How Is Force Calculated in a Tennis Serve?

[AnomalyCoder]

Homework Statement

A tennis player returns a 30m/s serve back at 25 m/s after making contact with the ball for .5 seconds. If the ball has a mass of .20kg, what is the force exerted on the ball?

Homework Equations

I = Force$$\Delta$$Time, or essentially the $$\Delta$$Momentum = Impulse
P=M*V

The Attempt at a Solution

Before: .2kg object traveling at -30m/s.
After: .2kg object traveling at 25m/s.

Yeah I'm lost. Not quite sure how to handle this.
How do I apply .5s?

 

[SammyS]

Homework Statement

A tennis player returns a 30m/s serve back at 25 m/s after making contact with the ball for .5 seconds. If the ball has a mass of .20kg, what is the force exerted on the ball?

Homework Equations

I = Force$$\Delta$$Time, or essentially the $$\Delta$$Momentum = Impulse
P=M*V

The Attempt at a Solution

Before: .2kg object traveling at -30m/s.
After: .2kg object traveling at 25m/s.

Yeah I'm lost. Not quite sure how to handle this.
How do I apply .5s?

0.5 s = Δtime
What was the change in momentum?

 

[AnomalyCoder]

Well, since momentum = mass * velocity...
The change in mass is none, since the ball doesn't change in terms of its mass?

Then if velocity = distance/time...
First it's -30m/s, goes to 25m/s...
-5m/s in velocity?

But that would mean the change in momentum is 0..
I think I messed up somewhere.

 

[SammyS]

The difference between -30m/s and 25m/s is 55 m/s, not 5 m/s.

25m/s - (-30m/s) = 55 m/s.

Also, m·25m/s - m·(-30m/s) = m·55 m/s ≠ 0.

Usually m doesn't change.

 

[rwisz]

To solve this problem, we can use the equation F = mΔv/Δt, where F is the force exerted on the ball, m is the mass of the ball, Δv is the change in velocity, and Δt is the time taken for the change in velocity to occur. In this case, we know that m = 0.2kg, Δv = 25m/s - (-30m/s) = 55m/s, and Δt = 0.5s. Plugging these values into the equation, we get F = (0.2kg * 55m/s) / 0.5s = 22N. This means that the force exerted on the ball by the tennis player is 22 Newtons.

We can also use the concept of impulse to solve this problem. Impulse is defined as the change in momentum, or I = Δp. In this case, the change in momentum of the ball is given by Δp = mΔv = (0.2kg) * (55m/s) = 11kgm/s. Since impulse is also equal to the force multiplied by the time, we can set up the equation I = FΔt and solve for F. Plugging in the known values, we get 11kgm/s = F * 0.5s, which gives us F = (11kgm/s) / 0.5s = 22N.

Therefore, both methods give us the same result of 22N for the force exerted on the ball. This is a reasonable amount of force for a tennis player to exert on a ball during a serve.