Distance Travelled Accounting for Friction

[merzperson]

Homework Statement

A 4.5 kg box slides down a 4.3-m-high frictionless hill, starting from rest, across a 2-m-long horizontal surface, then hits a horizontal spring with spring constant 460 N/m. The other end of the spring is frictionless, but the 2.0-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.

(a) What is the speed of the box just before reaching the rough surface?
(b) What is the speed of the box just before hitting the spring?
(c) How far is the spring compressed?
(d) Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

Homework Equations

W_f = -F_f*d

The Attempt at a Solution

I got parts a-c easily, but now I'm stuck on part d.

What I did first was calculate the work done by friction on the box (Wf):

Wf = -Ff*d
Wf = -(11.03)(2) = -22.05J

Then I simply divided the initial energy (before the first crossing of the 2m section with friction) by the work done by friction to get the number of crossings before the box stops (loses all of its kinetic energy to heat):

Ei / Wf = C
190.44/22.05 = 8.64

This means that the box makes 8 complete trips across the frictional surface before stopping. MasteringPhysics says this is incorrect, where did I go wrong? Thanks!

 

[denverdoc]

Homework Statement

A 4.5 kg box slides down a 4.3-m-high frictionless hill, starting from rest, across a 2-m-long horizontal surface, then hits a horizontal spring with spring constant 460 N/m. The other end of the spring is frictionless, but the 2.0-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.

(d) Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

[This means that the box makes 8 complete trips across the frictional surface before stopping. MasteringPhysics says this is incorrect, where did I go wrong? Thanks!

The assumption is that the energy robbed by friction is the same. Friction depends on the length of the path.

 

[merzperson]

Thanks denverdoc for your reply!

However, I'm not sure what you're telling me. I did assume that the energy robbed by friction is the same every pass over the rough surface (when I calculated work done by friction). I also accounted for the length of the path when calculating the work of friction:
Wf = -Ff * d
Where d is displacement (rough path length).

Any other ideas? Thanks again!

EDIT:
I found out the distance of the rough section was 1.8m, so I did everything correctly just with a wrong number. Thanks everyone for your help!