How Is Average Force Calculated in a Football Collision?

[woaini]

Homework Statement

A football player whose mass is 85 kg throws a football with a mass of 0.8 kg against a post. The football hits the post traveling horizontally with a speed of 25 m/s, and then it bounces back with about the same speed. The football is in contact with the post for 0.05 s. What average force is exerted on the post by the ball?

m = 0.8 kg
vi = 25 m/s
vf = -25 m/s
t= 0.05s

Homework Equations

FΔt=m(vf-vi)

F = $\frac{m(vf-vi)}{Δt}$

The Attempt at a Solution

F = $\frac{0.8(-25-25)}{.05-0}$ = -800N by the post.

Is the mass of the football player irrelevant?

 

[Legaldose]

Why would the mass of the football player be relevant? All he does is imparts the initial kinetic energy to the ball. The same thing could be done with a 3,000kg piece of equipment. So yes, the football player's mass is irrelevant.

 

[woaini]

So my calculations are correct without the football player's mass?

 

[Legaldose]

Looks good to me.

 

[Nickie]

I would say that the mass of the football player may not be completely irrelevant, but it does not directly affect the calculation of the average force exerted on the post by the ball. The mass of the football player is much larger than the mass of the football, therefore the contribution of their mass to the overall force is negligible. The key factors in determining the average force are the mass and velocity of the football, as well as the time it is in contact with the post. These variables are all included in the equation for impulse, which is equal to the change in momentum of the football. The mass of the player does not significantly impact the momentum of the football and therefore does not significantly impact the average force exerted on the post.