Question

A truck pulls boxes up an incline plane. The truck can exert a maximum force of `4,500 N`. If the plane's incline is `pi/8` and the coefficient of friction is `4/3`, what is the maximum mass that can be pulled up at one time?

Answer 1

The mass is `=284.4kg`

Explanation:

Resolving in the direction parallel to the plane `↗^+`

Let the force exerted by the truck be `F=4500N`

Let the frictional force be `=F_rN`

The coefficient of friction `mu=F_r/N=4/3`

The normal force is `N=mgcostheta`

The angle of the plane is `theta=1/8pi`

The acceleration due to gravity is `g=9.8ms^-2`
Therefore,

`F=F_r+mgsintheta`

`=muN+mgsintheta`

`=mumgcostheta+mgsintheta`

`m=F/(g(mucostheta+sintheta))`

`=4500/(9.8(4/3*cos(1/8pi)+sin(1/8pi))`

`=284.4kg`