A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30°, the box starts to slip, and it slides 2.2 m down the plank in 4.4 s at constant acceleration.

Question

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30°, the box starts to slip, and it slides 2.2 m down the plank in 4.4 s at constant acceleration.
(a) What is the coefficient of static friction?

(b) What is the coefficient of kinetic friction?

drwls · Answer

(a) Let s be the coefficient of statice froction and k be the coefficient of kinetic friction.

From the info on the angle at whic slidign starts,
M g sin 30 = M g s cos 30
tan 30 = s

(b) Solve for the acceleration rate a after sliding begins. It slides a distance X in time T.
a T^2/2 = X
a = 2X/T^2
Then solve for k using Newton's second law.
M a = Mg sin 30 - M g k cos 30
a/g = sin 30 - k cos 30