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Momentum in a collision Figure 3.12 shows a game in which a ball hangs from a length of string. The player hits the ball horizontally with a racket. How can we use the idea of momentum to describe what happens? We need to think about momentum before the racket collides with the ball, and then after the collision.
a Before the collision: The racket is moving to the right; it has momentum. The ball is stationary, so it has no momentum. b After the collision: The racket is moving to the right, but more slowly than before. It has lost momentum. The ball is moving rapidly to the right. It has gained momentum. So you can see that, when the racket exerts a force on the ball, momentum is transferred from the racket to the ball. Whenever a force acts on an object, its momentum changes. At the same time, the momentum of the object causing the force also changes. If one object gains momentum, then the other loses an equal amount of momentum. This is known as the principle of the conservation of momentum. We can state the principle in a different way. Whenever two objects interact, the total amount of momentum before they interact is the same as the total amount of momentum afterwards:
total momentum before = total momentum after
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Worked example 3.4 The illustration below shows the masses and velocities of the racket and ball shown in Figure 3.12. Find: a the momentum of the racket before and after the collision b the momentum of the ball after the collision c the velocity of the ball.
m = 3 kg m = 0.25 kg u = 20 m/s u = 0
m = 3 kg v = 18 m/s
before
a
m = 0.25 kg v = 24 m/s
after
We can calculate the momentum of the racket using momentum = mass × velocity. Before the collision: momentum = 3 kg × 20 m/s = 60 kg m/s After the collision, the racket is moving more slowly and so its momentum is less: momentum = 3 kg × 18 m/s = 54 kg m/s
b The momentum gained by the ball is equal to the momentum lost by the racket. So: momentum of ball = 60 − 54 = 6 kg m/s
The next worked example shows how we can use this to work out how fast the ball in Figure 3.12 will be moving after it has been hit by the racket.
c
We can calculate the velocity of the ball by rearranging the equation for momentum: velocity = =
momentum mass 6 kg m/s
0 25 kg = 24 m/s The ball will move off with a velocity of 24 m/s to the right. a Figure 3.12 the hit.
b Hitting a ball with a racket: a before the hit; b after
Original material © Cambridge University Press 2014
Chapter 3: Forces and motion
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