Question

A mass of 8 kg is placed on an incline with a coefficient of static friction of 1.67 and coefficient of kinetic friction of 1.29. No additional forces are acting on it and it is raised slowly from a small angle and it begins to slide at some angle. If 10 degrees is added to this angle, and the mass started from rest from a vertical height of 33 meters, how much longer would it take to travel down the incline to the bottom compared to if there was no friction on the incline? Answer in seconds

Answer 1

Angle when sliding begins = arctan us = arctan 1.67 = 59.09 degree

Final angle theta = 59.09+10 = 69.09 degree

acceleration with friction a1 = g sin theta - uk g cos theta

= 9.8*[sin 69.09 degree - 1.29* cos 69.09 degree]

a1 = 4.643 m/s^2

acceleration without friction a2 = g sin theta = 9.8*sin 69.09 degree = 9.155 m/s^2

slope distance s = 33/sin 69.09 degree = 35.33 s

using second equation of motion, time difference = sqrt(2*35.33/4.643) -  sqrt(2*35.33/9.155)

= 1.123 s answer