A50.0 kg piece of rock slides down the side of mt. etna. that part of the volcano slopes up at 30.0° (from the horizontal). if the rock accelerates at 3.0 m/s2, what is the coefficient of friction between the rock and the volcano?

0.224

Explanation:

There are two forces acting on the rock along the direction parallel to the slope:

- The component of the weight parallel to the slope, down, given by

where

m = 50.0 kg is the mass of the rock

is the acceleration of gravity

is the angle of the slope

- The force of friction, up along the slope, given by

where

is the coefficient of friction

R is the normal reaction

So the equation of the forces along the direction parallel to the slope is

(1)

where

is the acceleration

The normal reaction R can be found by looking at the equation of the forces along the direction perpendicular to the slope: in fact, we have that R balances the component of the weight perpendicular to the slope, so

And substituting into (1)

And solving for , we find the coefficient of friction: