# Calculating Tension in a String with Mass & Torsion

• jonny23
In summary, the question asks about the tension in a vertical string with a mass attached to its end that is twisted by an angle. The relevant equations are T=mg and torque= torsional constant x angular displacement. The attempt at a solution involved applying the equation T=mg, but there is confusion about the role of torsion. The forces on the mass include tension and torsion, but they cannot be added together as they are different types of forces. To find the tension, one can use the equation ##\Sigma F = ma## applied to the mass in the vertical direction.

## Homework Statement

if a vertical string hangs with mass M attached to its end and is twisted by angle (theta) then
what will be the tension in the string

2. relevant equations
T= mg

torque= torsional constant x angular displacement
3. attempt to solution

i am not able to start with solution but it seems that tension that is Mg and torsion must be added

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Sorry, jonny23, but PF isn't the Magic 8-Ball. There are three parts to the HW template and you have completed only the first part. You still must provide a listing of any equations you think are relevant to finding a solution, and then show some work actually leading up to a solution, even an incorrect one.

So you've applied the equation, come up with Mg as the answer, and are wondering what torsion has to do with it, right?
Consider the mass and the forces on it. What are they?

and tension and torsion would be 90 degrees right so i need to take vector sum

jonny23 said:
and tension and torsion would be 90 degrees right so i need to take vector sum
Torsion is a torque, not a linear force, so it doesn't really make sense to add them together.
Of the forces/torques exerted by the string on the mass, I would say that, by definition, the tension is the linear component acting along the string. On that basis, what does ##\Sigma F = ma## applied to the mass in the vertical direction tell you?

(To get a complete picture of the forces on the mass, bear in mind that something is applying a torque to the mass in order to twist the string.)