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Momentum Questions - Solution

Q2. A girl kicks a ball along the ground at a wall 2.0 m away. The ball strikes the wall normally at a velocity of 8.0 ms-1 and rebounds in the opposite direction with an initial velocity of 6.0 ms-1. The girl, who has not moved, stops the ball a short time later.

 

(a) Explain why the final displacement of the ball is not 4.0 m.

Displacement is a vector therefore although the distance travelled is 4.0 m the ball travels 2.0 m each way in opposite directions and cancels out the displacement

(1 mark)

(b) Explain why the average velocity of the ball is different from its average speed.

Velocity in a particular direction is the displacement in that direction divided by the time taken whereas average speed is the total distance travelled divided by the time taken.

Velocity is a vector quantity it has magnitude and direction whereas speed is a scalar quantity. As the displacement is different from the distance traveled the velocity will be different from the speed.

(2 marks)

(c) The ball has a mass of 0.45 kg and is in contact with the wall for 0.10 s. For the period of time the ball is in contact with the wall,

(i) calculate the average acceleration of the ball.

You need to think about signs here (parts a and b give you a clue to this!)… the change in velocity (final velocity – initial velocity) will be positive if the velocity increases giving you acceleration and negative as it decreases giving you deceleration. In this case the final velocity is not just smaller than the initial velocity – it is negative!

v = v - u = (-6m/s) - 8 m/s = - 14 m/s

a = v/t = - 14/0.10 = - 140 m/s 2

(ii) calculate the average force acting on the ball.

Ft = mv

so, F = mv/t = 0.45 x - 14/0.10 = - 63N

OR F= ma = 0.45 x - 140 = - 63N

(iii) state the direction of the average force acting on the ball.

The wall provides the force and pushes the ball away from the wall towards the girl – normally (at right angles to the wall) in the same direction as the final velocity

(5 marks)

(Total 8 marks)