Aperson pushes a crate up a 4-m high ramp for a distance of 18m.

a) what is the mechanical advantage of the ramp?

b) how hard does the person have to push if the crate weights 400 n

a) 4.5

The mechanical advantage of a frictionless ramp is given by:

where

L is the length of the ramp

h is the height of the ramp

In this problem,

L = 18 m

h = 4 m

Substituting these values into the formula, we find

b) 88.9 N

For a frictionless ramp, the input work is equal to the output work:

where

is the force applied by the person

L = 18 m is the length of the ramp

is the output force, which corresponds to the weight of the crate

h = 4 m is the height of the ramp

Solving the equation for ,

a and b sometimes have a positive value