physics question

Question

A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration 0.67 m/s² directed down the ramp. The ramp makes an angle of 36° with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?

Answer 1

Lets start by thinking about component of weight parallel to the plane - this is mg sin 36. The normal contact force is mg cos 36

Resultant force down the slope = mg sin 36 - f where is the frictional force

f = µ mg cos 36

So resultant force F down slope = mg sin 36 - µ mg cos 36, and acceleration = F/m (newton II)

a = g sin 36 - μ g cos 36

We need to isolate μ = (g sin 36 - a)/g cos 36)

If we use g = 9.8 m/s² the answer is 0.64 to 2 s f