A-level Physics (Advancing Physics)/Forces and Impulse in Collisions/Worked Solutions

'''1. Escape velocity from the Earth is 11.2 km−1. How much impulse must be exerted on a 47000 kg payload to get it to travel away from the Earth?'''

$$I = m(v - u) = 47000(11200 - 0) = 526.4\mbox{ MNs}$$

'''2. Two billiard balls, of mass 10g, collide. One is moving at 5ms−1, and the other at 2ms−1. After the collision, the first billiard ball is moving backwards at 4ms−1. The collision takes 1 ms. What force was exerted on this ball?'''

$$I = m(v - u) = 0.01(5 - (-4)) = 0.09\mbox{ Ns}$$

$$F = \frac{I}{\Delta t} = \frac{0.09}{0.001} = 90\mbox{ N}$$

3. What impulse and force were exerted on the second ball?

The impulse was -0.09Ns and the force was -90N.

'''4. A 60 kg spacewalker uses a jet of gas to exert an impulse of 10Ns. How many times would he have to do this to reach a speed of 1 ms−1 from stationary?'''

$$\Delta v = \frac{I}{m} = \frac{10}{60} = \frac{1}{6}\mbox{ ms}^{-1}$$

So, the spacewalker would have to do this 6 times to reach a speed of 1ms−1.

'''5. A 5 kg bowling ball collides with a stationary tennis ball of mass 0.1 kg at 3ms−1, slowing to 2.5ms−1. It exerts a force of 100N on the ball. How long did the collision take?'''

$$F = \frac{m(v - u)}{\Delta t}$$

$$\Delta t = \frac{m(v - u)}{F} = \frac{5(3 - 2.5)}{100} = 0.025\mbox{ s}$$