Problem 1

A mass

m

starts from rest and slides down a plane inclined by angle

\alpha

to the horizontal. The kinetic-friction coefficient is constant,

\mu_k

, and the plane is long enough; assume

\tan\alpha>\mu_k

so the object accelerates downhill. Take

g=9.8\,\mathrm{m/s^2}

. (a) Find the normal force and friction magnitude. (b) Find the acceleration along the plane. (c) Find speed after distance

s

along the plane and the time taken to travel that distance.

problems.proof.stepOf

a=g(\sin\alpha-\mu_k\cos\alpha)>0

problems.proof.analysis

Insert friction and the normal force into Newton's equation and cancel mass. The stated condition makes the bracket positive.