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Problem: A bag of cement weighing Fg = 325 N hangs in equilibrium from three wires as shown in the figure. Two of the wires make angles θ1 = 60.0° and θ2 = 40.0° with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires.

FREE Expert Solution

We're asked for the tension in each of the wires supporting the bag of cement.

This is a 2D Equilibrium type of problem with multiple forces in different angles. As usual for equilibrium problems, we'll follow these steps:

  1. Draw a free body diagram for each point of interest
  2. Set up our equilibrium equations
  3. Solve for the target.

In two dimensions, we use equilibrium equations in component form:

Fx=0Fy=0

Anytime we're working with forces that aren't at 90° angles to each other, we'll also need some of the equations to convert magnitude-angle notation to components.

Magnitude: |F|=Fx2+Fy2

Angle: tan θ=FyFx

Components of a force: Fx=|F| cos θFy=|F| sin θ

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Problem Details

A bag of cement weighing Fg = 325 N hangs in equilibrium from three wires as shown in the figure. Two of the wires make angles θ1 = 60.0° and θ2 = 40.0° with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the 2D Equilibrium concept. You can view video lessons to learn 2D Equilibrium. Or if you need more 2D Equilibrium practice, you can also practice 2D Equilibrium practice problems.