Statics and Pulleys

Question

Consider the 653 N weight held by two cables shown below. The left-hand cable had tension T2 and makes an angle of 35◦ with the ceiling. The right-hand cable had tension T1 and makes an angle of 36◦ with the ceiling.

What is the tension in the cable labeled T1 slanted at an angle of 36◦ ? Answer in units of N.

What is the tension in the cable labeled T2 slanted at an angle of 35◦ ? Answer in units of N.

Answer 1

The title of this problem references pulleys and the text of the problem mentions a diagram, but since there's no diagram, I'm not positive of how the problem is set up. However, it sounds to me like a situation where you should draw your free body diagram for the 653 N weight, showing the cable tensions and angles, and gravity force. You'll need to use some geometry to check which angles are equal to the angles to the ceiling, and this usually involves either alternate interior angles and/or right traingle properties (the two smaller angles in the right triangle are complementary).

You need to use your trig to find the components of your forces (tension and gravity) and set the sum of the forces along each axis to zero since you have static equilibrium. You will probably end up with a system of two equations and two unknowns (the two tensions) which you can then solve for the tension in each cable.