A motor M is at rest when someone flips a switch and it starts pulling in the ro

Question

A motor M is at rest when someone flips a switch and it starts pulling in the rope. The acceleration of the rope is uniform and is such that it takes 1s to achieve a retraction rate of 4 ft/s. After 1s the retraction rate becomes constant. Determine the tension in the rope during and after the initial 1s interval. The cargo C weighs 130lb, the weight of the ropes and pulleys is negligible, and friction in the pulleys is negligible.

Also this is for EML 3217.

A motor M is at rest when someone flips a switch and it starts pulling in the rope. The acceleration of the rope is uniform and is such that it takes 1s to achieve a retraction rate of 4 ft/s. After 1s the retraction rate becomes constant. Determine the tension in the rope during and after the initial 1s interval. The cargo C weighs 130lb, the weight of the ropes and pulleys is negligible, and friction in the pulleys is negligible. Also this is for EML 3217.

Explanation / Answer

Assume tension in rope = T total tension for weight = 2T +T = 3T for 1 sec acceleration of rope = a Then acceleration of weight will be = a/3 v = u + at 1 = 0 + a*1 a = 1 Now for weight 3T - mg = ma T = m(g+a)/3 = 130(32.174+ 1 )/3 = 1437.54 for t > 1sec 3T = mg T = 130*32.174/3 = 1394.21

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