# Finding Tension in a Pulley System

Homework Statement

A crate is pulled up using frictionless pulleys in the manner shown in the figure. The angle is 45 degrees. The masses are, for the small pulley, m1=4.1 kg, for the traveling pulley, M2=6.7 kg, and for the crate, MC=45.8 kg. What is the minimum tension with which the operator must pull on the cable (assume the cable is of neglible mass) in order to slowly raise the crate.
(The diagram of this is attached.)

The attempt at a solution

I've tried this a few times now and have yet to get the right answer. First, I took the Mc and M2 as the force down, which meant the tension in each of the cables it was attached to was g(1/2)(M2+Mc), which would be the y component of the triangle formed when the person pulled the cable, and used sin45 to get T. This was not correct.

(To be exact, my calculations were as follows)
Ty = (9.8)(1/2(45.8+6.7) = 33.495 N

sin45= 33.495/T
T=33.495/sin45
T=47.4 N

The answer is neither 33.5 nor 47.4 N. At this point, I don't know how to proceed with the question and I would really, really appreciate help.

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## Answers and Replies

Doc Al
Mentor
(To be exact, my calculations were as follows)
Ty = (9.8)(1/2(45.8+6.7) = 33.495 N
Redo that calculation. That will be the full tension, not the y-component.

Redo that calculation. That will be the full tension, not the y-component.

Oh, thank you. Originally thought that the angle was extraneous information and got it wrong, but I obviously did the math wrong.

I have the answer now. Thank you!