Question

A sign with a mass of 4.53 kg is being hung symmetrically by two cables which make an angle of 27.8° with the horizontal. How do you determine the tension in one of the cables?

Answer 1

47.6 N

Explanation:

We assume there are no horizontal forces perpendicular to the sign and that the system is in equilibrium.

For the sign to be in equilibrium, the sum of the forces in the x and y
direction must be zero.

Because the cables are symmetrically positioned, the tension (T) in both will be the same.

The only other force on the system is the weight (W) of the sign. This we calculate from the mass (m) and the gravitational acceleration (g).

If the upward vertical force component (V) in the cable is positive then from the force balance we have

2V - W = 0
V = W/2
`=(mg)/2`

As we know the angle of the cable with the horizontal and the vertical force component we can determine the cable tension using the Trigonometric function sin.

`T =( (mg)/2)/(sin (27.8))`