How to find the coefficient of friction between 2 surfaces?

Question

A 50kg rock slides down the side of a volcano that slopes up an angle of 30 degrees to the horizontal. If the rock accelerates at a rate of 3 m/s^2, what is the coefficient of sliding friction between the rock and the side of the volcano?

Answer 1

Your first step should be to draw a free body diagram of the problem; the trick to this one is to tilt your x-axis to 30 degrees above the horizontal, so that the object is accelerating only along the x-axis. Your y-axis should stay perpendicular to the x-axis! There should be only three forces - gravity (pointing straight down, not along either axis), the normal force (along the y-axis), and the frictional force (up the hill).

Your second step is to divide the gravitational force into component forces - the x-axis piece, which pulls it down the hill, and the y-axis piece, which attempts to pull it through the hill. The y-component is exactly equal to the normal force, since the rock doesn't accelerate into or away from the volcano. Getting the triangle correct is tricky; my tip is that the force of gravity should always be the hypoptenuse for these problems. Since we've tilted the axes, G_y = 500cos(30) and G_x = 500sin(30).

Third, we need to find the net force on the rock, so that we can find the magnitude of the frictional force. Since the acceleration is 3 m/s², we know that G_x - F_friction = 150 N; this means that F_friction must be 100 Newtons.

Since we know that F_friction = µF_N, µ is 100/500cos(30), or approximately 0.23.