Chapter 4 Dynamics: Force and Newton’s Laws of Motion

4.1 Development of Force Concept


  • Understand the definition of force.


(a) Overhead view of two ice skaters pushing on a third. One skater pushes with a force F two, represented by an arrow pointing up, and a second skater pushes with a force F one, represented by an arrow pointing from left to right. Vector F one and vector F two are along the arms of the two skaters acting on the third skater. A vector diagram is shown in the form of a right triangle in which the base is vector F one pointing east and perpendicular is shown by vector F two pointing north. The resultant vector is shown by the hypotenuse pointing northeast. (b) Free-body diagram showing only the forces acting on the skater.


A more quantitative definition of force can be based on some standard force, just as distance is measured in units relative to a standard distance. One possibility is to stretch a spring a certain fixed distance, as illustrated in Figure 2, and use the force it exerts to pull itself back to its relaxed shape—called a restoring force—as a standard. The magnitude of all other forces can be stated as multiples of this standard unit of force. Many other possibilities exist for standard forces. (One that we will encounter in Chapter 22 Magnetism is the magnetic force between two wires carrying electric current.) Some alternative definitions of force will be given later in this chapter.

(a) A spring of length x, fixed at one end, is shown in horizontal position. (b) The same spring is shown pulled by a person by a distance of delta x. The restoring force F restore is represented by an arrow pointing left toward the position where the spring is fixed. (c) A spring balance containing a spring stretched a distance delta x is shown. The restoring force is represented by an arrow F restore pointing toward the left in the direction opposite to the elongation of the spring.
Figure 2. The force exerted by a stretched spring can be used as a standard unit of force. (a) This spring has a length x when undistorted. (b) When stretched a distance Δx, the spring exerts a restoring force, Frestore, which is reproducible. (c) A spring scale is one device that uses a spring to measure force. The force Frestore is exerted on whatever is attached to the hook. Here Frestore has a magnitude of 6 units in the force standard being employed.


To investigate force standards and cause and effect, get two identical rubber bands. Hang one rubber band vertically on a hook. Find a small household item that could be attached to the rubber band using a paper clip, and use this item as a weight to investigate the stretch of the rubber band. Measure the amount of stretch produced in the rubber band with one, two, and four of these (identical) items suspended from the rubber band. What is the relationship between the number of items and the amount of stretch? How large a stretch would you expect for the same number of items suspended from two rubber bands? What happens to the amount of stretch of the rubber band (with the weights attached) if the weights are also pushed to the side with a pencil?

Section Summary


Conceptual Questions


2: What properties do forces have that allow us to classify them as vectors?



the study of how forces affect the motion of objects and systems
external force
a force acting on an object or system that originates outside of the object or system
free-body diagram
a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces are represented by vectors extending outward from the dot
a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force


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