Question

A truck pulls boxes up an incline plane. The truck can exert a maximum force of `4,000 N`. If the plane's incline is `(5 pi )/8` and the coefficient of friction is `9/8`, what is the maximum mass that can be pulled up at one time?

Answer 1

The mass is `=501.9kg`

Explanation:

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

Let the force exerted by the truck be `F=4000N`

Let the frictional force be `=F_rN`

The coefficient of friction `mu=F_r/N=9/8`

The normal force is `N=mgcostheta`

The angle of the plane is `theta=5/8pi`

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

Therefore,

`F=F_r+mgsintheta`

`=muN+mgsintheta`

`=mumgcostheta+mgsintheta`

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

`=4000/(9.8(9/8*cos(5/8pi)+sin(5/8pi))`

`=-501.9kg`