What Is the Change in Momentum of a Golf Ball During Impact?

[BuBbLeS01]

Homework Statement

A golf ball with a mass of 43.80 g can be blasted from rest to a speed of 64.60 m/s during impact with a club head. Assume that the impact lasts only about 0.980 ms. Calculate the change in momentum of the ball.

Homework Equations

P = mv
Change in P = Pf - Pi
J = 1/2 base * height
Favg = J/Change in time

The Attempt at a Solution

Mg = .04380kg
Vi = 0m/s
Vf = 64.60m/s
Time = .00098s

A.) Change in P = (.04380kg * 64.60m/s) - (.04380kg - 0m/s) = 2.83kg*m/s RIGHT
B.) J = 1/2 * 0.00098s * 2.83kg*m/s = .001386
Favg = (0.001386N/s)/(0.00098s) = 1.415N WRONG...But I don't know why. I think it has to do with when I calculated J I am not sure if my height (Fmax) is supposed to be the 2.83kg*m/s.

 

[BuBbLeS01]

Okay maybe I don't need Fmax is J = Change in P??

 

[ogb p]

I would like to provide a more accurate and comprehensive solution to this problem. It is important to note that in this scenario, we are assuming that the golf ball is a point mass and that the impact between the club head and the ball is perfectly elastic, meaning there is no loss of energy during the collision.

To calculate the change in momentum of the golf ball, we can use the equation P = mv, where P represents momentum, m is the mass of the ball, and v is its velocity. In this case, the initial momentum (Pi) of the ball is 0, since it is at rest, and the final momentum (Pf) can be calculated by multiplying the mass (43.80 g or 0.04380 kg) by the final velocity (64.60 m/s).

Pf = (0.04380 kg)(64.60 m/s) = 2.83 kg m/s

The change in momentum (ΔP) can then be calculated by subtracting the initial momentum from the final momentum:

ΔP = Pf - Pi = (2.83 kg m/s) - (0 kg m/s) = 2.83 kg m/s

This means that the golf ball experienced a change in momentum of 2.83 kg m/s during the impact with the club head.

In order to calculate the average force (Favg) exerted on the ball during the impact, we can use the equation Favg = ΔP/Δt, where Δt represents the change in time. In this case, we are given that the impact lasts for 0.980 ms, or 0.00098 s. Therefore:

Favg = (2.83 kg m/s)/(0.00098 s) = 2887 N

It is important to note that this is the average force exerted on the ball during the impact. The actual force may vary depending on the duration and intensity of the impact.

In conclusion, the change in momentum of the golf ball during the impact is 2.83 kg m/s and the average force exerted on the ball is approximately 2887 N. It is also worth mentioning that the J value calculated in the attempt at a solution is not necessary for this problem and may not be applicable in this scenario.