# Tension Problem!

1. Nov 21, 2006

### Cole07

:yuck: This is my problem:
1. A 56.2-kg high-school student hangs from an overhead bar with both hands. What is the tension in each arm if the bar is gripped with both arms raised vertically overhead?
2. What is the tension in each arm when the arms make an angle of 35.00 o with respect to the vertical?
I have two equations:
A.) sum of all forces=ma
B.) sum of all forces=0

i tried:
sum of all forces=56.2*9.81
but this was wrong

then for the second question i tried:
sum of all forces=56.2cos(35.00)
i found this equation after research and don't know too much about it.

I don't understand how to plug this into these equations or if the are the right ones. Could someone lead me in the right direction. any help would be greatly appreciated.

2. Nov 21, 2006

### Dorothy Weglend

Sounds to me like you need to draw a free body diagram, and that would sort out the confusion in short order.

Once you have this, translating it into mathematics and solving it is not difficult.

Dorothy

3. Nov 21, 2006

### ponjavic

What do you mean by sum of all forces = ...

That would literally mean that there would be no equilibrium and the student would be falling or flying or something.

First thing you do draw a FBD (see pic)

Now for equilibrium the two forces on the arms have to equal the force (weight) on the bar (coming from the person).

Now you should be able to work out the force on one arm!

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4. Nov 21, 2006

### Cole07

Ok i drew a free body diagram and i see
W=56.2
T1=?
T2=?
and i know that T1 and T2 are the same

5. Nov 21, 2006

### Cole07

"Now for equilibrium the two forces on the arms have to equal the force (weight) on the bar (coming from the person)."

would this be 551.322
(56.2*9.81)

6. Nov 21, 2006

### Dorothy Weglend

Good for you. Except W = mg, not m, right?

So T1 = T2, so just call it T. Call the vectors (T) pointing up positive. Add them together, subtract the vector going down, and then decide what they are all equal to.

Then solve for T, and you are done.

The same approach will work for part B. It is slightly more complicated, but only slightly.

Dorothy

7. Nov 21, 2006

### ponjavic

For equilibrium the sum of all the forces is equal to zero

IE

W + T1 + T2 = 0, and as you said T1 = T2 Solve this?

Ignore my FBD it was rubbish I forgot the weight of the person

I'll just leave this one to Dorothy ^^

8. Nov 21, 2006

### Cole07

"So T1 = T2, so just call it T. Call the vectors (T) pointing up positive. Add them together, subtract the vector going down, and then decide what they are all equal to."
To find what T is would you do 551.322+T=0 ?

9. Nov 21, 2006

### ponjavic

Is there just one T? As T1=T2

10. Nov 21, 2006

### Cole07

no there is two and they equal the same number. but i don't understand how to get the T1 or T2 i have the equation (sum of all forces)=0
and the sum of all force is sigmaF, is this not the equation i use?

11. Nov 21, 2006

### Cole07

W + T1 + T2 = 0
can you leave one T out since they are the same and it just be W+T=0 ?

12. Nov 21, 2006

### Dorothy Weglend

Hi Cole,

Your FBD diagram should have two vectors pointing up, representing the forces of the arms. And one vector pointing down, that represents the force of gravity, the weight.

So if the two vectors are pointing up (call that positive, as I suggested), and the weight vector is pointing downwards, then you have:

Sumof Forces in Y: 2T - mg = ???

I left the ??? for you to fill in...

Dorothy

13. Nov 21, 2006

### Dorothy Weglend

You can't leave out one T, because that doesn't represent the physics of the situation. That would be the case if the person were hanging by just one arm, and the force on that arm would be much greater than if he is hanging by two arms.

Dorothy

14. Nov 21, 2006

### ponjavic

No you cannot, it is like this: If T1=T2 then:

W+T1+T1=0 thus W+2T1=0 and mind the vectors as dorothy said IE

W-T1-T2=0 W-T1-T1=0 W-2*T1=0

15. Nov 21, 2006

### Cole07

oh this makes alot more since i used your formula 2T-mg=0

2T-56.2(9.81)=0

2T/2=551.322/2

T= 275.661

16. Nov 21, 2006

### ponjavic

So just by thinking about it logically you should understand that the force from the weight gets split up between each arm!

17. Nov 21, 2006

### Cole07

I still don't under stand what to do when i have an angle though would i use the formula
sum of all forces=56.2*9.81cos(35.00)

18. Nov 21, 2006

### Cole07

yes i did understand this part.

19. Nov 21, 2006

### Cole07

Is the vertical the person?

20. Nov 21, 2006

### Dorothy Weglend

Stop searching for formulas

When you have forces at an angle like this, you need to break them up into the component vectors.

If the arms are at an angle to the verticle, then part of the force on the arm is going straight up and down, and part is going left and right. These are the y and x components of the vectors. You can use trigonometry to get these.

Then you balance these forces in the Y and X direction, just as you did for the Y direction in part A.

Isn't this covered in your text book, or by your teacher? Just curious.

Dorothy