Question

A truck pulls boxes up an incline plane. The truck can exert a maximum force of `5,600 N`. If the plane's incline is `(2 pi )/3` and the coefficient of friction is `7/6`, what is the maximum mass that can be pulled up at one time?

Answer 1

979 kg

Explanation:

Note, by definition, an inclined plane cannot have an inclination more than `pi/2`. I take the angle is measured from positive x-axis, so it is just `theta = pi/3` the other way.

here `f` is the applied force, NOT the frictional force.

So, as we can easily observe in the picture, the forces that oppose will be (m is expressed in `kg`):

1. gravitational pull: `mgsintheta = 9.8xxsqrt3/2 m=8.49mN`

2. frictional force, opposite to the direction of tendency of movement: `mumgcostheta = 7/6xx9.8xx1/2 mN = 5.72m N`

Hence total is: `(8.49+5.72)m N=14.21m N`

So, for the truck the to be able to pull it up, the maximum force it can exert must be more than this:

`5600N>5.72m N => m<979 kg`