How is momentum linked to force?

Question

If an object with momentum mv were to collide with a stationary object of mass m, it would apply a force F.

What equations link momentum and force?

Answer 1

mv X m = f

Answer 2

You must apply the principle of momentum conservation in all interactions.
"The total momentum before a collision equals the total momentum after the collision". In your case, the moving object has mass m and velocity v, and the stationary object has mass m and velocity 0. So,
Momentum before collision = mv
Momentum after collision = (m+m)V (both objects stick together and have velocity V))
Thus mv = (m+m)V
i.e. mv=2mV, giving V=v/2

The force which either object feels depends on how long the collision lasts. So if the objects were to be very squishy balls of jelly, the collision may last a long time, and only a gentle force will be felt. If both objects were very hard (like, say, a couple of glass marbles) the collision would be over in a matter of milliseconds, resulting in an enormous force that could well shatter both..
The full answer to your question could be very complex if you do not allow the force that results from the collision to be a steady, or constant, one. So, for A-level's sake, let's assume a steady force.
The connection between Force and Momentum becomes a simple one, derived directly from Newton's Second Law of Motion
The change in momentum = Force x time
(Force x time is known as IMPULSE).
In your example, the change in momentum of the moving object is mv-mV, or m(v-V).
Look above to see that V=v/2, so
Change in momentum = m(v-v/2), or simplifying, mv/2
If the force experienced in the collision is F, then
Ft=mv/2, giving F = mv/2t.
It's up to you to supply the time of collision.
Hope this is of some use. Good luck in your Physics studies, it's good to see an interest being taken.

Answer 3

Force is simply the rate of change in momentum. If two objects collide, they change velocities. They may either change speed, change the direction the were going in, or change both. A force is required to make such a change.

The equation linking the two is

F = dp/dt

That is, if an object is travelling along at a constant velocity (remember, velocity measures both speed AND direction), no forces are acting on it (the derivative of a constant is zero).

If something happens to change that object's momentum, a force must be acting on it. So, if the object's mass changes (i.e. - a 3 kg brick falls out of a moving car), a force is acting on the object. If the object changes speed (i.e. - brakes are applied), a force is acting on the object. Finally, if the object changes direction (i.e. - the car rounds a corner.. ever notice the tugging sensation when that happens???), a force is being applied.

Good luck!

Answer 4

Ft=mv-mu

F= Force/N
t = Time/s
m = mass/Kg
(v= final speed u = initial speed)

Ft and mv-mu

are both equations to calculate impulse as they equal one another

and as momentum = mass x velocity then mv-mu = the change in momentum

so by rearranging the formula you get

t = m(v-u)/F

Time = Change in Momentum / Force

Answer 5

The differential version of Newton's Law links force and momentum.

F = dp/dt

The normal version of Newton's Law that we commonly employ is actually only valid in scenarios of constant mass. The true definition of force is that it is equal to the rate of change of momentum.

Answer 6

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http://en.wikipedia.org/wiki/Momentum#Relating_to_force