# Calculating tension?

1. Sep 12, 2006

### Energize

I need to work out the tension in a piece of string when hanging a picture off one nail on the wall. All I know is that the weight of the picture is 50N and the angle of the sides of the string are at a 40 degree angle from the top of the picture. I have no idea of even how to start working this out. Can anyone help?

2. Sep 12, 2006

### Hootenanny

Staff Emeritus
Welcome to the Forums,

I would begin by drawing a free body diagram labelling all the forces and their orientations.

3. Sep 12, 2006

Draw a force diagram
Apply Newton's Laws

Realize that the picture is not moving, thus it's velocity is zero. Newton's law will drop down to:

$$\sum \vec F_i = 0$$

Remember that you can write a vector as:
$$\vec T = \hat T |\vec T|$$

or in a more familiar notation,
$$\vec T = \hat i \, T \cos \theta + \hat j \, T \sin \theta$$

does that help?

hint: you will need to solve for T

4. Sep 12, 2006

### Staff: Mentor

Are you familiar with free body diagrams, which show all the forces on objects? Does you textbook have a similar examples worked out for you where there are cables or strings involved?

EDIT -- Oops, I was too slow!

5. Sep 12, 2006

### Cyrus

Um, I disagree with this:

$$\vec T = \hat i \, T \cos \theta + \hat j \, T \sin \theta$$

This is bad practice and should be avoided.

6. Sep 12, 2006

### Energize

The only force acting on it is gravity, our class hasn't drawn any of these diagrams you speak of or seen that formulae before, I've just started AS and our teacher just gave us this sheet with loads of questions on without even teaching us about tension yet.

/\
/ \
/ \
/40o 40o\
------------
| |
| |
--------------
50 Newtons

Last edited: Sep 12, 2006
7. Sep 12, 2006

### Staff: Mentor

See if this info from wikipedia helps:

http://en.wikipedia.org/wiki/Free_body_diagram

8. Sep 12, 2006

Yeah, I posted that rather quickly. I disagree with it too.

I should have just said something along the lines of resolving the vector into its components via the angle between them. Because what I wrote only holds for a subset of problems.

Do you think I should edit it out?

On a side note, I personally hate the $\hat i, \,\, \hat j \,\, \hat k$ notation.

9. Sep 12, 2006

If the only force acting on it was gravity it would continue to fall forever in the direction of the gravity vector.

Imagine a balloon hovering in the air. What forces act on it?
Well of course gravity does.
Then the helium in the baloon is trying to rise which creates an upwards force right?

Well since the balloon is hovering (ie not moving) the "helium" upward force, and the gravity downward force must be equal. You can think of that "helium" force as the force applied to the string. That force is the tension.

Does that makes sense?

10. Sep 12, 2006

### Cyrus

Nah, so long as he knows its not a 'formula'