A 562 N truck slides down a frictionless plane inclined at an angle of 30.0 degrees from the
horizontal.
A Find the acceleration of the trunk.
B Find the acceleration of the trunk if the coefficient

A)

B)

Explanation:

A)

When the truck is sliding down the frictionless ramp, the only force acting along the direction parallel to the ramp (downward) is the component of the weight of the truck parallel to the ramp, which is given by

where

is the weight of the truck

is the angle of the ramp

So the net force on the truck is

The mass of the truck is given by

where is the acceleration due to gravity.

Therefore, the acceleration of the truck along the ramp can now be found using Newton's Second Law of motion:

B)

In this case, there is another force acting on the truck: the  force of friction.

This force acts in the direction opposite to the component of the weight along the plane (so, up along the ramp), and its magnitude is

where

is the weight of the truck

is the angle of the ramp

is the coefficient of friction between the truck and the ramp

Therefore, the net force acting on the truck in this second case is:

Therefore, since the mass of the truck is

m = 57.3 kg

We can find the new acceleration of the truck: