Question

A person 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

Answer 1

a) 4.5

The mechanical advantage of a frictionless ramp is given by:

`MA=(L)/(h)`

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

`MA=(18 m)/(4 m)=4.5`

b) 88.9 N

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

`W_i = W_o\\F_i L = F_o h`

where

`F_i` is the force applied by the person

L = 18 m is the length of the ramp

`F_o = 400 N` 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
`F_i`,

`F_i = (F_o h)/(L)=((400 N)(4 m))/(18 m)=88.9 N`