A ball has a mass of 0.14 kg and is pitched w/ velocity of 38 m/s. The batter hits the ball & departs w/ a velocity of 58 m/s. Contact time b/w the bat and ball is 4.0 x 10-3seconds. What is avg force exerted on ball?
Divide the momentum change (0.14)*(38 +58) kg*m/s by the contact time (0.004 s)
The answer (average force) will be in Newtons.
This assumes a "line drive" is being hit, so that the incoming pitch and the hit ball are in exactly opposite directions. For a "pop fly", the average force would be less.
To find the average force exerted on the ball, you can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
1. First, let's calculate the initial momentum of the ball. The momentum of an object is calculated by multiplying its mass by its velocity. Given that the ball has a mass (m) of 0.14 kg and is pitched with a velocity (v) of 38 m/s, the initial momentum (p_initial) can be calculated as:
p_initial = m * v
2. Next, calculate the final momentum of the ball. The ball is hit by the batter, causing it to depart with a velocity (v') of 58 m/s. So, the final momentum (p_final) is given by:
p_final = m * v'
3. Calculate the change in momentum (Δp) by subtracting the initial momentum from the final momentum:
Δp = p_final - p_initial
4. Now, divide the change in momentum (Δp) by the contact time (t) to find the average force (F_avg) exerted on the ball:
F_avg = Δp / t
Substituting the values given in the question, where the contact time (t) is 4.0 x 10^-3 seconds, you can calculate the average force exerted on the ball.