Question

PLZ help: An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two cables as shown in the figure. To two decimal places, what is the tension in the two cables?

Answer 1

This system is in static equilibrium. Therefore the forces must be balanced both vertically and horizontally.

Each cable provides a vertical and horizontal component of tension.

The sum of the vertical tensions must equal 50lbs (otherwise the speaker would fall). The horizontal tensions must be equal and opposite (otherwise the speaker would accelerate left or right).

When solving these problems, it helps to draw a diagram. You will have two right triangles with the mass hanging from the center.

Lets say that:
T1 = tension in rope at 35 deg
T2 = tension in rope at 45 deg

Then for the vertical components:
T1vertical = T1*sin(35)
T2vertical = T2*sin(45)
T1vertical + T2vertical = 50lbs

Now for the horizontal:
T1horizontal = T1cos(35)
T2horizontal = T2cos(45)
T1horizontal = T2horizontal

You have two eqns and two unknowns. Use substitution or your favorite method to solve.

Answer 2

@Agl202

Answer 3

you were already helping but i dont understand what to do next