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# How does Momentum Relate to Force?

Two different concepts are more related than you think

You may think that the two concepts are different but they are more closely related than you think. Momentum is defined as the product of an objects mass and its velocity, or ∆p=m∆v. Meaning then that objects with a higher mass and higher velocity have a higher momentum associated with them than with objects with smaller mass and velocity. This is why a tennis ball is easier to stop than say a moving truck. The truck just has a greater momentum than the tennis ball.

Have you ever noticed that when you get struck with a tennis ball in the face (lets hope this hasn’t happened), you feel like someone slammed a weight on your head? That is because for a moment, the ball exerted a force onto your face, and that was because the ball had momentum. Let’s derive this using Newton’s Second Law. We know:

F=ma and we know that acceleration is equal to a=Δv⁄Δt, so plugging that in, we get:

F=m Δv/Δt and then rearranging that using parenthesis, we see that:

F=(m∆v)/∆t

The numerator should look familiar. That’s right, it’s momentum! Simplifying that equation even further we get:

F=∆p/∆t

This states that the force is equal to the change in momentum divided by the change in time. So, going back to the tennis ball example, when it hits you in the face, what’s actually happening is that there is a change in momentum over a certain time interval and that change in momentum is translated to a force that you feel. You know for sure that momentum changes because after the ball hits you, the velocity of the ball decreases indicating that the momentum decreased as well.

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