How Much Work Does Friction Do on a Crate Sliding Down a Ramp?

[cbeeson23]

A 70 kg crate starting at rest slides down a rough ramp 4.0 meters long, inclined at 30 degrees above horizontal. At the bottom, it is moving at 5.0 m/s. what was the work done by friction on the crate?

Answers=
A. -500 Joules
B. 500 Joules
C. 460 Joules
D. -460 Joules
E. 0.0 Joules

I got this answer wrong and i was wondering why... so here is my work. i got the height to be 2meters by using sin 30

Mgh - Wf = 1/2MV^2

70 * 9.81 * 2 - wf = .5 * 70 * 5.0^2
875 - wf = 1373.4
wf =1373.4-875
wf = 500 joules

so i got positive 500 joules. So is the answer actually -500 joules since friction forces go up the ramp>

 

[Andy Resnick]

The question is worded poorly, IMO. The proper phrase should be "how much energy is dissipated by friction?" The ambiguity is in the definition of 'work'. Since the frictional force acts to oppose the motion, the frictional force can be thought of as removing some fraction of the total gravitational potential energy available to perform work.

Of course, the energy is removed as heat and plastic deformation of the materials.

 

[Doc Al]

Mgh - Wf = 1/2MV^2

Instead, think:
Total Work done by all forces = ΔKE
Wg + Wf = ΔKE