# Simple Tension Problem

1. Mar 20, 2005

### wetcarpet

There are two wires connected to a ceiling with a light fixture hanging at their ends. The light fixture exerts a force of 80N, while the wires make a 40 degree angle with the ceiling. What is the tension in the two strings? The diagram roughly looks like this:

---------------
- 40 40 -
- -
- -
-
-
80N

I assumed that this was a simple trigonometry problem and set about solving it like so:
{a} I assumed that since the object was not moving downward, there had to be an 80N force exterted upward. Hence, I split the large triangle into two parts using a positive 80N force, making a 90 degree angle with the ceiling, and a 50 degree angle at the base of the larger triangle.
{b} From there I used trigonometry:
cos(50) = 80N/Hyp.
Hyp. = 80N/cos(50)
Hyp. = 124.5N

Yet, the software (Webassign.com) is telling me that the tension is not 124.5N. What am I doing wrong?

P.S.- I also tried assuming that there is not an 80N positive force exerted upward, and thereby tried isolating each X and Y vector for each string seperately. I still got the same answer of 124.5N.

2. Mar 20, 2005

### wetcarpet

3. Mar 20, 2005

### Nylex

If they want the value for T in each string, you need to divide that value by 2. Resolve the forces perpendicular to the string and you get 2Tsin 40 = 80.

4. Mar 20, 2005

### wetcarpet

I thank you kindly, dividing 124.5N by two did work, and I appreciate your explanation as well.

Last edited: Mar 20, 2005