You slide a box of books at constant speed up a 30° ramp, applying a force of 200 n directed up the slope. the coefficient of sliding friction is 0.18. (a) how much work have you done when the box has risen 1 m vertically? (b) what's the mass of the box?

The box is moving at constant speed, so acceleration=0 and the equation of the forces acting on the box along the ramp becomes:

(1)

where F=200 N is the force that pushes the box, Ff is the frictional force, and Wp is the component of the weight parallel to the ramp.

The frictional force can be written as

where is the coefficient of friction, m is the mass of the box, is the frictional force and is the angle of the ramp.

The component of the weight along the ramp is

Substituting this into eq.(1), we have

and we can find the mass of the box:

Now we can also find the work done on the box. this is given by the gain in potential energy of the box, since there is no change in kinetic energy (the speed of the box is constant). Since the box has risen vertically by 1 m, the gain in potential energy (and the work done) is

So, the two answers are

(a) 304.8 J

(b) 31.1 kg