More practice questions

4. Q4. A truck of mass 4000 kg and a car of mass 1000 kg have the same kinetic energy. Find the ratio of their speeds and the ratio of their momenta.

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   Equal kinetic energy means that mv² is the same for both, so the ratio of speeds is $\sqrt{1000/4000} = 1/2$: the truck moves at half the car’s speed. Momentum is $\sqrt{2mK}$, so the ratio of momenta is $\sqrt{4000/1000} = 2$: the truck has twice the momentum.

5. Q5. The speed of a body increases by 20%. By what percentage does its kinetic energy increase?

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   The kinetic energy is multiplied by 1.2² = 1.44, an increase of 44%.

6. Q6. A body has momentum 20 kg m s^⁻¹ and kinetic energy 50 J. Find its mass and speed.

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   From K = p²/2m, the mass is p²/2K:

   $$m = \frac{400}{2 \times 50} = 4\ \text{kg}$$

   and the speed is p/m = 20/4, that is 5 m s^⁻¹.

7. Q7. A 60 kg runner is moving at 5 m s^⁻¹. A 0.06 kg ball is moving at 30 m s^⁻¹. Which has more kinetic energy, and which has more momentum?

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   For the runner, K = ½ × 60 × 5^², which is 750 J, and p = 60 × 5, which is 300 kg m s^⁻¹. For the ball, K = ½ × 0.06 × 30^², which is 27 J, and p = 0.06 × 30, which is 1.8 kg m s^⁻¹. The runner has more of both.