In order to determine the coefficients of friction between rubber and various surfaces, a student uses a rubber eraser and an incline. In one experiment, the eraser begins to slip down the incline when the angle of inclination is 35.6° and then moves down the incline with constant speed when the angle is reduced to 30.8°. From these data, determine the coefficients of static and kinetic friction for this experiment.

The coefficients of static and kinetic friction for this experiment are 0.716 and 0.596, respectively.

Explanation:

The Free Body Diagram associated with the experiment is presented as attachment included below.

Friction is a contact force that occurs as a reaction against any change in state of motion, which is fostered by gravity.

Normal force is another contact force that appears as a reaction to the component of weight perpendicular to the direction of motion. Let consider a framework of reference consisting in two orthogonal axes, one being parallel to the direction of motion (x-axis) and the other one normal to it (y-axis). Equations of motion are described herein:

Where:

- Weight of the eraser, measured in newtons.

- Friction force, measured in newtons.

- Normal force, measured in newtons.

- Angle of the incline, measured in degrees.

The maximum allowable static friction force is:

Where:

- Coefficient of static friction, dimensionless.

- Normal force, measured in newtons.

Likewise, the kinetic friction force is described by the following model:

Where:

- Coefficient of static friction, dimensionless.

- Normal force, measured in newtons.

And weight is equal to the product of the mass of eraser and gravitational constant ()

In this exercise, coefficients of static and kinetic friction must be determined. First equation of equilibrium has to be expanded and coefficient of friction cleared:

But , so that:

Now, coefficients of static and kinetic friction are, respectively:

The coefficients of static and kinetic friction for this experiment are 0.716 and 0.596, respectively.