A small block of mass m is held at the top of a rough quarter-circle ramp of radius R as shown in the figure, and then released from rest. When it reaches the bottom of the ramp, it is moving with speed V. How much work did friction do on the block from the top to the bottom? Express your answer in terms of m, g, V and R.
W (nc) = [tex]\Delta[/tex]K + [tex]\Delta[/tex]U
The Attempt at a Solution
Work done by gravitational potential energy is equal to mgR. It turns into kinetic energy at the bottom. Therefore,
W = ((1/2)mv^2 - 0) + (0 - mgR)
W = (1/2)mv^2 - mgR
And since this the work done by the object, the work done by friction would be the negative value. Thus,
W = -(1/2)mv^2 + mgR
Am I on the right track?