A street lamp weighs 150 N. It is supported by two wires that form an angle of 120.0 degrees with each other.?

Question

A street lamp weighs 150 N. It is supported by two wires that form an angle of 120.0 degrees with each other. The tensions in the wires are equal.

a. What is the tension in each wire supporting the street lamp.
b. If the angle between the wires supporting the street lamp is reduced to 90 degrees, what is the tension in each wire.

Please help me show all the work involved in the steps.
I need help understanding it.

Answer 1

First of course you have to understand two or more forces have one resultant and the other way one force can be divided to many forces.
In this case, One force that is the lamp's weight will be divided into two forces along the wires that support it.
To calculate it you'd better take a piece of blank paper and draw it.
The weigh of lamp is drawn as an arrow facing down and the arrow length say 2 cm
in order to keep the lamp steady, you must counter it with an equal counter force , that is you can draw another arrow with the same length with direction exactly the opposite of the first arrow.
Place the beginning of second arrow exactly at the beginning of first arrow. (point X)
The beginning of both arrows represent the point where the two wires support it.
from the other end (sharp end) of counter arrow draw 2 lines perpendicular with both wires.
this two new lines will intersect with the wires at say point A and B respectively.
draw arrows from X to A and to B.
These Arrow A and B are exactly the tension in the wires that support the lamp, and creates resultant counter arrow.

You can calculate with trigonometry and you will find that each tension in the wire is equal 150 N
So if the angle becomes 90,
then the tension becomes (150)*0.5*2**-2 =106.066 N

Answer 2

a. I'd very much like to show you how it is done but to enable me to make you understand we need a diagram of the forces involved. The weight of the lamp of 150N is the resultant of the force T on each wire. If you can manage to draw the forces, you will see that T =[150/2]/sin30=150N.

b. At 90 degrees, T=150sin45=106N.

The work will not be easy to understand if you don't have the diagram.