Question

A) An object with mass M=10kg is held on a incline. The object and the incline surfaces have a static friction coefficient of 0.3. What is the maximum angle at which the object starts moving?

B) Again, suppose that the force in A) is a push applied horizontally on the mass instead of a pull directed parallel to the plane.
What is the angle other than 90o for the plane at which no horizontal force can keep the mass moving at constant speed?

Thank you very much!

Answer 1

a. TanTheta=mu
theta=arctan mu

b. horizonal force resolves into an upward the plane component, and a normal component which increases normal force.
friction=(mg+FsinTheta)mu
downplane force=mg*sinTheta
upplane force= F cosTheta
so the question is what is theta such that friction is greater than net upward force
friction > pushing up -weight down
(mg+FsinTheta)mu +mgSinTheta>FcosTheta

sinTheta(f*mu+mg)>FcosTheta-mg*mu

so, so you can solve this on your calculator by plotting two graphs and see where they cross, or use Newtons' method.