# In vertical circular motion of a mass attached to a rope, where does the elastic potential energy stored in the tension goes?

When a bob is attached to a rope where the rope has negligible mass, the bob undergoing circular motion will have its KE1+PE1 at any point of the circular motion equal to KE2+PE2 at another point of the circular motion; however what happened to the elastic potential energy stored in the tension? When the bob is at the bottom of the circular motion, tension will be maximum; whereas when the bob is at the top of the circular, tension will be minimum (or even zero).

From my understanding, if there is a tension in a rope, then there should be elastic potential energy stored so then where did the elastic potential energy stored in the rope go when the bob is at the top of the circular motion?

• If you are working with an elastic rope, the trajectory of the mass won't be a perfect circle. Commented Oct 29, 2018 at 17:37

I think you are just missing a key point.

From my understanding, if there is a tension in a rope, then there should be elastic potential energy stored so then where did the elastic potential energy stored in the rope go when the bob is at the top of the circular motion?

Elastic energy occurs when objects are compressed or stretched.The presence of tension doesn't necessarily imply that there will be elastic potential energy.In general cases of vertical circular motion we assume that string is inextensible and therefore we don't have to consider any elastic energy.

Note:

It is a well-known fact that no body is perfectly rigid. So,theoretically there might be a little extension in the string but practically it doesn't matter in general cases.

Reference:

https://en.wikipedia.org/wiki/Elastic_energy

• The presence of tension does imply the existence of elastic energy. Commented Oct 29, 2018 at 17:58
• @user190081 Could you elaborate your point.Because,like I have mentioned string is inextensible in general cases,and this implies that there isn't any deformation and hence no elastic potential energy. Commented Oct 29, 2018 at 17:59
• Well, unless you have a perfectly rigid material, any load applied to it will cause some deformation based on the material's modulus of elasticity, the stored energy in the material (per unit volume) is given then by the integral of the strain-stress curve. Commented Oct 29, 2018 at 18:13
• @user190081 Agreed. But I have already mentioned that string is assumed to be inextensible right!.lets say that we have a little elongation,but it's effect will be negligible. Theoretically you are right, but practically it doesn't matter in general cases. Commented Oct 30, 2018 at 1:43