Q 38 A tennis player swings her 1000 ... [FREE SOLUTION]

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Chapter 11: Q 38 (page 288)

A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s.
a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.
b. If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball? How does this compare to the gravitational force on the ball?

Short Answer

Expert verified

a) Speed of the racket is 6.4 m/s

b) Average force that the racket exerts is 360 N and $F = 610.17 脳 F_{G}$ where $F_{G}$ is the gravitational force.

Step by step solution

Step 1. Given information is :Mass of the Racket, m1 = 1000gSpeed of the Racket, v1.i = 10 m/sMass of the tennis ball, m2 = 60gSpeed of the tennis ball, v2.i = 20 m/sRebound speed of the tennis ball, v2.f = 40 m/s

We need to find out :

a) Speed of the racket moving immediately after the impact.

b) Average force that the racket exerts on the ball and its relation with Gravitational force.

Step 2. Part a)Using Law of conservation of Momentum.

The collision occurring as an elastic collision.

Therefore,

Using Law of Conservation of Momentum,

$\overset{鈫�}{P_{i}} = \overset{鈫�}{P_{f}} m_{1} v_{1 . i} + m_{2} v_{2 . i} = m_{1} v_{1 . f} + m_{2} v_{2 . f} m_{1} v_{1 . f} = m_{1} v_{1 . i} + m_{2} v_{2 . i} - m_{2} v_{2 . f} v_{1 . f} = \frac{m_{1} v_{1 . i} + m_{2} (v_{2 . i} - v_{2 . f})}{m_{1}} P u t t i n g v a l u e s, v_{1 . f} = \frac{(1 k g) (10 m / s) + (0.060 k g) (- 20 - 40) m / s}{1 k g} v_{1 . f} = 6.4 m / s$

Step 3. Part b)The force for a short period of time is called Impulse.Expressing Impulse along with momentum.

Impulse can be expressed as :

$p_{f} = p_{i} + J J = p_{f} - p_{i} J = m_{2} v_{2 . f} - m_{2} v_{2 . i} J = (0.060 k g) (40 m / s) - (0.060 k g) (- 20 m / s) J = 3.6 k g m / s F o r c e c a n b e e x p r e s s e s a s, F = \frac{J}{鈭� t} 鈭� t = 10 m s = 10 脳 10^{- 3} s = 10^{- 2} s F = \frac{3.6}{10^{- 2}} = 360 N A n d G r a v i t a t i o n a l f o r c e f o r t h e b a l l i s : F_{G} = m g = (0.060 k g) (9.8 m / s^{2}) = 0.59 N$