The position of the L-shaped rod shown is controlled by a cable attached at poin

Question

The position of the L-shaped rod shown is controlled by a cable attached at point B. Knowing that the rod supports a load of magnitude P = 200 N, calculate the tension T in the cable (BE) as a function of = 90 degrees.

Notes:
• P is always vertical.
• BE is not vertical in general!
MY ATTEMPT AT FINDING THE APPROPRIATE EQUATIONS: I cannot find the angle or , if anyone could please help! The position of the L-shaped rod shown is controlled by a cable attached at point B. Knowing that the rod supports a load of magnitude P = 200 N, calculate the tension T in the cable (BE) as a function of theta = 90 degrees. Notes: P is always vertical. BE is not vertical in general! MY ATTEMPT AT FINDING THE APPROPRIATE EQUATIONS: Free Body Diagram Equation Development: Find the angles: Using law of cosines, find side BE: Using Pythagorean Theorem, find side AE: Using law of sines, find angles alpha Taking moment about A, find tension in BE. I cannot find the angle alpha or gamma, if anyone could please help!

Explanation / Answer

Everything looks OK to me: you have as a function of . Angle cannot be found because the diameter of the pulley is not known; assume the pulley is small. So this is angle that directs vector T, not +. Remember that is a varying parameter input to the problem, not an unknown quantity to be found. A little Matlab coding and you get a nice graph of tension T as a function of . As a check for your general derivation, input =90°and see if the tension you get is the same you get from the simple FBD drawn for =90° and solved as requested by your instructor.

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