Question

A 0.150-kg baseball traveling in a horizontal direction with a speed of 21.0 m/s hits a bat and is popped straight up with a speed of 24.0 m/s. a) What is the magnitude of the change in momentum of the baseball? b) At what angle with respect to the horizontal does the change in momentum of the baseball occur? c) If the bat was in contact with the ball for 51.0 ms, what was the average force of the bat on the ball? Enter a positive answer if the average force is in the direction of momentum change and enter a negative answer if the average force is opposite to the direction of momentum change.

Answer 1

a) To find the magnitude of the change in momentum of the baseball, you can use the following equation:

Change in Momentum (Δp) = Final Momentum - Initial Momentum

First, calculate the initial momentum of the baseball:

Initial Momentum = Mass * Initial Velocity

Initial Momentum = 0.150 kg * 21.0 m/s

Now, calculate the final momentum of the baseball:

Final Momentum = Mass * Final Velocity

Final Momentum = 0.150 kg * 24.0 m/s

Now, find the change in momentum:

Δp = Final Momentum - Initial Momentum

Δp = (0.150 kg * 24.0 m/s) - (0.150 kg * 21.0 m/s)

Δp = 3.6 kg·m/s - 3.15 kg·m/s

Δp = 0.45 kg·m/s

The magnitude of the change in momentum of the baseball is 0.45 kg·m/s.

b) The angle at which the change in momentum of the baseball occurs can be found using trigonometry. The change in momentum is vertical (upward) because the baseball is popped straight up.

You can use the following equation:

tan(θ) = (change in vertical momentum) / (change in horizontal momentum)

θ is the angle with respect to the horizontal.

θ = arctan((0.45 kg·m/s) / (0))

Since the horizontal component of the change in momentum is 0, the angle θ is 90 degrees (straight up).

c) To find the average force of the bat on the ball, you can use the impulse-momentum theorem, which relates impulse (change in momentum) to force and the time over which the force is applied:

Impulse = Force × Time

Impulse (Δp) = Change in Momentum

We've already calculated the change in momentum (Δp) as 0.45 kg·m/s.

Now, you're given the time (Δt) as 51.0 ms, which needs to be converted to seconds:

Δt = 51.0 ms = 0.051 seconds

Now, you can find the average force:

Force = Δp / Δt

Force = (0.45 kg·m/s) / (0.051 seconds)

Force ≈ 8.8235 N

The average force of the bat on the ball is approximately 8.8235 Newtons in the direction of the momentum change.