Question

Problem 4. Consider the same spool considered in a previous problem (mass m = 2 kg, outer radius 3 m, inner drum radius 2 m, centroidal radius of gyration of the spool is kC = 2 m). However, in this case, there is an inextensible cord wrapped around the outside of the spool, which passes over a massless pulley and down to a mass of weight 16 N (mD = 1.631 kg). (a) Assuming that the inner drum of the spool rolls without slip on the ground, find the angular acceleration of the spool just after being released from rest. (b) Find the minimum coefficient of friction between at point A to maintain pure rolling. (c) If the actual coefficient of friction is half the value found in part (b), find the downward acceleration of the mass D just after being released from rest. Ans: (a) ? = 0.9075 rad/s² ccw, (b) ?min = 0.9251, (c) aD = 4.015 m/s² downward.

          Problem 4.
Consider the same spool considered in a previous problem
(mass m = 2 kg, outer radius 3 m, inner drum radius 2 m,
centroidal radius of gyration of the spool is kC = 2 m). However,
in this case, there is an inextensible cord wrapped around the
outside of the spool, which passes over a massless pulley and
down to a mass of weight 16 N (mD = 1.631 kg).
(a) Assuming that the inner drum of the spool rolls without slip
on the ground, find the angular acceleration of the spool
just after being released from rest.
(b) Find the minimum coefficient of friction between at point A
to maintain pure rolling.
(c) If the actual coefficient of friction is half the value found in
part (b), find the downward acceleration of the mass D just after being released from rest.
Ans: (a) ? = 0.9075 rad/s² ccw, (b) ?min = 0.9251, (c) aD = 4.015 m/s² downward.

Problem 4.
Consider the same spool considered in a previous problem
(mass m = 2 kg, outer radius 3 m, inner drum radius 2 m,
centroidal radius of gyration of the spool is kC = 2 m). However,
in this case, there is an inextensible cord wrapped around the
outside of the spool, which passes over a massless pulley and
down to a mass of weight 16 N (mD = 1.631 kg).
(a) Assuming that the inner drum of the spool rolls without slip
on the ground, find the angular acceleration of the spool
just after being released from rest.
(b) Find the minimum coefficient of friction between at point A
to maintain pure rolling.
(c) If the actual coefficient of friction is half the value found in
part (b), find the downward acceleration of the mass D just after being released from rest.
Ans: (a) ? = 0.9075 rad/s² ccw, (b) ?min = 0.9251, (c) aD = 4.015 m/s² downward.

Added by Inmaculada B.

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