What is the Formula for Calculating Tension in Physics?

[liuquinlin]

Hello... I'm brand new to Physics, going into 9th grade and got put into AP Physics BC so I got a large packet of Physics work and was told to learn the material and do all the work. I've been sort of stressed out since I barely understood half the questions, much less knew where to begin solving them. But hopefully this forum will be able to help me out.

This isn't really a question for a specific problem so I can really use the template. So my question is, is there a formula for tension? In other words, how would I find the tension on a string attached to a mass. I know that if the forces were equal then the tension = the weight, but what should I do if the mass is being pulled upwards/lowered downwards? I think the formula would be something like: Tension = Weight +/- Mass * Acelleration, but how would I write that scientifically?

Thanks in advance, and sorry for not using the template...

 

[LBloom]

First off, let me say wow if your in 9th grade taking AP physics C. Thats unheard of in my school. Secondly, there really is no equation for tension, as its just another force, and the cardinal equation for forces is $$\Sigma$$F=ma (or in this case, F with a t subscript for tension). I suppose your equation Tension=weight +/-mass*acceleration is correct, but again, there is no formal equation for tension. The most important thing above all else, and this can never be stressed enough, is to draw a freebody diagram to see how each force is acting on each body.

Now suppose you had a system where a rope is pulling up a block of mass m with force F_t, and acceleration (a). Heres how i would write out my work if this were a test:
1)$$\Sigma$$F=ma
2)Then specify each force: F_t-F_g=ma
3)move around: F_t=ma+F_g (or you can make in mg at this point)
4)Simplify:F_t=m(a+g)

Now of course, this problem gets more annoying if it involves an atwood machine, or a machine that has two masses connected by a rope over a pulley. the problem becomes an even bigger pain when the pulley is given a moment of inertia, but you can save that for later

 

[ideasrule]

In almost all cases where you're asked to find the tension, you have to use Newton's second law. In the case of a mass hanging on a string, that would be mg-T=ma, a=0, so T=mg.

Other than that, there can be no formula for tension any more than there can be a formula for speed. The tension on a rope is simply the force exerted on it, and that depends on what's exerting the force.

 

[ideasrule]

The tension in a string, rope, or cable is a force that acts to pull the object it's attached to. The formula for calculating tension depends on the specific situation. Here are the basic tension formulas for some common cases:

1. Tension in a Vertical String or Cable:When you have an object hanging from a vertical string or cable, you can calculate the tension using the following formula:
   T = m * g
   Where:
   • T is the tension in the string (in newtons, N).
   • m is the mass of the object (in kilograms, kg).
   • g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth).
2. Tension in an Inclined String or Cable:If the string or cable is at an angle (θ) to the vertical, you can use the following formula:
   T = m * g / cos(θ)
   Here, θ is the angle between the string and the vertical direction.
3. Tension in a Horizontal String or Cable:If the string or cable is horizontal, and there is no vertical movement, the tension is equal to the force needed to overcome other forces acting on the object.
4. Tension in a Pulley System:In more complex systems involving pulleys and multiple strings, the tension can vary depending on the arrangement. You might need to consider the mechanical advantage and equilibrium conditions to calculate the tension accurately.
5. Tension in a Spring:For situations involving springs, Hooke's Law can be used to calculate the tension in the spring when it's stretched or compressed. The formula is:
   F = k * x
   Where:
   • F is the force (tension) applied to the spring (in newtons, N).
   • k is the spring constant (a measure of the stiffness of the spring, in N/m).
   • x is the displacement from the spring's equilibrium position (in meters, m).

Remember that in real-world situations, friction, air resistance, and other factors can also affect tension. These formulas provide simplified models for understanding tension in idealized situations.

 

[liuquinlin]

Oh, I understand now. I somehow overlooked gravity. The rest of the explanation makes sense too... no wonder nothing came up when I searched for the "tension formula". Thanks!

 

[Greg Bernhardt]

The Tension Formula in physics is a formula that is used to calculate the tension in a string. The formula is: T = 1/2 π λ (N/m) The formula requires three things: the tension (T), the length (λ), and the force (N). The formula is used to calculate the required force (N).