A hollow cylinder of outer radius R and mass M with moment of inertia about the center of mass Icm=MR2 starts from rest and moves down an incline tilted at an angle θ from the horizontal. The center of mass of the cylinder has dropped a vertical distance h when it reaches the bottom of the incline. Let g denote the acceleration due to gravity. The coefficient of static friction between the cylinder and the surface is μs. The cylinder rolls without slipping down the incline. The goal of this problem is to find an expression for the smallest possible value of μs such that the cylinder rolls without slipping down the incline plane and the velocity of the center of mass of the cylinder when it reaches the bottom of the incline.
(a) What is the magnitude of the acceleration a of the center of mass of the cylinder on the incline? Express your answer in terms of θ and g as needed (enter theta for θ and g for g).
a=
unanswered
(b) What is the minimum value for the coefficient of static friction μs such that the cylinder rolls without slipping down the incline plane? Express your answer in terms of θ (enter theta for θ).
μs min=
unanswered
(c) What is the magnitude of the velocity of the center of mass of the cylinder when it reaches the bottom of the incline? Express your answer in terms of g and h as needed (enter g for g and h for h).
vf=
1 answer
http://web.mit.edu/8.01t/www/materials/ProblemSets/Raw/old_files_fall07/ps10sol.pdf
0 answers