A container weighing 850 Ibf is moved by using a winch and cable as shown in the

Question

A container weighing 850 Ibf is moved by using a winch and cable as shown in the figure. The cylindrical drum of the winch weighs 100 Ibf and its radius of gyration is 1.75 ft. The kinetic coefficient of friction between the container and the horizontal surface is 0.25. If the container slides on the horizontal surface but does not tip, determine: (a) The maximum tension permissible in the cable, (b) The acceleration of the container when the maximum tension is applied, (c) The maximum couple that can be applied to the winch. [Ref. "Engineering Mechanics: Dynamics", W.F. Riley and L.D. Sturges, Wiley] The maximum cable force will just prevent the container from tipping. That should tell you something about the location of normal reaction on container. The motion of the container and rotation of winch are related because of the rope which raps around winch.

Explanation / Answer

a) let T be the tension => for no tipping net torque = 0

=> 9T = 850*2.5*9.8 => T = 2361.1 lbf

b) T - umg = ma

=> a = 2.77 - ug = .27

c) C - 2T = I*alpha => alpha = .27 / 2 = .135 (alpha = a/r no slipping)

I = 306.25

=> C = 4763

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