The tennis ball hits the racket at a speed of 52m/s. The average force on the ball during the time that is in contact with the racket is 350N. The speed of the ball after it leaves the racket is 26m/s in the opposite direction to the initial speed of the ball. The mass of the ball is 58g. Calculate the change in momentum of the ball while it is in contact with the racket.
Question
The tennis ball hits the racket at a speed of 52m/s. The average force on the ball during the time that is in contact with the racket is 350N. The speed of the ball after it leaves the racket is 26m/s in the opposite direction to the initial speed of the ball. The mass of the ball is 58g. Calculate the change in momentum of the ball while it is in contact with the racket.
Solution
To calculate the change in momentum of the ball while it is in contact with the racket, we first need to calculate the initial and final momentum of the ball.
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Convert the mass of the ball to kg, since the standard unit of mass in physics is kg. So, 58g = 0.058 kg.
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Calculate the initial momentum of the ball. Momentum (p) is calculated as the product of mass (m) and velocity (v). So, p_initial = m * v_initial = 0.058 kg * 52 m/s = 3.016 kg*m/s.
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Calculate the final momentum of the ball. The final velocity is given as 26 m/s in the opposite direction, so we take it as -26 m/s. So, p_final = m * v_final = 0.058 kg * -26 m/s = -1.508 kg*m/s.
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The change in momentum (Δp) is the final momentum minus the initial momentum. So, Δp = p_final - p_initial = -1.508 kgm/s - 3.016 kgm/s = -4.524 kg*m/s.
So, the change in momentum of the ball while it is in contact with the racket is -4.524 kg*m/s. The negative sign indicates that the direction of the momentum has reversed, as expected.
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