How to calculate tension in hanging ropes

[slyskittle]

Homework Statement

a box (10kg) is suspended by a pair of v-shaped ropes, each at an angle of 42 degrees, with the ceiling. what is the tension in the pair of ropes

Homework Equations

??

The Attempt at a Solution

?? I'm not sure how to do this question at all!

 

[Tedjn]

Have you drawn a free body diagram? What are the forces on the box? There are too many different directions. How would you break your analysis down into only two directions? What are the forces in those directions?

 

[slyskittle]

are the two forces: mg (pushing downwards) and tension (pushing up)?
is the tension in each rope just half of the downwards force?
or do i solve this question differently to how i approach two vertical ropes?

 

[Tedjn]

It is true that the tensions in both ropes are equal because when you draw a picture, the picture is symmetric. However, if the ropes were not at 42 degrees, the tension would be different. To experience this, imagine yourself to be the box and your arms the ropes. Try to pull yourself up on a pull-up bar with your hands extremely far apart and your hands close together. Which is easier and what does that mean?

It is important to understand in what direction the forces point. You are right that the weight points downward. This is because weight is actually the gravitational force exerted by Earth on the box. This points to the center of the Earth, but from our perspective, it appears to be straight down. The tension forces always point in the same direction as the string. Thus, they do not point straight up. However, you can see that they point in an upwards direction to help counteract the downward weight and keep the box not moving up or down. Because the tensions point partly horizontally also, you must also find the horizontal component of the force. Then, you can find the ultimate magnitude of the tension.