Question

A 0.145-kg baseball pitched at 37.5 m/s is hit on a horizontal line drive straight back toward the pitcher at 57.0 m/s . If the contact time between bat and ball is 2.50×10−3 s , calculate the average force between the ball and bat during contact.

Answer 1

The average force between the ball and bat during contact is 1131N.

Step-by-step explanation:

The average force can be found employing Newton's second law:

`F = ma` (1)

Where F is the force, m is the mass and a is the acceleration.

The acceleration can be determined employing the equations for a Uniformly Accelerated Rectilinear Motion:

`v_(f) = v_(i) + at` (2)

Where
`v_(f)` is the final velocity,
`v_(i)` is the initial velocity and t is the time.

Then, a will be isolated from equation 2:

`a = (v_(f)-v_(i))/(t)` (3)

Replacing equation (3) in equation (1) it is gotten:

`F = m(v_(f)-v_(i))/(t)`

`F = (0.145Kg)((57.0m/s-37.5m/s))/((2.50x10^(−3)s))`

`F = (0.145Kg)((19.5m/s))/((2.50x10^(−3)s))`

`F = 1131Kg.m/s{2}`

But
`1N = 1Kg.m/s^(2)`, therefore:

`F = 1131N`

So, the average force between the ball and bat during contact is 1131N.