# Work Done By Friction on a Circular Ramp

1. Jun 20, 2009

### MyNewPony

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

W (nc) = $$\Delta$$K + $$\Delta$$U

3. 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?

2. Jun 20, 2009

### ideasrule

Yes, that's actually the right answer. Why did you doubt that it was?

3. Jun 20, 2009

### MyNewPony

Haha, I'm not sure. I was never really good at deriving equations.