# Triangle of forces

Both ends of a rope of length 4.8m are attached to a horizontal beam, at points 4.2m apart. A chandelier hangs on the rope, 1.2m from one of its ends.

See attached for diagram

(a) Calculate the angles that the two sections of the rope make with the beam, in degrees correct to two decimal places. The chandelier has mass 14 kg. Assume that the only forces acting on it are its weight and the tensions in the two sections of the rope. Take the magnitude of the acceleration due to gravity to be g = 10ms-2.

(b) Draw a force diagram for the forces acting on the chandelier, giving the sizes of the angles between the forces, and defining any symbols that you use to denote the forces.

(c) Draw a corresponding triangle of forces, indicating the sizes of the angles.

(d) Use the triangle of forces to find the magnitudes of the tensions in the two sections of the rope, in newtons correct to three significant figures.

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#### Solution Summary

The expert calculates the angles that the two sections of the rope make with the beam is determined.