what is the equation to find tension in a string?

Answer 1

Depends on the configuration of the string system. The key to any string configuration is to recognize that a fixed string and whatever is attached to it are not moving. This means that the sum of all forces acting on that string and attachments is zero (i.e., f = 0; where f is the net force acting on the string).

If f were not zero (e.g., f > 0), the string and everything else attached to it, like a weight (W), would be accelerating. This stems from f = ma; where m is the mass of the system and a is its acceleration. You can see from this that the only way the string system can remain static is for f = ma = 0; so that a = 0 and the system is not accelerating.

So to find that "equation":

First, identify ALL the forces acting on the system (string plus whatever else is attached to it, like a weight). Then add them up as vectors (magnitude with direction). If the sum you get (f) is not zero (e.g., f<>0), then you've overlooked a force or did the math wrong. This follows from f = ma = 0 for a non-accelerating string system.

Second, identify the force vector that follows the length of the string. That's the so-called tension. Understand, it's tension if and only if the string is tense (taut). If it's flopping about, there is no tension per se.

Third, divide all the forces into their X and Y components; e.g., F = Fx + Fy as vectors.

Fourth, write two equations, which are in general:

Sum of Fx to the left = Sum of Fx to the right
Sum of Fy up = Sum of Fy down

We know all the forces in the X directions (left and right) add up to zero (are equal but opposite) and all the forces in the Y directions (up and down) also add up to zero. Why? Because that string system is static, it is not moving in any direction; so the net forces up and down, and left and right have to be zero as well. In fact, this is what we really mean when we say f = ma = 0; that is, all the forces (up, down, left, right) add up to zero and give the system a = 0 acceleration.

Fifth, solve the two equations for the tension force.

EXAMPLE:

Look at a massless string hanging down with a weight (W) on the end. What's the tension?

First, ID all the forces.

Clearly there is the force of gravity, which is called weight; where W = mg, m = the mass (kg) and g = 9.81 m/sec^2 the acceleration due to gravity on Earth's surface.

Are there other forces? Yes. How do we know this? Because the string system is just hanging there, not moving. Thus, there must be an equal and opposite force (T) to cancel out the weight (W). Otherwise, the system would be moving.

Second, find the force that follows the string. There are only two forces in this example: T and W. W is down along the weight; so the only force left (T) has to be the one along the string. And that's the one we call tension.

Third, divide the forces into their X and Y components.

This is a snap, there are no X components because the string is hanging straight down and not moving sideways. So we have only vertical forces at work. Thus, Fx = 0 and T and W <> 0 are the vertical forces on this system.

Fourth, write the X and Y equations of force.

Fx = 0
Fy = T - W = 0; where W has the negative sign showing the weight is acting downward, while T, the tension, is acting equal and opposite in the upward direction.

Fifth, solve the equation for the tension.

Fy = T - W = 0; so that, T = W = mg. Presuming you know either the weight or the mass of the thing dangling on the end of the string, you can easily find T, the tension.

Two keys to finding tension equations:

1. Tension runs along the string.
2. The sum of X and Y forces acting on the string system must be zero if the system is static.

Answer 2

Tension Equation

Answer 3

Finding Tension

Answer 4

ahh gotta love physics ;P

Well, first off, you need to do sum of all the forces then you can get the tension by itself then if the equation has all knowns then you can solve!!!

I hope this helps, otherwise go to this site: http://www.fearofphysics.com/Probs/mech037.html

it explains very well on what to do in this situation :)

Good luck!!!!!