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?

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

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?

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

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

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?

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

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?

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

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