a) 4.5
The mechanical advantage of a frictionless ramp is given by:
[tex]MA=\frac{L}{h}[/tex]
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
[tex]MA=\frac{18 m}{4 m}=4.5[/tex]
b) 88.9 N
For a frictionless ramp, the input work is equal to the output work:
[tex]W_i = W_o\\F_i L = F_o h[/tex]
where
[tex]F_i[/tex] is the force applied by the person
L = 18 m is the length of the ramp
[tex]F_o = 400 N[/tex] 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 [tex]F_i[/tex],
[tex]F_i = \frac{F_o h}{L}=\frac{(400 N)(4 m)}{18 m}=88.9 N[/tex]
