2.6 Sample Problem

Solving the following problem requires us to apply the knowledge gained by our study of kinetics thus far:

A 10.0 kg block is allowed to slide down a ramp with m _k = 0.15 and an angle of elevation equal to 20° . Calculate a) the value of the frictional force opposing the block’s slide down the ramp and b) the block’s acceleration.

Solution a)

Equation 2.2 states that the force of kinetic friction is the product of the coefficient of kinetic friction (0.15) and the normal force. But what is the normal force? The ramp is not parallel to the ground, so the normal force does not equal the gravitational force. Similar to velocity and acceleration, forces can be broken down into directional components. To find the normal force exerted by the ramp, we will calculate the component of the gravitational force in the direction perpendicular to the ramp’s surface.

Therefore

Solution b)

To find the acceleration of the box, we’ll first find the net force that causes the acceleration. This net force will be the sum of the gravitation force in the direction parallel to the ramp’s surface and the friction force (calculated in part a).

Since we know the net force and the object’s mass, we can now calculate its acceleration down the ramp: