Block accelerates at 3.7m/s^2 down an incline plane at a 30 degree angle. find coefficient of kinetic friction

coefficient of kinetic friction= 0.14

Explanation:

In the attached image we can see a free body diagram where the forces act on the block.

From the analysis of forces on the y-axis (equal to zero, because there is no movement) we can find the equation of normal force.

By performing an analysis of forces equal to mass by acceleration we can find an equation that relates the acceleration (3.7 m/s^2) to the friction force. As the block descends with constant acceleration, the friction force is directed in the opposite direction.

If we use the definition of friction force.

By combining these equations we can find an expression where the mass is cancelled, and the value of the coefficient of friction can be cleared.