At the instant shown, the center of a spool with inner and outer radii r=2 ft an

Question

At the instant shown, the center of a spool with inner and outer radii r=2 ft and R=11ft, respectively, is moving down an incline at a speed v0= 11.9ft/s.  If the spool does not slip relative to the rope and if the rope is fixed at one end, determine the velocity of point c ( the point on the spool that is in contact with the incline) as well as the ropes unwinding rate, that is, the length of rope being unwound per unit time.

At the instant shown, the center of a spool with inner and outer radii r=2 ft and R=11ft, respectively, is moving down an incline at a speed v0= 11.9ft/s. If the spool does not slip relative to the rope and if the rope is fixed at one end, determine the velocity of point c ( the point on the spool that is in contact with the incline) as well as the ropes unwinding rate, that is, the length of rope being unwound per unit time.

Explanation / Answer

velocity of point C is zero, because the spool is rolling with out slipping.


vo = 11.9 ft/s = 11.9*0.3048 = 3.627 m/s


w = vo/R = 11.9/11 = 1.08 rad/s


r = 2 ft = 2*0.3048 = 0.6096 m

velocity at the innere rim

v = r*w = 0.6096*1.08 = 0.659 m/s

so the, rope's unwinding rate is 0.659 m/s

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