section_path: Laws/Examples/Objects with variable mass
section_name: Objects with variable mass
paragraph_text: Objects with variable mass
  
  Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter, keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass M (t) {\displaystyle M(t)}, moving at velocity v (t) {\displaystyle \mathbf {v} (t)}, ejects matter at a velocity u {\displaystyle \mathbf {u} } relative to the rocket, then F = M d v d t − u d M d t {\displaystyle \mathbf {F} =M{\frac {d\mathbf {v} }{dt}}-\mathbf {u} {\frac {dM}{dt}}\,} where F {\displaystyle \mathbf {F} } is the net external force (e.g., a planet's gravitational pull).