A box of mass 2 kg has an initial speed of 10 m/s at the foot of the ramp. Given that the friction along the ramp is 2 N, calculate the height h that it reaches when the speed of the box is 5 m/s. (g = 10 m/s2 )
For this question, the additional thing to note is the work done against friction. All the energy possesses by the box at bottom is KE. This KE will decrease and be converted to remaining KE at height h + gain in GPE + work done against friction.
To find the work done against friction, we need to find the distance moved by the box on the inclined ramp, d.
sin60 = h / d
d = h / sin60
Conservation of energy,
KE at bottom = KE at h + GPE at h + friction force
1/2mv2 = 1/2mv2 + mgh + F x d
(1/2 x 2 x 102) = (1/2 x 2 x 52) + (2 x 10 x h) + (2 x h/sin60)
h = 3.36 m