"A sled has an initial velocity up a ramp of 5 m/s, the ramp has an angle of 20 degrees to the horizontal, and the coefficient of dynamic friction between the sled and the plane is 0.5. Find the maximum height the sled will travel to."
So this is a problem I gave my students, as an energy problem (yes you can do it with dynamics, but I'm focused on energy here) and I tell them that they need to include the friction in their conservation formula as work. Now, what I'm not 100% on is do you take the net work force on the sled or not? That is to say, in the work term, do you take build into it both the force down the ramp by the friction AND the force down the ramp by the earth, or do you just use the frictional force? My reasoning is, if you're including a potential energy term in the conservation of energy formula, then don't include it in the work term because you'll be counting it twice. Is this correct? My model for this problem assumes that the friction is a non-conservative energy, and the gravitational potential energy is both conservative and within the system of the sled.
Any help is greatly appreciated!