When we apply the energy conservation principle to a cylinder rolling down an in

Question

When we apply the energy conservation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because: (a) there is no friction present (b) the angular velocity of the center of mass about the point of contact is zero (c) the coefficient of kinetic friction is zero (d) the linear velocity of the point of contact (relative to the inclined surface) is zero (e) the coefficients of static and kinetic friction are equal A spool of wire of mass M = 0.2 kg and radius R = 0.4 m is unwound under a horizontal constant force F = 1.2 N, as shown in the figure. Assuming that the spool is a uniform solid cylinder (with momentum of inertia I = MR^2/2) that roles without sliding, determine: (a) The acceleration of the center of mass of the spool. (b) The static friction force (both magnitude and orientation) acting on the spool. (c) If the cylinder starts from rest, what is the speed v of its center of mass after it has rolled through a distance d = 4 m.

Explanation / Answer

here,

3)

for a cyclinder rolling down an inclined plane

the work done by the friction is zero

because the point of contact of the surface of cycliner has zero velocity relative with the inclined

so the correct option is d) the linear velocity of the point of contact (relative to the inclined surface) is zero

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