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 `(7 pi )/8` and the coefficient of friction is `5/3`, what is the maximum mass that can be pulled up at one time?

Answer 1

The mass is `=396.8kg`

Explanation:

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

Let the force exerted by the truck be `=FN`

Let the frictional force be `=F_rN`

The coefficient of friction `mu=F_r/N`

The normal force is `N=mgcostheta`

Therefore,

`F=F_r+mgsintheta`

`=muN+mgsintheta`

`=mumgcostheta+mgsintheta`

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

`=4500/(9.8(5/3*cos(7/8pi))+sin(7/8pi))`

`=-396.8kg`