Question

145−kg bagebal plahod al 33.0 m/s is hit on a horizsetal Ine drive atraight back at the pitcher :t! 490 m/s It the contact fime between bat and ball it 5.80×10 ⁻³ s, calculate the magritude of the torce (assumed to be constant) exorted on the ball by the bat. Express your answer to three significant figures and include the appropriate units.

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Answer 1

To calculate the magnitude of the force exerted on the ball by the bat, we can use the principle of Newton's second law of motion. By calculating the initial and final momenta of the ball, we can find the change in momentum. Dividing this change in momentum by the contact time will give us the magnitude of the force exerted.

Step-by-step explanation:

To calculate the magnitude of the force exerted on the ball by the bat, we can use the principle of Newton's second law of motion, which states that force is equal to the change in momentum over time.

First, we need to calculate the initial momentum of the ball by multiplying its mass (145 kg) by its initial velocity (-33.0 m/s):

1. Initial momentum = (145 kg) * (-33.0 m/s) = -4785 kg·m/s

The final momentum of the ball can be calculated by multiplying its mass (145 kg) by its final velocity (-490 m/s):

1. Final momentum = (145 kg) * (-490 m/s) = -71050 kg·m/s

Next, we can calculate the change in momentum by subtracting the initial momentum from the final momentum:

1. Change in momentum = Final momentum - Initial momentum = -71050 kg·m/s - (-4785 kg·m/s) = -66265 kg·m/s

Finally, we can calculate the magnitude of the force by dividing the change in momentum by the contact time of 5.80×10⁻³ s:

1. Magnitude of force = Change in momentum / Contact time = -66265 kg·m/s / 5.80×10⁻³ s = -1.14 x 10^7 N

The magnitude of the force exerted on the ball by the bat is 1.14 x 10^7 N, where the negative sign indicates that the force is in the opposite direction to the initial velocity of the ball.