Simple problem on tension and force

k1point618

1. The problem statement, all variables and given/known data
Ropes 3m and 5m in length are fastened to an object that is suspended over a cieling. the object has a mass of 5kg. the ropes, fastened at different heights, make angles of 52 degree and 40 degree with the horizontal. Find the tension in each wire, and the magnitude of each tention.


2. Relevant equations



3. The attempt at a solution
I kno that the tension on one rope, A and the tension on the other rope, B equal to the mass times gravity.
so A_T+B_T = mg
and i want to find the a equation for A_T and B_T

Just wondering, since i kno the angle and length of the rope, i know the verticle component of the rope. But then i don't kno where to go after that

jaseh86

What you need to do is draw a force diagram and write down all the horizontal and vertical components of tension as a result of the mass.

Next, you need to use Newton's second Law and find the net force in both horizontal and vertical directions.

Just remember that net force (vector sum of components) = ma, and if the object is not moving, then the net force is zero.

tiny-tim

Hi k1point618!
No, that's wrong … that only works if both ropes are vertical.

As jaseh86 says, you must treat the horizontal and vertical components separately.

The vertical ones will add to mg, and the horizontal ones to … ?

k1point618

Horizontal adds to Zero!

Well, then i have
A_Tsin52 + B_Tsin40 = mg, and also


A_Tcos52 + B_Tcos40 = 0 ?

tiny-tim

Yes!

k1point618

So i was wondering, why does the problem give the length of the ropes? and how does the high difference of the cieling affects the problem?

tiny-tim

hmm … it's a weird question, because you suspend things under a ceiling, not over it.

Are you sure you have given us the full correct question?

k1point618

Sorry, Over a ceiling, but the ropes are fastened at different heights.

tiny-tim

Then I've no idea why they give you that information.

k1point618

so the different hieghts of the ceiling does not matter to the problem?

tiny-tim

No!!

k1point618

K, THANK YOU!!