The Ramp: A Simple Machine that Reduces Effort Force h
mg
Fperp
Fpara
The box weighs 155N = 15.5 kg
1. How much Potential Energy is developed if you have to lift the box 1.8 m off the floor from A, straight up to a height at B?
PE = mgh = (155N)(1.8m) = 279 J
2. How much Work is done moving the box along the ramp from A to B?
W = Fd but which force do we use? We must use the parallel force to the ramp surface. Notice: the angle of the ramp is θ = tan­1= (1.8/5.3) = 18.75o
Fpara = mg sinθ = 155 sin (18.75o) = 49.8 N (you push with only this much force) Fperp = mg cosθ =155 cos (18.75o) = 146.7 N (the ramp holds up most of the boxes' weight)
So... W = Fpara d = (49.8N)(5.6m) = 279 Nm (Joules)
Clearly, either way up the ramp will require the same energy, however, lifting the box vertically requires more force for a shorter distance, while using the ramp reduces the required effort force but requires a longer distance over which to move the box. (49N)(5.6m) = 279 = (155N)(1.8m)
Fpara d = 279 = mg h