Say a mass is sliding down a plane. Is the work done by friction with the plane positive or negative? What about the work done by gravity?

I ask because of this link: http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/work-and-energy/MIT8_01SC_problems11_soln.pdf (Problem 3, page 3).

I assume that if my positive x-direction is down the slope, the friction work is negative and the gravitational work is positive. But what of the official answer in the PDF? Perhaps they neglected to worry about signs?

Question

Say a mass is sliding down a plane.  Is the work done by friction with the plane positive or negative?  What about the work done by gravity?

I ask because of this link:  http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/work-and-energy/MIT8_01SC_problems11_soln.pdf (Problem 3, page 3).

I assume that if my positive x-direction is down the slope, the friction work is negative and the gravitational work is positive.  But what of the official answer in the PDF?  Perhaps they neglected to worry about signs?

jamesj · Answer

I don't understand your query, because the answer on page 3 says explicitly:
"While the object is sliding down the inclined plane the kinetic energy is increasing due to the positive work done on the object by the gravitational force and the negative work (smaller in magnitude) done by friction."

jamesj · Answer

And on page 4, going from equation 3.2 to equation 3.3, there is a negative sign that should have been carried over.  

So yes, the final answer should also be a negative number:
W_friction = -20.4 J

underhill · Answer

Ah, thanks for pointing that out, JamesJ.

So I was correct - I just need to allow for the humanity of the question writers, I suppose.