(a) State the principle of conservation of linear momentum. (b) Explain the mode of action of a propelled rocket. (c) During a training session, two footballers pass a ball repeatedly between themselves. Give two reasons why the to and fro motion of the ball is not simple harmonic. (d) A ball is dropped from a height, at the same time as another ball is projected horizontally from the same height. (i) Would the balls hit the ground at the same time? (ii) Explain your answer in (i). (e) A ball of mass 0.10 kg is projected horizontally onto a vertical wall with a speed of 17 ms\(^{-1}\). The ball makes contact with the wall for 0.15 s and rebounds horizontally with a speed of 13 ms\(^{-1}\). Calculate the: (i) change in momentum of the ball; (ii) average force exerted on the ball during its collision with the wall.
Explanation
(a) Principle of conservation of linear momentum states that if two or more bodies collide in a closed system, the total momentum after the collision is equal to the total momentum before the collision.
(b) The principle of action of a propelled rocket is that gas burnt within the combustion chamber of the rocket engine is expelled downwards through the exhaust (tail nozzle) at very high speed, hence an equal and opposite momentum is given to the rocket which moves the rocket upward.
(c) The motion is not simple harmonic because: -there is no equilibrium position -acceleration of the ball is not directly proportional to displacement -acceleration of the ball is not directed towards a fixed point.
(d)(i) Both balls will hit the ground at the same time. (ii) All free falling objects fall at the same rate because they are pulled towards the earth by gravity and accelerate at a constant rate.
(e)(i) Charge in momentum = m(v-u) = 0.10(13 - 17) = 3 kgms\(^{-1}\) (ii) Average force F = \(\frac{\text{change in momentum}}{\text{time}}\) = \(\frac{3}{0.15} = 20N\)
