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# Tension in Pulley Systems

A winch is used to raise a 500 kg crate at a constant velocity (a = 0 m/s2). Determine the tension in the support arm and the angle theta. Note: the cable that runs from the motor, over the pulley, and to the 500 kg crate is continuous.

The picture consists of a motor that has a cable running up to a pulley (which has the 500kg crate hanging on the other side of the pulley), the cable makes a 45 degree angle with the ground. The pulley is held up by the support arm which is attached to a ceiling like structure in the right corner. The theta angle is the angle between the support arm and the ceiling.

#### Solution Preview

Let angle theta be x
Tension in support Arm = T
Tension in Cable = T'

For equilibrium of the system the resultant force must be zero or algebraic sum of vertical and horizontal components of forces must be zero.

T sinx = T' +T'sin45 ..............(1)
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#### Solution Summary

This solution contains step-by-step calculations to determine the tension int he support arm of the pulley-crate system. All formulas are accompanied with brief notes for further understanding.

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