic concept of revenue is well understood by business people, but complex and important accounting issues complicate the recognition and reporting of revenue. Sometimes, the complexity of these issues can lead to erroneous or inappropriate recognition of revenue. In 2007, Nortel Networks Corporation paid a $35 million settlement in response to a Securities and Exchange Commission (SEC) investigation into its reporting practices. Although several problems were identified, one of the specific issues that the SEC investigated was Nortel's earlier accounting for bill-and-hold transactions. In a separate matter, Nortel was also required to restate its financial statements due to errors in the timing of revenue recognition for bundled sales contracts. In this chapter, we will examine these issues and determine the appropriate accounting treatment for revenues.


12.E: Static Equilibrium and Elasticity (Exercises)
Conceptual Questions
12.1 Conditions for Static Equilibrium
- What can you say about the velocity of a moving body that is in dynamic equilibrium?
- Under what conditions can a rotating body be in equilibrium? Give an example.
- What three factors affect the torque created by a force relative to a specific pivot point?
- Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this help? For the next four problems, evaluate the statement as either true or false and explain your answer.
- If there is only one external force (or torque) acting on an object, it cannot be in equilibrium.
- If an object is in equilibrium there must be an even number of forces acting on it.
- If an odd number of forces act on an object, the object cannot be in equilibrium.
- A body moving in a circle with a constant speed is in rotational equilibrium.
- What purpose is served by a long and flexible pole carried by wire-walkers?
12.2 Examples of Static Equilibrium
- Is it possible to rest a ladder against a rough wall when the floor is frictionless?
- Show how a spring scale and a simple fulcrum can be used to weigh an object whose weight is larger than the maximum reading on the scale.
- A painter climbs a ladder. Is the ladder more likely to slip when the painter is near the bottom or near the top?
12.3 Stress, Strain, and Elastic Modulus
Note : Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in Table 12.1.
- Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?
- When a glass bottle full of vinegar warms up, both the vinegar and the glass expand, but the vinegar expands significantly more with temperature than does the glass. The bottle will break if it is filled up to its very tight cap. Explain why and how a pocket of air above the vinegar prevents the bottle from breaking.
- A thin wire strung between two nails in the wall is used to support a large picture. Is the wire likely to snap if it is strung tightly or if it is strung so that it sags considerably?
- Review the relationship between stress and strain. Can you find any similarities between the two quantities?
- What type of stress are you applying when you press on the ends of a wooden rod? When you pull on its ends?
- Can compressive stress be applied to a rubber band?
- Can Young’s modulus have a negative value? What about the bulk modulus?

- Discuss how you might measure the bulk modulus of a liquid.
12.4 Elasticity and Plasticity
Note : Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in Table 12.1.
- What is meant when a fishing line is designated as “a 10-lb test?”
- Steel rods are commonly placed in concrete before it sets. What is the purpose of these rods?
Problems
12.1 Conditions for Static Equilibrium
- When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. How much torque are you exerting relative to the center of the bolt?
- When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges?
- Find the magnitude of the tension in each supporting cable shown below. In each case, the weight of the suspended body is 100.0 N and the masses of the cables are negligible.
- What force must be applied at point P to keep the structure shown in equilibrium? The weight of the structure is negligible.
- Is it possible to apply a force at P to keep in equilibrium the structure shown? The weight of the structure is negligible.
- Two children push on opposite sides of a door during play. Both push horizontally and perpendicular to the door. One child pushes with a force of 17.5 N at a distance of 0.600 m from the hinges, and the second child pushes at a distance of 0.450 m. What force must the second child exert to keep the door from moving? Assume friction is negligible.
- A small 1000-kg SUV has a wheel base of 3.0 m. If 60% if its weight rests on the front wheels, how far behind the front wheels is the wagon’s center of mass?
- The uniform seesaw is balanced at its center of mass, as seen below. The smaller boy on the right has a mass of 40.0 kg. What is the mass of his friend?
12.2 Examples of Static Equilibrium
- A uniform plank rests on a level surface as shown below. The plank has a mass of 30 kg and is 6.0 m long. How much mass can be placed at its right end before it tips? ( Hint : When the board is about to tip over, it makes contact with the surface only along the edge that becomes a momentary axis of rotation.)
- The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
- In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tree 15 m away, as shown below. He then pulls on the center of the rope with a force of 400 N, which causes its center to be displaced 0.30 m, as shown. What is the force of the rope on the car?
- A uniform 40.0-kg scaffold of length 6.0 m is supported by two light cables, as shown below. An 80.0-kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.5 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the equipment.
- When the structure shown below is supported at point P, it is in equilibrium. Find the magnitude of force F and the force applied at P. The weight of the structure is negligible.
- To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2.00 m from the bottom.  Find the normal reaction and friction forces on the ladder at its base.
- A uniform horizontal strut weighs 400.0 N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 200.0 N. The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.
- The forearm shown below is positioned at an angle \(\theta\) with respect to the upper arm, and a 5.0-kg mass is held in the hand. The total mass of the forearm and hand is 3.0 kg, and their center of mass is 15.0 cm from the elbow. (a) What is the magnitude of the force that the biceps muscle exerts on the forearm for \(\theta\) = 60°? (b) What is the magnitude of the force on the elbow joint for the same angle? (c) How do these forces depend on the angle \(\theta\)?
- The uniform boom shown below weighs 3000 N. It is supported by the horizontal guy wire and by the hinged support at point A. What are the forces on the boom due to the wire and due to the support at A? Does the force at A act along the boom?
- The uniform boom shown below weighs 700 N, and the object hanging from its right end weighs 400 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom?
- A 12.0-m boom, AB, of a crane lifting a 3000-kg load is shown below. The center of mass of the boom is at its geometric center, and the mass of the boom is 1000 kg. For the position shown, calculate tension T in the cable and the force at the axle A.
- A uniform trapdoor shown below is 1.0 m by 1.5 m and weighs 300 N. It is supported by a single hinge (H), and by a light rope tied between the middle of the door and the floor. The door is held at the position shown, where its slab makes a 30° angle with the horizontal floor and the rope makes a 20° angle with the floor. Find the tension in the rope and the force at the hinge.
- A 90-kg man walks on a sawhorse, as shown below. The sawhorse is 2.0 m long and 1.0 m high, and its mass is 25.0 kg. Calculate the normal reaction force on each leg at the contact point with the floor when the man is 0.5 m from the far end of the sawhorse. ( Hint : At each end, find the total reaction force first. This reaction force is the vector sum of two reaction forces, each acting along one leg. The normal reaction force at the contact point with the floor is the normal (with respect to the floor) component of this force.)
12.3 Stress, Strain, and Elastic Modulus
- The “lead” in pencils is a graphite composition with a Young’s modulus of approximately 1.0 x 10 9 N/m 2 . Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.
- TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 72.0-kg physicist placed himself and 400 kg of equipment at the top of a 610-m-high antenna to perform gravity experiments. By how much was the antenna compressed, if we consider it to be equivalent to a steel cylinder 0.150 m in radius?
- By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping? (For nylon, Y = 1.35 x 10 9 Pa.)
- When water freezes, its volume increases by 9.05%. What force per unit area is water capable of exerting on a container when it freezes?
- A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2%. Calculate the force exerted by the juice per square centimeter if its bulk modulus is 1.8 x 10 9 N /m 2 , assuming the bottle does not break.
- A disk between vertebrae in the spine is subjected to a shearing force of 600.0 N. Find its shear deformation, using the shear modulus of 1.0 x 10 9 N/m 2 . The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.
- A vertebra is subjected to a shearing force of 500.0 N. Find the shear deformation, taking the vertebra to be a cylinder 3.00 cm high and 4.00 cm in diameter. How does your result compare with the result obtained in the preceding problem? Are spinal problems more common in disks than in vertebrae?
- Calculate the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, if the wire is originally 1.35 m long and its diameter is 0.850 mm.
- A 20.0-m-tall hollow aluminum flagpole is equivalent in strength to a solid cylinder 4.00 cm in diameter. A strong wind bends the pole as much as a horizontal 900.0-N force on the top would do. How far to the side does the top of the pole flex?
- A copper wire of diameter 1.0 cm stretches 1.0% when it is used to lift a load upward with an acceleration of 2.0 m/s 2 . What is the weight of the load?
- As an oil well is drilled, each new section of drill pipe supports its own weight and the weight of the pipe and the drill bit beneath it. Calculate the stretch in a new 6.00-m-long steel pipe that supports a 100-kg drill bit and a 3.00-km length of pipe with a linear mass density of 20.0 kg/m. Treat the pipe as a solid cylinder with a 5.00-cm diameter.
- A large uniform cylindrical steel rod of density \(\rho\) = 7.8 g/cm 3 is 2.0 m long and has a diameter of 5.0 cm. The rod is fastened to a concrete floor with its long axis vertical. What is the normal stress in the rod at the cross-section located at (a) 1.0 m from its lower end? (b) 1.5 m from the lower end?
- A 90-kg mountain climber hangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m long and its diameter is 1.0 cm, what is Young’s modulus for the nylon?
- A suspender rod of a suspension bridge is 25.0 m long. If the rod is made of steel, what must its diameter be so that it does not stretch more than 1.0 cm when a 2.5 x 10 4 -kg truck passes by it? Assume that the rod supports all of the weight of the truck.
- A copper wire is 1.0 m long and its diameter is 1.0 mm. If the wire hangs vertically, how much weight must be added to its free end in order to stretch it 3.0 mm?
- A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and 2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?
- The bulk modulus of a material is 1.0 x 10 11 N/m 2 . What fractional change in volume does a piece of this material undergo when it is subjected to a bulk stress increase of 10 7 N/m 2 ? Assume that the force is applied uniformly over the surface.
- Normal forces of magnitude 1.0 x 10 6 N are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from 50.000 cm to 49.995 cm. What is the bulk modulus of the liquid?
- During a walk on a rope, a tightrope walker creates a tension of 3.94 x 10 3 N in a wire that is stretched between two supporting poles that are 15.0 m apart. The wire has a diameter of 0.50 cm when it is not stretched. When the walker is on the wire in the middle between the poles the wire makes an angle of 5.0° below the horizontal. How much does this tension stretch the steel wire when the walker is this position?
- When using a pencil eraser, you exert a vertical force of 6.00 N at a distance of 2.00 cm from the hardwood-eraser joint. The pencil is 6.00 mm in diameter and is held at an angle of 20.0° to the horizontal. (a) By how much does the wood flex perpendicular to its length? (b) How much is it compressed lengthwise?
- Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.0 cm. If the pressure on the surface is increased by 200 MPa, by how much does the radius of the sphere decrease?
12.4 Elasticity and Plasticity
- A uniform rope of cross-sectional area 0.50 cm 2 breaks when the tensile stress in it reaches 6.00 x 10 6 N/m 2 . (a) What is the maximum load that can be lifted slowly at a constant speed by the rope? (b) What is the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s 2 ?
- One end of a vertical metallic wire of length 2.0 m and diameter 1.0 mm is attached to a ceiling, and the other end is attached to a 5.0-N weight pan, as shown below. The position of the pointer before the pan is 4.000 cm. Different weights are then added to the pan area, and the position of the pointer is recorded in the table shown. Plot stress versus strain for this wire, then use the resulting curve to determine Young’s modulus and the proportionality limit of the metal. What metal is this most likely to be?
| Added load (including pan) (N) | Scale reading (cm) |
|---|---|
| 0 | 4.000 |
| 15 | 4.036 |
| 25 | 4.073 |
| 35 | 4.109 |
| 45 | 4.146 |
| 55 | 4.181 |
| 65 | 4.221 |
| 75 | 4.266 |
| 85 | 4.316 |
- An aluminum (\(\rho\) = 2.7 g/cm 3 ) wire is suspended from the ceiling and hangs vertically. How long must the wire be before the stress at its upper end reaches the proportionality limit, which is 8.0 x 10 7 N/m 2 ?
Additional Problems
- The coefficient of static friction between the rubber eraser of the pencil and the tabletop is \(\mu_{s}\) = 0.80. If the force \(\vec{F}\) is applied along the axis of the pencil, as shown below, what is the minimum angle at which the pencil can stand without slipping? Ignore the weight of the pencil.
- A pencil rests against a corner, as shown below. The sharpened end of the pencil touches a smooth vertical surface and the eraser end touches a rough horizontal floor. The coefficient of static friction between the eraser and the floor is \(\mu_{s}\) = 0.80. The center of mass of the pencil is located 9.0 cm from the tip of the eraser and 11.0 cm from the tip of the pencil lead. Find the minimum angle θ for which the pencil does not slip.
- A uniform 4.0-m plank weighing 200.0 N rests against the corner of a wall, as shown below. There is no friction at the point where the plank meets the corner. (a) Find the forces that the corner and the floor exert on the plank. (b) What is the minimum coefficient of static friction between the floor and the plank to prevent the plank from slipping?
- A 40-kg boy jumps from a height of 3.0 m, lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is 3.0 cm 2 , what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than 1.7 x 10 8 Pa. Is the boy in danger of breaking his leg?
- Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod is 2.0 m long and has cross-sectional area 9.1 mm 2 . If a 10,000-N tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.
- Two rods, one made of copper and the other of steel, have the same dimensions. If the copper rod stretches by 0.15 mm under some stress, how much does the steel rod stretch under the same stress?
Challenge Problems
- A horizontal force \(\vec{F}\) is applied to a uniform sphere in direction exact toward the center of the sphere, as shown below. Find the magnitude of this force so that the sphere remains in static equilibrium. What is the frictional force of the incline on the sphere?
- When a motor is set on a pivoted mount seen below, its weight can be used to maintain tension in the drive belt. When the motor is not running the tensions T 1 and T 2 are equal. The total mass of the platform and the motor is 100.0 kg, and the diameter of the drive belt pulley is 16.0 cm. when the motor is off, find: (a) the tension in the belt, and (b) the force at the hinged platform support at point C. Assume that the center of mass of the motor plus platform is at the center of the motor.
- Two wheels A and B with weights w and 2w, respectively, are connected by a uniform rod with weight w/2, as shown below. The wheels are free to roll on the sloped surfaces. Determine the angle that the rod forms with the horizontal when the system is in equilibrium. Hint : There are five forces acting on the rod, which is two weights of the wheels, two normal reaction forces at points where the wheels make contacts with the wedge, and the weight of the rod.
- Weights are gradually added to a pan until a wheel of mass M and radius R is pulled over an obstacle of height d, as shown below. What is the minimum mass of the weights plus the pan needed to accomplish this?
- In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance l 2 from the end, as shown below. The weight of the shovel is m\(\vec{g}\) and acts at the point of application of \(\vec{F}_{2}\). Calculate the magnitudes of the forces \(\vec{F}_{1}\) and \(\vec{F}_{2}\) as functions of l 1 , l 2 , mg, and the weight W of the load. Why do your answers not depend on the angle \(theta\) that the shovel makes with the horizontal?
- A uniform rod of length 2R and mass M is attached to a small collar C and rests on a cylindrical surface of radius R, as shown below. If the collar can slide without friction along the vertical guide, find the angle \(\theta\) for which the rod is in static equilibrium.
- The pole shown below is at a 90.0° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4.00 x 10 4 N, at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the strength of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0° with the vertical. The guy wire is in the opposite direction of the bend.
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a
Creative Commons Attribution License (by 4.0)
.


7.4.2: Clouds
Clouds form by the condensation of water into extremely small droplets of liquid or ice. Clouds are classified according to the height at which they form and their structure. High clouds form above 7,000 m (23,000 ft) and are primarily composed of ice crystals. Meteorologists call these cirro-form clouds. Mid-level clouds form between 2,000 and 7,000 m. The prefix alto is applied to these clouds. Low clouds form between the surface and 2,000 m.
Clouds are also classfied based on their form or structure. If they take on a layered appearance they are strati-form. If they show vertical development they are cumulo-form. To indicate they are precipitating, meteorologists apply the prefix nimbo or suffix nimbus to their name. There are many other terms used to describe cloud form but they are beyond the scope of this textbook.
High clouds
High clouds are cirro-form clouds being composed mostly of ice. Generally found above 7,000 meters, these clouds include: cirrus, cirrostratus and cirrocumulus.
Cirrus clouds appear as wispy thin veils or detached filaments composed mostly of ice. Strong winds aloft often create the fibrous ice trails which tend to curl at their ends. Cirrus clouds with hooked filaments are sometimes called "mare's tails". Cirrus clouds are associated with an approaching warm front.
Cirrostratus is a transparent, whitish veil of cloud that usually covers much of the sky. Sometimes cirrostratus clouds are so transparent that you can barely see them. They often create a halo around the sun or moon. Cirrostratus clouds thicken and grade into altostratus clouds with the approach of a warm front.
 The globules of cloud are arranged in a regular pattern and are commonly called "mackerel sky" for their similarity to the scales of a fish.
Middle Clouds
Clouds found in the middle levels of the troposphere have the prefix alto attached to their name. Two clouds are described here: altocumulus and altostratus.
Altocumulus form as large masses in patches or rows that may or may not merge with one another. Individuals usually have a sharp outline as they are composed of water and not ice. Altocumulus clouds are easily confused with cirrocumulus and stratocumulus clouds. Cirrocumulus are smaller and less dense than altocumulus. Elements of stratocumulus are larger than altocumulus.
Altostratus are a formless layer of grayish cloud that cover most if not all the sky. Altostratus clouds are more dense than the cirrostratus. The sun is barely visible through altostratus clouds giving the appearance of a "watery sun". Where enough light shows through cirrostratus clouds to create shadows, it does not with altostratus. Altostratus thicken into nimbostratus as a warm front approaches your location.
Low Clouds
Low clouds are those that form from the surface up to 2,000 meters. Low clouds include: stratus, stratocumulus, and nimbostratus.
Stratus clouds appear as a uniform dark-gray layer of clouds covering the entire sky. Stratus clouds often form along warm fronts and can give way to nimbostratus as the front approaches your location. Stratus clouds may also form by the lifting of a fog bank.
Stratocumulus clouds appear as lumpy, low lying clouds that cover much of the sky. They form patches or rows of clouds with some blue sky between the individual cloud units.
Nimbostratus clouds are dark-gray layer of clouds that cover the entire sky. The prefix "nimbo" indicates that these clouds are precipitating. Nimbostratus clouds are typically found along a warm front producing low intensity precipitation that lasts for several hours.
Vertically Developed Clouds
Cumulus-type clouds are those that primarily exhibit vertical development. Two of the more common types are the cumulus and cumulonimbus.
Cumulus clouds appear as small, cotton ball-like clouds that generally form by convection. Cumulus are also called "fair-weather" clouds as pleasant conditions usually prevail while they are around.
Cumulonimbus clouds form during very unstable conditions. They are the tallest clouds, and can reach to the stratosphere. Cumulonimbus clouds are associated with thunderstorms capable of generating locally high winds, hail, lightning, and torrential down pours.


2.2.1: Introduction
The development of the axiomatic method is a significant achievement in the history of science, and is of special importance in the history of mathematics. An axiomatic development of a field involves the clarification of many questions: What is the field about? What are the most fundamental concepts? How are they related? Can all the concepts of the field be defined in terms of these fundamental concepts? What laws do, and must, these concepts obey?
The axiomatic method and logic were made for each other. Formal logic provides the tools for formulating axiomatic theories, for proving theorems from the axioms of the theory in a precisely specified way, for studying the properties of all systems satisfying the axioms in a systematic way.
A set of sentences \(\Gamma\) is closed iff, whenever \(\Gamma \Entails A\) then \(A \in \Gamma\) . The closure of a set of sentences \(\Gamma\) is \(\Setabs{A}{\Gamma \Entails A}\) .
We say that \(\Gamma\) is axiomatized by a set of sentences \(\Delta\) if \(\Gamma\) is the closure of \(\Delta\) .
We can think of an axiomatic theory as the set of sentences that is axiomatized by its set of axioms \(\Delta\) . In other words, when we have a first-order language which contains non-logical symbols for the primitives of the axiomatically developed science we wish to study, together with a set of sentences that express the fundamental laws of the science, we can think of the theory as represented by all the sentences in this language that are entailed by the axioms. This ranges from simple examples with only a single primitive and simple axioms, such as the theory of partial orders, to complex theories such as Newtonian mechanics.
The important logical facts that make this formal approach to the axiomatic method so important are the following. Suppose \(\Gamma\) is an axiom system for a theory, i.e., a set of sentences.
- We can state precisely when an axiom system captures an intended class of structures. That is, if we are interested in a certain class of structures, we will successfully capture that class by an axiom system \(\Gamma\) iff the structures are exactly those \(\Struct M\) such that \(\Sat{M}{\Gamma}\) .
- We may fail in this respect because there are \(\Struct M\) such that \(\Sat{M}{\Gamma}\) , but \(\Struct M\) is not one of the structures we intend. This may lead us to add axioms which are not true in \(\Struct M\) .
- If we are successful at least in the respect that \(\Gamma\) is true in all the intended structures, then a sentence \(A\) is true in all intended structures whenever \(\Gamma \Entails A\) . Thus we can use logical tools (such as proof methods) to show that sentences are true in all intended structures simply by showing that they are entailed by the axioms.
- Sometimes we don’t have intended structures in mind, but instead start from the axioms themselves: we begin with some primitives that we want to satisfy certain laws which we codify in an axiom system. One thing that we would like to verify right away is that the axioms do not contradict each other: if they do, there can be no concepts that obey these laws, and we have tried to set up an incoherent theory. We can verify that this doesn’t happen by finding a model of \(\Gamma\) . And if there are models of our theory, we can use logical methods to investigate them, and we can also use logical methods to construct models.
- The independence of the axioms is likewise an important question. It may happen that one of the axioms is actually a consequence of the others, and so is redundant. We can prove that an axiom \(A\) in \(\Gamma\) is redundant by proving \(\Gamma \setminus \{A\} \Entails A\) . We can also prove that an axiom is not redundant by showing that \((\Gamma \setminus \{A\}) \cup \{\lnot A\}\) is satisfiable. For instance, this is how it was shown that the parallel postulate is independent of the other axioms of geometry.
- Another important question is that of definability of concepts in a theory: The choice of the language determines what the models of a theory consists of. But not every aspect of a theory must be represented separately in its models. For instance, every ordering \(\le\) determines a corresponding strict ordering \(<\) —given one, we can define the other. So it is not necessary that a model of a theory involving such an order must also contain the corresponding strict ordering. When is it the case, in general, that one relation can be defined in terms of others? When is it impossible to define a relation in terms of other (and hence must add it to the primitives of the language)?


6.2: Electromotive Force
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Learning Objectives
By the end of the section, you will be able to:
- Describe the electromotive force (emf) and the internal resistance of a battery
- Explain the basic operation of a battery
If you forget to turn off your car lights, they slowly dim as the battery runs down.  Their gradual dimming implies that the battery output voltage decreases as the battery is depleted. The reason for the decrease in output voltage for depleted batteries is that all voltage sources have two fundamental parts—a source of electrical energy and an internal resistance. In this section, we examine the energy source and the internal resistance.
Introduction to Electromotive Force
Voltage has many sources, a few of which are shown in Figure \(\PageIndex{2}\). All such devices create a potential difference and can supply current if connected to a circuit. A special type of potential difference is known as electromotive force (emf) . The emf is not a force at all, but the term ‘electromotive force’ is used for historical reasons. It was coined by Alessandro Volta in the 1800s, when he invented the first battery, also known as the voltaic pile . Because the electromotive force is not a force, it is common to refer to these sources simply as sources of emf (pronounced as the letters “ee-em-eff”), instead of sources of electromotive force.
If the electromotive force is not a force at all, then what is the emf and what is a source of emf? To answer these questions, consider a simple circuit of a 12-V lamp attached to a 12-V battery, as shown in Figure \(\PageIndex{2}\). The battery can be modeled as a two-terminal device that keeps one terminal at a higher electric potential than the second terminal. The higher electric potential is sometimes called the positive terminal and is labeled with a plus sign. The lower-potential terminal is sometimes called the negative terminal and labeled with a minus sign. This is the source of the emf.
When the emf source is not connected to the lamp, there is no net flow of charge within the emf source. Once the battery is connected to the lamp, charges flow from one terminal of the battery, through the lamp (causing the lamp to light), and back to the other terminal of the battery. If we consider positive (conventional) current flow, positive charges leave the positive terminal, travel through the lamp, and enter the negative terminal.
Positive current flow is useful for most of the circuit analysis in this chapter, but in metallic wires and resistors, electrons contribute the most to current, flowing in the opposite direction of positive current flow. Therefore, it is more realistic to consider the movement of electrons for the analysis of the circuit in Figure \(\PageIndex{2}\). The electrons leave the negative terminal, travel through the lamp, and return to the positive terminal. In order for the emf source to maintain the potential difference between the two terminals, negative charges (electrons) must be moved from the positive terminal to the negative terminal. The emf source acts as a charge pump, moving negative charges from the positive terminal to the negative terminal to maintain the potential difference. This increases the potential energy of the charges and, therefore, the electric potential of the charges.
The force on the negative charge from the electric field is in the opposite direction of the electric field, as shown in Figure \(\PageIndex{2}\). In order for the negative charges to be moved to the negative terminal, work must be done on the negative charges. This requires energy, which comes from chemical reactions in the battery. The potential is kept high on the positive terminal and low on the negative terminal to maintain the potential difference between the two terminals. The emf is equal to the work done on the charge per unit charge \(\left(\epsilon = \frac{dW}{dq}\right)\) when there is no current flowing. Since the unit for work is the joule and the unit for charge is the coulomb, the unit for emf is the volt \((1 \, V = 1 \, J/C)\).
The terminal voltage \(V_{terminal}\) of a battery is voltage measured across the terminals of the battery when there is no load connected to the terminal. An ideal battery is an emf source that maintains a constant terminal voltage, independent of the current between the two terminals. An ideal battery has no internal resistance, and the terminal voltage is equal to the emf of the battery. In the next section, we will show that a real battery does have internal resistance and the terminal voltage is always less than the emf of the battery.
The Origin of Battery Potential
The combination of chemicals and the makeup of the terminals in a battery determine its emf. The lead acid battery used in cars and other vehicles is one of the most common combinations of chemicals. Figure \(\PageIndex{3}\) shows a single cell (one of six) of this battery. The cathode (positive) terminal of the cell is connected to a lead oxide plate, whereas the anode (negative) terminal is connected to a lead plate. Both plates are immersed in sulfuric acid, the electrolyte for the system.
Knowing a little about how the chemicals in a lead-acid battery interact helps in understanding the potential created by the battery. Figure \(\PageIndex{4}\) shows the result of a single chemical reaction. Two electrons are placed on the anode , making it negative, provided that the cathode supplies two electrons. This leaves the cathode positively charged, because it has lost two electrons. In short, a separation of charge has been driven by a chemical reaction.
Note that the reaction does not take place unless there is a complete circuit to allow two electrons to be supplied to the cathode. Under many circumstances, these electrons come from the anode, flow through a resistance, and return to the cathode. Note also that since the chemical reactions involve substances with resistance, it is not possible to create the emf without an internal resistance.
Internal Resistance and Terminal Voltage
The amount of resistance to the flow of current within the voltage source is called the internal resistance . The internal resistance r of a battery can behave in complex ways. It generally increases as a battery is depleted, due to the oxidation of the plates or the reduction of the acidity of the electrolyte. However, internal resistance may also depend on the magnitude and direction of the current through a voltage source, its temperature, and even its history. The internal resistance of rechargeable nickel-cadmium cells, for example, depends on how many times and how deeply they have been depleted. A simple model for a battery consists of an idealized emf source \(\epsilon\) and an internal resistance r (Figure \(\PageIndex{5}\)).
Suppose an external resistor, known as the load resistance R , is connected to a voltage source such as a battery, as in Figure \(\PageIndex{6}\). The figure shows a model of a battery with an emf ε , an internal resistance r , and a load resistor R connected across its terminals. Using conventional current flow, positive charges leave the positive terminal of the battery, travel through the resistor, and return to the negative terminal of the battery. The terminal voltage of the battery depends on the emf, the internal resistance, and the current, and is equal to
Note
\[V_{terminal} = \epsilon - Ir \nonumber \]
For a given emf and internal resistance, the terminal voltage decreases as the current increases due to the potential drop Ir of the internal resistance.
A graph of the potential difference across each element the circuit is shown in Figure \(\PageIndex{7}\). A current I runs through the circuit, and the potential drop across the internal resistor is equal to Ir . The terminal voltage is equal to \(\epsilon - Ir\), which is equal to the potential drop across the load resistor \(IR = \epsilon - Ir\). As with potential energy, it is the change in voltage that is important. When the term “voltage” is used, we assume that it is actually the change in the potential, or \(\Delta V\). However, \(\Delta\) is often omitted for convenience.
The current through the load resistor is \(I = \frac{\epsilon}{r + R}\). We see from this expression that the smaller the internal resistance r , the greater the current the voltage source supplies to its load R . As batteries are depleted, r increases. If r becomes a significant fraction of the load resistance, then the current is significantly reduced, as the following example illustrates.
Example \(\PageIndex{1}\): Analyzing a Circuit with a Battery and a Load
A given battery has a 12.00-V emf and an internal resistance of \(0.100 \, \Omega\). (a) Calculate its terminal voltage when connected to a\(10.00 \, \Omega\) load. (b) What is the terminal voltage when connected to a \(0.500 \, \Omega\) load? (c) What power does the \(0.500 \, \Omega\) load dissipate? (d) If the internal resistance grows to \(0.500 \, \Omega\), find the current, terminal voltage, and power dissipated by a \(0.500 \, \Omega\) load.
Strategy
The analysis above gave an expression for current when internal resistance is taken into account. Once the current is found, the terminal voltage can be calculated by using the equation \(V_{terminal} = \epsilon - Ir\). Once current is found, we can also find the power dissipated by the resistor.
Solution
- Entering the given values for the emf, load resistance, and internal resistance into the expression above yields \[I = \frac{\epsilon}{R + r} = \frac{12.00 \, V}{10.10 \, \Omega} = 1.188 \, A. \nonumber \] Enter the known values into the equation\(V_{terminal} = \epsilon - Ir\) to get the terminal voltage: \[V_{terminal} = \epsilon - Ir = 12.00 \, V - (1.188 \, A)(0.100 \, \Omega) = 11.90 \, V. \nonumber \] The terminal voltage here is only slightly lower than the emf, implying that the current drawn by this light load is not significant.
- Similarly, with \(R_{load} = 0.500 \, \Omega\), the current is \[I = \frac{\epsilon}{R + r} = \frac{12.00 \, V}{0.600 \, \Omega} = 20.00 \, A. \nonumber \] The terminal voltage is now \[V_{terminal} = \epsilon - Ir = 12.00 \, V - (20.00 \, A)(0.100 \, \Omega) = 10.00 \, V. \nonumber \] The terminal voltage exhibits a more significant reduction compared with emf, implying \(0.500 \, \Omega\) is a heavy load for this battery. A “heavy load” signifies a larger draw of current from the source but not a larger resistance.
- The power dissipated by the \(0.500 \, \Omega\) load can be found using the formula \(P = I^2R\). Entering the known values gives \[P = I^2R = (20.0 \, A)^2(0.500 \, \Omega) = 2.00 \times 10^2 \, W. \nonumber \] Note that this power can also be obtained using the expression \(\frac{V^2}{R}\) or \(IV\), where V is the terminal voltage (10.0 V in this case).
- Here, the internal resistance has increased, perhaps due to the depletion of the battery, to the point where it is as great as the load resistance. As before, we first find the current by entering the known values into the expression, yielding \[I = \frac{\epsilon}{R + r} = \frac{12.00 \, V}{1.00 \, \Omega} = 12.00 \, A. \nonumber \] Now the terminal voltage is \[V_{terminal} = \epsilon - Ir = 12.00 \, V - (12.00 \, A)(0.500 \, \Omega) = 6.00 \, V, \nonumber \] and the power dissipated by the load is \[P = I^2R = (12.00 \, A)^2(0.500 \, \Omega) = 72.00 \, W. \nonumber \] We see that the increased internal resistance has significantly decreased the terminal voltage, current, and power delivered to a load.
Significance
The internal resistance of a battery can increase for many reasons. For example, the internal resistance of a rechargeable battery increases as the number of times the battery is recharged increases. The increased internal resistance may have two effects on the battery. First, the terminal voltage will decrease. Second, the battery may overheat due to the increased power dissipated by the internal resistance.
Exercise \(\PageIndex{1}\)
If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Why do you suppose this happens?
- Solution
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If a wire is connected across the terminals, the load resistance is close to zero, or at least considerably less than the internal resistance of the battery. Since the internal resistance is small, the current through the circuit will be large, \(I = \frac{\epsilon}{R + r} = \frac{\epsilon}{0 + r} = \frac{\epsilon}{r}\). The large current causes a high power to be dissipated by the internal resistance \((P = I^2r)\). The power is dissipated as heat.
Battery Testers
Battery testers , such as those in Figure \(\PageIndex{8}\), use small load resistors to intentionally draw current to determine whether the terminal potential drops below an acceptable level. Although it is difficult to measure the internal resistance of a battery, battery testers can provide a measurement of the internal resistance of the battery. If internal resistance is high, the battery is weak, as evidenced by its low terminal voltage.
Some batteries can be recharged by passing a current through them in the direction opposite to the current they supply to an appliance. This is done routinely in cars and in batteries for small electrical appliances and electronic devices (Figure \(\PageIndex{9}\)). The voltage output of the battery charger must be greater than the emf of the battery to reverse the current through it. This causes the terminal voltage of the battery to be greater than the emf, since \(V = \epsilon - Ir\) and I is now negative.
It is important to understand the consequences of the internal resistance of emf sources, such as batteries and solar cells, but often, the analysis of circuits is done with the terminal voltage of the battery, as we have done in the previous sections. The terminal voltage is referred to as simply as V , dropping the subscript “terminal.” This is because the internal resistance of the battery is difficult to measure directly and can change over time.


16: Two Independent Sample Means Comparison Given Statistics
Two Independent Samples with statistics Calculator
This calculator performs the hypothesis test and also constructs a confidence interval for \(\mu_1\)−\(\mu_2\) for two population means given statistics. Please report the error to Dr. Jessica Kuang at jkuangATvcccd.edu.
To learn how to use this calculator, please watch a short video here (coming up).
Input
Enter the statistics, the tail type, and the confidence level and hit Calculate and the test statistic, p-value, and the boundaries for the confidence interval. Be sure to enter the confidence level as a decimal, e.g., 95% should be entered as 0.95.
| Sample Size | Sample Mean | Sample Standard Deviation | |
| First Sample | |||
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choose a test
\(\lt\)
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|||
| Second Sample |
| Confidence Level (Enter a Decimal): |
Output
| Test Statistics (t): | p-value: | Lower Bound: | Upper Bound: |
(Powered by Desmos)


31.5: Arguments for and Against Protectionist Policy
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National Security Argument
National security protectionist arguments pertain to the risk of dependency upon other nations for economic sustainability.
learning objectives
- Evaluate the arguments in favor of the use of trade protectionism in the security industry
Economic interdependence and globalization has resulted in a system, where each country is largely dependent upon other countries for economic sustainability (though to varying degrees). This results in a substantial national security threat in the form of conflicting or offensive trade strategies between countries. Indeed, economics is often used directly as a weapon of war and conflict via trade sanctions. This highlights a critical protectionist argument pertaining to the very real risk of dependency upon other nations for economic sustainability.
Trade and Conflict
An interesting discussion in economics is the relationship between trade and conflict. It has been noted, somewhat intuitively and empirically, that conflict reduces trade. However, is it also the case that trade reduces conflict? This question is largely unanswered, although the stances are becoming more highly developed. It is hypothesized that trade does not necessarily reduce conflict, but instead changes the nature of the conflict. Economic levers are much more practical than military levers, and are often used for similar reasons. For this reason, it is difficult to separate trade and conflict completely because there is some critical overlap between the two. This is a fundamental foundation for the trade protectionism logic from a national security perspective.
Trade During Conflict
A more specific context for trade and conflict can be the way in which trade is complicated during wartime. Indeed, trade during wartime can be a substantial threat to a nation depending on the scale and scope of the conflict (most notably who is involved). For example, consider World War II. In this scenario Germany was largely isolated in the conflict, and therefore had extremely limited trade partners. Direct conflict will almost always result in a complete cease in trading not only between the country in which the war is occurring, but also any of that country’s allies (who may or may not be directly involved). However, some argue self-sufficiency (via protectionism) in war is not necessary, as friendly nations will still provide trade and economic support.
Sanctions also play a dramatic role as an offensive militaristic maneuver. Iran and North Korea are strong modern examples as well as the recent history of the U.S.-Iraq war. In all of these circumstances, either the U.S. alone or along with a number of allies (representing substantial consumption percentages) actively limited the ability for these countries to trade and generate economic value for their nations (and subsequently their people). While this looks purely economic, it has important social and humanitarian implications as well. The chart makes this case quite clearly, pointing out the death toll in wartime if economic levers are utilized.
Infant Mortality in Iraq During Sanctions : This graphic underlines the indirect consequences of employing economic levers (i.e. sanctions) in a militaristic fashion during a conflict. While the justification for these figures is complex, including other war-related factors, the correlation is quite clear. Diminishing a country’s economic prospects will in turn result in loss of life, particularly in developing nations.
Protectionism
Combining these ideas, it is clear that there is substantial national security value to trade protectionism. However, the opportunity cost of leveraging the ever-growing global markets make this an unattractive prospect if taken to any extreme, as the benefits of global trade rapidly offset the risk of economic dependency upon hostile nations.
Infant Industry Argument
Economic markets are inherently competitive and newer economies are vulnerable to their more developed counterparts in other countries.
learning objectives
- Discuss the use of trade protectionism to promote new industries
Trade protectionism is defined as national policy restricting international economic trade to alter the balance between imports and goods manufactured domestically, usually executed via policies and governmental regulations such as import quotas, tariffs, taxes, anti-dumping legislation, and other limitations.
Arguments for Protecting Infant Industry
The primary purpose for this system is as the name implies: protection. Economic markets are inherently competitive, and newer economies are highly vulnerable to their more developed counterparts in other countries for a variety of reasons. The infant industry argument is that new industries need protection until they have become efficient enough to compete in the world market.
Despite the standard argument from mainstream economists postulating that free trade and open markets is the ideal system to allow for capitalistic development, there are many economists who believe that some degree of protectionism is the only way to minimize income gaps and substantial inequity from economy to economy (see ). The primary advantage to countries with higher economic power and bigger corporations is simply economies of scale and economies of scope, in addition to being further along the experience curve.
Economies of Scale : The basic premise behind economies of scale is that higher production quantity reduces cost per unit, ultimately allowing for the derivation of economic advantage in the market. Infant industries generally do not have the capacity to do this.
GDP by Country : This map demonstrates the vast difference in overall economic power across the globe, underlining the inequities that need to be addressed in economic policy formulation.
History has proven the value of protection for the countries employing tariff-based international trade policies. Alexander Hamilton first pointed out the inequities of developing economies with young industry in 1790, which was later picked up and developed by Daniel Raymond and Friedrich List in the 19th century. Around this time frame, the United States was employing heavy tariffs to protect their fragile economic system as the economy began to achieve autonomy after British rule. Indeed, Britain employed similarly protectionist policies during this time frame, setting the tone for large economic expansion in the longer term.
Criticism
Of course, protective policy while industry develops domestically is not a cure all. In Brazil in the 1980’s there were heavy protective policies in place to defend Brazil’s nascent computer industry from highly evolved competitors internationally. While this seemed practical, what ended up happening was quite damaging for Brazil. Technology advanced rapidly, and without strategic alliances on a global scale, Brazil largely missed out on these advances. This protectionism seems to have damaged industry prospects on a global level for Brazil in this scenario.
From a broader and more far-reaching perspective, protectionism as a general principle has been heavily criticized (even in infant industry situations). The reason for this is quite simply the significant jump in prosperity as international trade expanded, and the huge capacity for specialization, economies of scale, technology sharing, and a host of other advantages that have been a direct result of free global markets. The problem still remains, however, that this prosperity is often unregulated and of the greatest benefit to the influential players in established economies, sometimes at the expense of exploitation of developing nations (cheaper labor, reduced governmental oversight, etc.). As a result of this, protecting infant industries can benefit the nation employing them, but generally with the opportunity cost of global value.
Unfair Competition Argument
One of the strongest arguments for trade protectionism is unfair competition emerging due to differences in policy and enforcement ability.
learning objectives
- Examine the use of protectionism as a way of addressing unfair competitive practices
Protectionist policies are a highly charged topic in economic debates, as economies work to attain the optimal balance of free trade and trade protectionism to capture the most value. In many ways, the global markets are torn between pursuing what is best on the global level and what is best at the domestic level, and there is sometimes dissonance between the two. One of the strongest arguments for some degree of trade protectionism is the tendency for unfair competition to emerge, particularly in developing markets without the infrastructure to monitor their businesses and enforce penalties. This is called the unfair competition argument.
Dumping
A popular recent topic is anti-dumping policies directed at international players looking to undercut domestic business through selling at dramatically reduced prices. This can be a substantial threat, particularly from economies where labor laws are lax and workers are exploited to create extremely low cost goods. This is also a risk when governments get too involved in business, a criticism often pointed out in China. Governments can provide subsidies to reduce costs for domestic companies. This can also be a threat in infant industries, where larger and more established players can push out smaller players via undercutting prices, absorbing losses until the competition goes bankrupt.
Offsetting this threat has been an ongoing struggle, with the emergence of international trade agreements and organizations like the World Trade Organization (WTO) playing an increasingly large role. One of the struggles with international trade is the difficulty of enforcement between nations, and the WTO plays a critical role in identifying malpractice and addressing it.
Intellectual Property
Another critical risk in the global market is intellectual property (IP) protection. Patents, in a domestic system, protect the innovator to allow them to generate returns on the substantial time investment required to invent or innovate new products or technologies. On a global scale, however, it is quite common for developing nations to copy new technologies via reverse engineering. This results in copycats violating the patents in an environment where the infrastructure domestically will probably not take legal action. This reduces the desire for innovation and places large economic risks on countries dependent upon this for growth.
This is addressed through international patent laws and trade agreements as well, alongside political pressures such as raising tariffs and placing import quotas on countries suspected to be in violation of patents. The downside to this is that utilizing these measures creates political unrest, global factions, and strained business relationships.
Mergers, Acquisitions, and Market Dominance
Another unfair competition threat is the emergence of global monopolies. Some of the larger ones attain enough global power and geographic diversification to be difficult to break up via domestic antitrust laws. demonstrates the substantial threat of deadweight losses being incurred in economies where consolidation results in a lack of competitive forces to drive down price.
Economic Losses in a Monopoly : This chart highlights the very real risk of lost economic value in a monopolistic situation (deadweight loss in yellow).
On the domestic level monopolies are widely seen as being addressed (though this is hotly debated by many economists in light of the ‘too big to fail’ and ‘too big to jail’ banks). On a global scale it is even more difficult to regulate, as the size and scale of these companies often extends beyond the power of the governments where these companies are located. This is addressed through international standards and trade agreements, standardizing governmental policy on a global level to reduce the risk of monopoly and unfair consolidation towards market dominance.
Jobs Argument
Many policy makers who are proponents of trade protectionism argue that limiting imports will create or save more jobs at home.
learning objectives
- Analyze the use of trade restrictions for strategic purposes
Many policy makers who are proponents of trade protectionism make the argument that limiting imports will create more jobs at home. This argument is predicated on the idea that buying more domestically will drive up national production, and that this increased production will in turn result in a healthier domestic job market. Domestic industries will not have to compete with foreign producers, and are therefore protected from losing marketshare to cheaper imports.
Trade Balance
It is useful to consider the concept of a trade balance, or net exports, in the context of the jobs argument. It is interesting to look at to assess the extremity to which some nations are ‘consumer nations’ and others are ‘producer nations’. The U.S. and China are a great example of opposite sides of the spectrum, where the trade balance is heavy on one side of the spectrum.
Trade Balances on a Global Scale : It is interesting to look at this graph and assess the extremity to which some nations are ‘consumer nations’ and others are ‘producer nations. ‘ The U.S. and China are a great example of opposite sides of the spectrum, where the trade balance is heavily on one side of the spectrum.
In the U.S. this has created a dramatic push for trade protectionism policies; something the United States has not actively pursued in quite some time. The disastrous 2008 economic collapse via the clear-cut abuses by the banks, and the resulting drop in employment rates, has created an incredibly tangible social and political agenda to bring production back to domestic jobs from overseas. This sentiment towards protectionism is a direct result of the jobs argument in view of an imbalanced trade ratio, where more exports (production and jobs at home) are required to sustain the ongoing consumption of imports.
Outsourcing
Along similar lines, it is common practice for companies to identify strategic alliances abroad and send much of the production work to these locations. This is often a result of cheaper labor and easier systems of governance in those regions. The obvious perspective, from a policy making context, is that these are jobs lost to overseas competitors. While this perspective is often criticized for being short-sighted and against the modern economic view of free markets, it has resulted in policy makers providing incentives to ‘bring jobs back home. ‘
This idea of limiting outsourcing in light of the protectionist jobs argument has resulted in governmental subsidies that work to offset the costs of manufacturing domestically (in the U.S. particularly). These subsidies are essentially grants or tax breaks for companies operating domestically and creating jobs, driving up employment rates via protectionist strategies.
Trade Restriction Strategies
Offsetting the threats of outsourcing and trade imbalances and driving domestic purchasing, and thus domestic production, is done through a variety of political vehicles. Most notable among them are:
- Import Quotas: This is the act of limiting the number of a certain good that can be purchasing from a given country, ensuring that domestic producers maintain a portion of the market share.
- Tariffs: Tariffs are fairly straight-forward, essentially taxes to bring goods into a given country. High tariffs will raise the cost for foreign producers to sell their goods in a domestic system, providing strategic advantages for local producers. One of the pitfalls of tariffs is the likelihood of retaliation, where the foreign government returns with similar tariffs. This will in turn damage global prospects for domestic suppliers.
- Anti-dumping:Anti-dumping legislation actively offsets the ability of low cost or highly subsidized producers in foreign countries to undercut prices in a domestic system. Dumping is the process of selling goods far below market value to drive out competition, often in pursuit of creating a monopoly.
- Subsidies: On the other end of the spectrum, and as noted above, governments can provide subsidies to domestic producers to lower their costs and drive up competitive ability. This can in turn create jobs.
A Summary of International Trade Agreements
International trade agreements are agreements across national borders that reduce or eliminate trade barriers to promote economic exchange.
learning objectives
- Identify at least three main international trade agreements
International trade agreements are trade agreements across national borders intended to reduce or eliminate trade barriers to promote economic exchange. International trade encounters a variety of obstacles, some of which pertain to the protectionism identified in other atoms, which reduce trade incentives. This is usually through tariffs, quotas, taxes, and other trade restrictions. It is also useful to create standards and norms across different countries, particularly for things like intellectual property law recognition, which enables businesses to operate across borders.
There are quite a few international trade agreements, some of which are more formal than others. The trade agreements below provide a fairly comprehensive overview of the current international trade environment:
World Trade Organization (WTO)
The WTO is the largest international trade organization, replacing the General Agreement on Tariffs and Trade (GATT) in 1995, designed to enable international trade while reducing unfair practices. In many ways, the WTO is more complex than other international trade agreements because it incorporates a variety of smaller agreements into a larger framework. The WTO includes upwards of 60 different agreements alongside 159 official members and 25 observers. underlines how effective and universal international trade agreements are becoming. The WTO performs several objective functions as well if trade disputes arise, acting as a framework for assessing appropriate international trade practices.
WTO Members : The World Trade Organization (WTO) is an organization designed to oversee and enable international trade. This map shows how successful this has been on a global scale.
The core of the WTO is the most-favored nation (MFN) rule, which states that each WTO member must be charged the lowest tariffs that an importer places on any country. For example, if the US charges Brazil a 5% tariff on imported clothes, and this is the lowest tariff it has placed on any country in the WTO, all other WTO members must also be charged a 5% tariff. Every WTO member gets charged the lowest tariff that an importer charges any other member.
North American Free Trade Agreement (NAFTA)
Unlike the WTO, which is an entirely global approach, most international agreements stem from geographic proximity. NAFTA is a trilateral agreement between the United States, Canada and Mexico designed to minimize any trade or investment barriers between any of these countries (primarily in the form of tariffs). Generally speaking, the United States demonstrates a trade deficit with these countries relative to goods and a surplus relative to services. The United States also demonstrates high and fast-growing foreign direct investment (FDI) in both regions.
NAFTA Participants : This map outlines each of the countries involved in the North American Free Trade Agreement, an international trade agreement focused on a geographic proximity.
There has been a great deal of controversy surrounding this trade agreement. Agriculture is not included in this agreement, and is often a tough point of discussion for the WTO as well. Mexico is also a point tension due to the fact that it is developing economically (compared to the U.S. and Canada who are considered already developed). Finally, Canadians have often objected to the NAFTA agreements due to the way in which the United States FDI employs hostile takeovers. These agreements demonstrate some of the validity behind trade protectionism and isolationism (as discussed in other atoms in this chapter).
Asia-Pacific Economic Cooperation (APEC)
The APEC forum is particularly interesting in the context of the above agreements, as it is slightly less formal than the above two (it is referred to as a ‘forum’). The APEC forum is a cooperative discussion between 21 countries in the Pacific Rim region promoting free trade, with a focus on newly industrialized economies (NIE). Developing nations gaining access to capital investment and export agreements is the central outcome of APEC, driving economic growth through controlled global expansion. This region represents over half of the world’s GDP and 40% of the overall world population, making this a critical region of the world economy.
APEC Participants : The Asia-Pacific Economic Cooperation (APEC) is a forum of 21 countries in the Pacific Rim region, focusing on free trade and economic cooperation.
Key Points
- Economic interdependence and globalization has resulted in a unique capitalistic system, where each country is largely dependent upon other countries for economic sustainability.
- It has been noted, somewhat intuitively and empirically, that conflict reduces trade. This highlights the risk of conflict harming an economy.
- A more specific context for trade and conflict can be the way in which trade is complicated during wartime. Indeed, trade during wartime can be a substantial threat to a nation, as economic levers such as sanctions can be utilized.
- Iran and North Korea are strong modern examples as well as the recent history of the U.S.-Iraq war. All of these economies struggle(d) against harsh economic sanctions.
- Combining these ideas, it is clear that there is substantial national security value to trade protectionism.
- Trade protectionism is national policies restricting international economic trade to alter the balance between imports and goods manufactured domestically through import quotas, tariffs, taxes, anti-dumping legislation, and other limitations.
- The primary advantage to countries with higher economic power and bigger corporations is simply economies of scale, which infant industries in developing countries often protect against.
- The United States was employing heavy tariffs to protect their fragile economic system as the economy began to achieve autonomy after British rule, which proved effective.
- From a broader and more far-reaching perspective, protectionism as a general principle has been heavily criticized (even in infant industry situations). The argument is that free markets add value on a global level, while protectionism confines economic value to the nation employing it.
- Protectionist policies are a highly charged topic in economic debates, as economies work to attain the optimal balance of free trade and trade protectionism to capture the most value.
- A recent topic is anti- dumping policies directed at international players looking to undercut domestic business through selling at dramatically reduced prices.
- Another critical risk in the global market is intellectual property (IP) protection as patents are often ignored globally, particularly by countries which lack the infrastructure to enforce IP laws.
- Another unfair competition threat is the emergence of global monopolies. Some of the larger ones attain enough global power and geographic diversification to be difficult to break up via domestic anti-trust laws.
- This argument is predicated on the simply fact that buying more domestically will drive up national production, and that this increased production will in turn result in a healthier domestic job market.
- Local governments leverage subsidies, tariffs, import quotas, and anti- dumping policies to maximize strategic capacity domestically, thus creating jobs.
- A sentiment towards protectionism has developed in the U.S. due to the jobs argument in view of an imbalanced trade ratio, where more exports (production and jobs at home) is required to sustain the ongoing consumption of imports.
- Along similar lines, it is common practice for companies to identify strategic alliances abroad and send much of the production work to these locations (outsourcing), motivating governments to bring these jobs back home.
- Local governments leverage subsidies, tariffs, import quotas, and anti-dumping policies to maximize strategic capacity domestically, thus creating jobs.
- International trade encounters a variety of obstacles which reduce trade incentives. This is usually through tariffs, quotas, taxes, and other trade restrictions.
- The WTO is the largest international trade organization, replacing the General Agreement on Tariffs and Trade (GATT) in 1995, designed to enable international trade while reducing unfair practices.
- NAFTA is a trilateral agreement between the United States, Canada and Mexico designed to minimize any trade or investment barriers between any of these countries (primarily in the form of tariffs).
- The APEC forum is a cooperative discussion between 21 countries in the Pacific Rim region promoting free trade, with a focus on newly industrialized economies (NIE).
Key Terms
- sanction : A penalty, or some coercive measure, intended to ensure compliance; especially one adopted by several nations, or by an international body.
- Self-sufficiency : Able to provide for oneself independently of others.
- Nascent : Emerging; just coming into existence.
- Dumping : Selling goods at less than their normal price, especially in the export market as a means of securing a monopoly.
- Subsidies : Financial support or assistance, such as a grant.
- Reverse engineering : The process of analyzing the construction and operation of a product in order to manufacture a similar one.
- Import Quota : A restriction on the import of something to a specific quantity.
- Trade Balance : The difference between the monetary value of exports and imports in an economy over a certain period of time.
- Foreign direct investment : Investment into production or business in a country by an individual or company of another country.
- tariff : A system of government-imposed duties levied on imported or exported goods; a list of such duties, or the duties themselves.
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