Work Question

Question

You wish to push a box up a curved ramp. You exert a force parallel to the ramp with magnitude Wsin(x/R), where W is the weight of the box and R is the radius of curvature of the ramp.

How much work do you do in pushing the box along the ramp from x = 0 to x = R/2?

Answer 1

A = Int (Wsin(x/R)dx)|[from x = 0 to x = R/2]

 

A = WR * Int (Wsin(x/R)d(x/R))|[from x = 0 to x = R/2] = WR(1 - cos0.5)

 

Note: here I assume that x represents position of box on/along the ramp