Question

A block is held in place by a string on an incline of

50.0º above the horizontal. If the string breaks, the

block slides down the incline with an acceleration

of 3.50 m/s. What is the coefficient of kinetic

friction between the block and the incline?

Answer 1

force acting down the plane = mg sin $\theta$

Friction force acting up the plane = uN

normal force = mg cos $\theta$

acceleration = Net force / mass

= (mg sin $\theta$ - umg cos $\theta$) / m

= g sin $\theta$ - ug cos $\theta$

3.5 = 9.8*(sin 50 - u*cos 50)

u = 0.636

so the coefficient of kinetic friction is 0.636