This was an exam question. The question simply states "What does a force acting on an object do to that object's motion?"

The answer is A force changes an object's momentum. I thought the answer was A force changes an object's momentum and changes an object's acceleration.

My thought process is that if a force acts on an object then the object must change acceleration.

Momentum = m*v;

F = ma; F = m ((v2 - v1)/t)

I feel in order to have a change in momentum there must also be a change in acceleration at some point.

Why am I not correct in this assumption? Many thanks!

  • 1
    $\begingroup$ The wording in "What does a force acting [...] do" makes it likely that you should consider the situation where the force is already acting on the the object - not one where a force that wasn't there before arises. It also appears that that's the only force acting on the body (or the net force), so that you can use the 2nd law of Newton ($F=dp/dt$). What this equation tells you is that $F\ne 0$ is equivalent to $p$ changing; and, with mass $m=\,$const., that means $F=d(mv)/dt=m\cdot dv/dt=ma$: so, if $F$ is constant, then $a$ is constant too - thus, no obligatory change in the acceleration. $\endgroup$ – stafusa Jan 26 '18 at 19:22

A force of nonzero magnitude definitely causes a change in momentum. Force could even be defined as the change in momentum over time, just by using Newton's second law and the definition of momentum: $$\vec{F}_{\text{net}} = m\vec{a} = m\frac{\text{d}\vec{v}}{\text{d}t} = \frac{\text{d}(m\vec{v})}{\text{d}t} = \frac{\text{d}\vec{p}}{\text{d}t}$$

Now, of course, usually, when you start applying a force to something, it has a new acceleration it may not have had before. But, strictly speaking, this only happens when the net force on an object changes. You could, for example, replace one force on an object with a separate but equal force, and its acceleration would not change. In this case, though, the object's momentum would continue to change, thanks to the relationship between force and momentum above.


That's true, as long as the mass is constant. But a variation of mass can also change momentum without changing velocities.


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