# How does the force needed to change momentum depend on the time rate at which momentum changes.

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How does the force needed to change momentum depend on the time rate at which momentum changes.

In: Physics

They are equal according to Newton’s second law. F = dp/dt. Force is on the left side. On the right side is the change of momentum divided by corresponding change in time – that is, the rate at which momentum changes.

Think about a car or bicycle, if you press on the brake slightly, you’ll slow down, but quite slowly, if you press really slam on the brakes, you slow down faster, so more force means your momentum changes faster

Momentum is mass x velocity

Change in momentum is thus usually a change in velocity (unless the object is falling apart i guess).

Change in velocity over time is acceleration

Force is mass x acceleration

So (assuming constant mass) the rate you change momentum depends on the rate you change velocity, which is acceleration. acceleration depends on force

If you lift up a thing that weighs 1kg. How fast you pick it up depends on how much energy you spend.

If you pick it up super slow, you only need to put like 1.05kg of force into doing it.

If you want to snatch it up super fast, and speed it up quickly, you need to put lots of force into it. 4-6kg for example.

So the amount of force you need to change something’s momentum depends on 1. How much you want to change its momentum. And 2. How fast you want that change to happen. So time is important.

If you think of the force you need to push a nail into a block of wood, you need a lot. But you do it with a pretty light hammer. If you pushed the hammer onto the nail, you aren’t going to drive that nail far. But when you swing the hammer and hit the nail, all the momentum of the hammer is stopping on that nail really fast. Generating loads more force.

Momentum changes need a time aspect in order to make any sense.