# 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/3  and the coefficient of friction is 4/3 , what is the maximum mass that can be pulled up at one time?

Jan 13, 2018

293.73 Kg

#### Explanation:

To pull maximum mass by the truck,it should be such that the force due to the component of its weight acting downwards and frictional force against the motion should just get balanced by the amount of maximum force it can apply and as a result it will move upwards with constant velocity.
So, frictional force (f) acting on it is$u \cdot m g \cos \left(\frac{\pi}{3}\right)$ (where m is that maximum mass it can carry at one time)
And component of weight acting downwards along the plane (W) is $m g \sin \left(\frac{\pi}{3}\right)$
So,using equation of force we can say,
Maximum force that can be applied by the truck i.e
$4500 = f + w$
Solving it we get, m = 293.73 Kg