Question

Consider a 145 gram baseball being thrown by a pitcher. The ball approaches the batter with a speed of 44 m/s. The batter swings and sends the ball flying back at a speed of 90 m/s into the outfield.

If the ball was in contact with the bat for a time of 3 ms, what is the average force exerted by the bat during the collision?

Answer 1

The average force exerted by the bat during the collision is approximately 6238.33 N.

Step-by-step explanation:

To find the average force exerted by the bat during the collision, we can use the equation:

Faverage = Δp / Δt

where Faverage is the average force, Δp is the change in momentum, and Δt is the time of collision.

We are given the mass of the baseball and the change in velocity before and after the collision. The change in momentum is calculated as:

Δp = m * (vf - vi)

where m is the mass of the baseball, vf is the final velocity, and vi is the initial velocity.

Plugging in the given values, we have:

Δp = (0.145 kg) * (90 m/s - (-44 m/s))

Calculating this, we get:

Δp = 18.715 kg·m/s

Next, we need to convert the time of collision from milliseconds to seconds:

Δt = 3 ms = 0.003 s

Finally, we can calculate the average force:

Faverage = Δp / Δt = (18.715 kg·m/s) / (0.003 s)

Calculating this, we get:

Faverage ≈ 6238.33 N

Therefore, the average force exerted by the bat during the collision is approximately 6238.33 N.

Answer 2

For the development of this problem it is necessary to apply the concepts related to Force, momentum and time.

By definition we know that momentum can be expressed as

`P = F*t`

Where

P = Momentum

F = Force

t = Time

At the same time, another way of expressing the momentum is through mass and speed, that is,

P = mv

Where

m = Mass

v = Velocity

Equating both equations

F*t = mv

`F = (mv)/(t)`

Our values are given as

`m = 145*10^(-3)Kg`

`t = 3*10^(-3)s`

`v = 90-44 = 46m/s \rightarrow` Net velocity

Replacing we have then,

`F = (mv)/(t)`

`F = (3*10^(-3)*46)/(3*10^(-3))`

`F = 2223.33N`

Therefore the average force exerted by the bat during the collision is 2223.3N