Momentum and impulse

You have probably noticed that it takes more effort to get a heavier object into motion than a lighter one. Or stop it! Similarly, it's harder to brake an object that's moving fast, than one that's moving slowly. This combination of mass and velocity has a name: Momentum! The greater the velocity: the greater the momentum.

And the greater the mass: the greater the momentum. Momentum is written as p and the unit is kilogram-meter per second. Momentum is mass times velocity. Kim's Momentum is the mass of Kim times the velocity of Kim Velocity has direction. Hence Momentum must also have direction.

Momentum is a vector. When Kim has a velocity towards the left the Momentum must also be towards the left. So what happens when Philip pushes Kim? Philip changes the Momentum of Kim since the velocity is changed. In this case, enough even to change direction.

Let´s look at the formula, too. To change Momentum we need to change either mass or velocity. Here we change the velocity. The change in momentum, P-"after" minus P-"before"... ... we write as delta-p Is the same as mass... ...

times the change in velocity... delta-v The change takes time. We put in the time it takes to change the velocity. delta-t Now, change in velocity over time is... acceleration.

The change in momentum over time is... mass times acceleration. Wait... we know that! That's called Force!

Think back to Newton's Second Law: F equals m times a So the rate at which the momentum changes gives us the Force. The earlier example of slowing something down showed us this. The more Force Philip uses, the faster Kim is slowed down. Back to Philip and Kim. When Philip pushes Kim with a Force during a specific time, the momentum changes.

Force times time results in a change in momentum. Let's compare... A small Force affecting an object during a long period of time ... results in the same Momentum as a large Force affecting the same object during a shorter period of time. The change in Momentum has a name.

Impulse! And Impulse equals Force times time. Why does Impulse matter? Look! Philip is high-jumping and lands on a foam mattress.

It's soft and dampens the fall with a small force but a longer time. Try jumping without the mattress. The change in momentum is the same. From this velocity to zero. The impulse is as great as in the previous example.

But the braking is much quicker. Hence the Force is much greater in this example. Poor Philip. Now we know all this, let's do some calculation! A football has a mass of 450 grams and is passed to Jenny with a velocity of 8 meters per second...

to the right. Jenny kicks it really hard towards the goal in the opposite direction. The contact between the ball and Jenny's leg lasts zero point two-five seconds. The velocity of the ball after Jenny's kick is minus fifteen meters per second. Minus fifteen? ...

Exactly. The direction. It was positive in this direction, so it must be negative in that direction. What Force did Jenny kick the ball with? Pause and try solving it yourself!

Momentum is the mass times the velocity and Impulse is the change in Momentum, that is, Force times time. The momentum before is zero-point-four-five-O times eight. Three-point-six-O. The momentum after is zero-point-four-five-O times minus-fifteen. Minus six-point-seven-five.

Thus the change is minus ten-point-three-five... Kilogram-meters per second. Divide by the duration of the Impulse. There, the Force is... Minus forty-one-point-four kilogram-meters per second-squared.

Which is the same as... Newtons. Round off to the correct number of significant numbers and the answer is, minus forty-one Newtons. Momentum is the mass times the velocity. Impulse is the change in Momentum.

Which equals the Force times time.