Inextensible string exerts no force?

[simpleton]

Hi all,

I am thinking about a problem and am currently quite confused about it. Suppose I have 2 identical balls on the x-axis, tied together by a loose inextensible string. When I hit the ball on the right to the right, the string will eventually get taut and the ball on the left will get pulled along. My question is, will the string become loose after that, and will the two balls rebounce towards each other?

My answer is yes, but apparently I am wrong. I think of it as something like an elastic collision. When the string becomes taut, it is as if the two balls collided, and thus you can use conservation of momentum and the equation for the relative velocities. However, apparently I am wrong. My friend says that the ball will not rebounce, because the string is inextensible. If it is inextensible, it cannot store energy and thus cannot pull the balls back together.

But I am not sure about this explanation. Does this mean that if a string is inextensible, it cannot exert tension? If it can still exert tension, shouldn't the balls bounce back towards each other, because the tension will pull them back?

Also, say I tie the ball to a wall this time, and I kick the ball out really hard. The ball will rebounce back. Why is it that if I tie it to an identical ball, it will not? How do you know when it will bounce back and when it will not? Also, if the balls are not identical and are of different mass, what will happen?

Sorry if I am spamming a lot of questions. I just got quite confused here :S

 

[rcgldr]

You'd also have to assume the balls were incompressable. Then you end up with instantaneous (infinite acceleration) collisions. Although it seems logical to assume the interactions are inelastic, I'm not sure you can rule out elastic interactions when the interactions are instantaneous, where the energy is stored and released in zero time.

 

[simpleton]

Hmm, actually I assumed the collisions are elastic XD.

So may I know your take on this question? Do you think the balls will stay apart? And if they do/do not, why so?

 

[IttyBittyBit]

I would like to insert a parantheses in this discussion, if I may.

There is no such thing as an inextensible string. They are nonphysical, like matter accelerating to faster than the speed of light. All strings, heck, all matter, can be stretched or compressed to some degree. One reason is because as Jeff Reid pointed out, you'd end up with collisions with infinite acceleration.

 

[simpleton]

If there is no such thing as an inextensible string, are you saying that the balls will bounce back towards each other?

Actually, I was working on a problem. I have two identical balls, one directly above the other. They are distance a apart. They are tied together by an inextensible string of length 2a (So the string is loose at first). Let's call the top ball A and the bottom ball B. A is projected horizontally at speed v while B is released from rest. You are required to find out the minimum time it takes for A and B to be at the same horizontal level.

My friend told me that you calculate the time it takes for the string to become taut. When it becomes taut, it will remain taut. After that, you calculate the angular momentum and then use that to find the answer.

However, I am not convinced that the string will remain taut, so I posted here. I would also like to know whether the string will still remain taut if the balls have different masses.

 

[IttyBittyBit]

If there is no such thing as an inextensible string, are you saying that the balls will bounce back towards each other?

I'm saying that you can model an 'inextensible' string as a regular extensible string with a very high spring constant.

 

[rcgldr]

Although you could consider an abstract string as the limit as it's load (stress) versus deformation (strain) approaches infinity, it wouldn't have any effect on it's elasticity. For an abstract string with zero deformation, it would seem elasticity would be indeterminant, other than what you define it to be.