Question

The grooved pulley of mass m is acted on by a constant force F through a cable which is wrapped securely around the exterior of the pulley. The pulley supports a cylinder of mass M which is attached to the end of a cable which is wrapped securely around an inner hub. If the system is stationary when the force F is first applied, determine the upward velocity v of the supported mass after 4 seconds. Use the values m = 30 kg, M = 11 kg, ro = 345 mm, ri = 230 mm, kO = 250 mm, and F = 85 N. Assume no mechanical interference for the indicated time frame and neglect friction in the bearing at O. What is the time-averaged value of the force T in the cable which supports the 11-kg mass?

Answer 1

Answer:

Answer; v= 1.2654m/s

T= 110.76N

Explanation:

Apply Momentum Principle

Fdtro - Mgridt = Iow +Mvr

Fdtro - Mgridt = mK2 v/r1 + Mvr1

85 x 3x 0.345 -11 x 9.81 x 0.23 x 3 =30 x 0.25 x 0.25 x v/0.23 + 11 x v x 0.23 =

v = 1.2654m/s

To find the timed average value

Tdt -Mgdt =MV

T x 3 - 11 x 9.81 x 3 = 11 x 0.778

T= 110.76N