A 0.145 kg baseball pitched at 44.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is 3.00 ✕ 10-3 s, calculate the average force between the ball and bat during contact.
V = Vo + a*t = -52 m/s
44 + a*0.003 = -52
0.003a = -52 - 44 = -96
a = -0.032 m/s^2
F = M*a
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To calculate the average force between the ball and bat during contact, we can use the impulse-momentum principle.
The impulse-momentum principle states that the change in momentum of an object is equal to the applied force multiplied by the contact time. Mathematically, it can be written as:
Impulse = Change in momentum
Impulse = Force * Contact time
Momentum is defined as mass multiplied by velocity.
Change in momentum = Final momentum - Initial momentum
Let's break down the steps to solve the problem:
1. Calculate the initial momentum of the baseball.
Initial momentum = mass * initial velocity
mass = 0.145 kg
initial velocity = 44.0 m/s
Initial momentum = 0.145 kg * 44.0 m/s
2. Calculate the final momentum of the baseball.
Final momentum = mass * final velocity
mass = 0.145 kg
final velocity = -52.0 m/s (negative sign indicates the opposite direction)
Final momentum = 0.145 kg * (-52.0 m/s)
3. Calculate the change in momentum.
Change in momentum = Final momentum - Initial momentum
4. Calculate the average force during contact.
Average force = Change in momentum / Contact time
Note: Make sure to convert the contact time from seconds to milliseconds.
Now, let's calculate the values using the given information:
Initial momentum = 0.145 kg * 44.0 m/s
Final momentum = 0.145 kg * (-52.0 m/s)
Change in momentum = Final momentum - Initial momentum
Contact time = 3.00 × 10^(-3) s
Average force = Change in momentum / Contact time
By plugging in the values and performing the calculations, you can find the average force between the ball and bat during contact.