Nonconservative collision - Work

[en bloc]

Homework Statement

An 85kg baseball player is running towards home base at 8.0 m/s when he crashes into the catcher who is initially at rest. the two players slide together along the base path toward home plate. If the mass of the catcher is 95 kg and the coefficient of kinetic friction between the players and the ground is .70, how far will the players slide?

Homework Equations

1) Wnc = ΔKE + ΔPE

2) mv + mv = (m+m)v

The Attempt at a Solution

I found the final velocity using equation 2, and used it to find Δx in equation 1. I'm not sure if this is right.

.70*1764N*Δx*cos180=(1/2)*180kg*(3.78 m/s)^(2) - (1/2)85kg*(8 m/s)^(2)
-1235N*Δx = -1434N
Δx=1.16m

 

[QuarkCharmer]

The initial velocity seems correct.

For the next part try this:

$$\frac{1}{2}(M+m)v^{2} - W_{f} = \frac{1}{2}(M+m)v^{2}$$

That is, their initial kinetic energy, minus the work done by friction, equals their final kinetic energy. Well, after they are done sliding their final KE is 0 right?

$$\frac{1}{2}(M+m)v^{2} - u(M+m)gx = 0$$

 

[en bloc]

Well, after they are done sliding their final KE is 0 right?

Oooooh. That's right. KEf is 0, so equation 1 should've been like this:

Wnc= ΔKE + 0

.7 * 1764N * Δx * cos180 = 0 - 1/2 * 180kg * (3.78 m/s)^2
Δx= 1.04m

Thanks!

 

[QuarkCharmer]

Thats it!

 

[asteriatic]

Based on your attempt at a solution, it seems like you have correctly applied the equations for nonconservative collisions and conservation of momentum. However, it is important to note that the work done in a nonconservative collision is not just equal to the change in kinetic energy, but also includes the change in potential energy. In this case, the potential energy would be due to the force of friction acting on the players as they slide along the base path.

To find the correct solution, you would need to set up the equation for work done by friction (Ffriction * distance) and solve for the distance. This would give you the total distance the players slide, taking into account both the change in kinetic energy and potential energy. Additionally, it may be helpful to draw a free body diagram to better visualize the forces acting on the players during the collision.