Question

A grocery cart with mass of 16 kg is being pushed at constant speed up a 12∘ ramp by a force FP which acts at an angle of 17∘ below the horizontal.

a) Find the work done by the force F⃗ P on the cart if the ramp is 7.5 m long.

b) Find the work done by the force mg⃗ on the cart.

c) Find the work done by the force F⃗ N on the cart.

Answer 1

a) if ramp is 7.5 m long, height of ramp will be
7.5sin12 = 1.56 m
Ep = mgh = 16(9.81)(1.56) =244.86 J
Since its constant speed, the resultant force is zero

b) W = Fd

F(gravity) = mgsin(12°) = (16)(9.81)(0.208) = 32.63 N
This is the force of gravity along the incline.
W(gravity) = (32.63)(7.5) = 244.75 Joules

c) The normal force is perpendicular to the incline, therefore does NO work

Answer 2