A dynamics cart with a friction pad is placed at the top of an inclined track and released fromrest. The cart accelerates down the incline at a rate of 0.60 m/s2. If the track is angled at 10degrees above the horizontal, determine the coefficient of kinetic friction between the cart andthe track.

0.114

Explanation:

There are two forces acting on the cart in the direction along the cart:

- The component of the gravitational force in the direction parallel to the ramp, , down along the ramp

- The force of friction, , up along the ramp

So the equation of motion along this direction is:

(1)

where

m is the mass of the cart

is the acceleration due to gravity

is the angle of the ramp

is the coefficient of kinetic friction

N is the normal force exerted by the ramp on the cart

is the acceleration of the cart

The normal force can be found from the equation of the forces along the direction perpendicular to the ramp; in fact, the normal force is balanced by the component of the weight perpendicular to the ramp, so we have:

From which we get:

Substituting into (1),

And solving for , we find the coefficient of friction:

answer( sicar );