Friction force?

Question

If an object with constant velocity travels down an inclined plane, what is the magnitude of friction force?

Answer 1

If an object is travelling with constant velocity then the net force on it is zero. That can be broken up into the component of the weight of the object acting down the plane mgsin(theta), where theta is the angle of the plane from the horizontal, and the frictional force F, which acts against the motion or back up the plane. Since F+mgsin(theta) = 0, then F =-mgsin(theta)

Answer 2

A constant rate of motion down the plane implies a constant rate of change in the potential energy of the object. Where does that potential energy go? it obviously isn't accelerating the object, so it's all being spent on frictional heating.

We know that energy = force x distance. Calculate the change in potential energy after the object slides some distance down the length of the plane (you'll have to use the change in height for that, PE = mgh (mass * gravity * height).

Divide that amount of energy by the distance, d that it travelled down the plane to get the force of the friction;

E = f x d

so

f = E/d

or

force = delta(E)/delta(d)