How to determine the force that stretches a rubber band

[Sanev]

Homework Statement

Let's put a ball in an empty space with a mass of 280 kg and a radius of 6 meters. Imagine that there is a rubber band around this ball. The initial radial extent of the rubber band is 2 meters. How can I determine the force that stretches the rubber band?
And can i say that the energy (M.c2) of the ball is the potential energy in rubber band

Homework Equations

[/B]

The Attempt at a Solution

 

[Chestermiller]

What are your thoughts on this?

 

[Sanev]

I don't see acceleration so how can i determine the force? Clearly there is a force because the rubber band is stretch. So may by i can find the force if i now what is the potential energy stored in the rubber band. In relaxed state rubber band has no potential energy. So when i put the ball and she stretch the rubber band the energy stored will be the energy of the ball ( i assume E=mc2).

 

[Chestermiller]

You don't need to have acceleration to have a force. If you stretch a spring, the spring exerts a force even if neither you nor the spring it is accelerating. And, the energy of the ball is not equal to the energy of the rubber band). In order to get the tension in the rubber band, you need to first measure (in a laboratory) the relationship between the tension developed in the rubber band and the amount that the rubber band stretches (as determined by the ratio of its stretched length to its un-stretched length).

 

[Sanev]

So from the Hooke's law k.x(square)/2=Work done. Were the displacement is "x" and "k" is the spring constant. Can we say that the "x" is diameter of the ball and the E is Work done? I Guess we can not?

 

[Chestermiller]

So from the Hooke's law k.x(square)/2=Work done. Were the displacement is "x" and "k" is the spring constant. Can we say that the "x" is diameter of the ball and the E is Work done? I Guess we can not?

Hooke's law does not apply to rubber. Rubber is a non-Hookean material, and the stress is not proportional to the strain.

 

[Sanev]

I'm little bit confused because i use to look for the units. For example if i take E of the ball and divided by the R(squared) i will get in "SI derived unit" surface tension. So this is has to be the surface tension of the ball?

 

[Chestermiller]

I'm little bit confused because i use to look for the units. For example if i take E of the ball and divided by the R(squared) i will get in "SI derived unit" surface tension. So this is has to be the surface tension of the ball?

This makes absolutely no sense to me. Maybe someone else can help you.

 

[Sanev]

E/R(squared) =kg/s(squared) which is surface tension.

 

[Isaac0427]

And can i say that the energy (M.c2) of the ball is the potential energy in rubber band

I’m not sure why you are employing relativity right here. Or at all in this problem.

The issue here is that you do not have enough information to answer this problem. Every rubber band is different. Are you sure you are giving the full problem here?

 

[rcgldr]

There isn't enough information. I measured tension versus stretch for latex tubing used to launch radio control gliders, it matched the data provided by one of the providers (no longer in business).

   strain versus tension: (strain == pull distance)

     0% =   0 lb / in^2
    50% =  70 lb / in^2
   100% =  95 lb / in^2
   150% = 115 lb / in^2
   200% = 135 lb / in^2
   250% = 160 lb / in^2
   300% = 175 lb / in^2
   350% = 195 lb / in^2
   400% = 205 lb / in^2  (not recommended).

I smoothed the data with a cubic equation:

which is similar to the experimental data portion of the graph shown in a wiki article:

https://en.wikipedia.org/wiki/Rubbe...ar_Kink_Paradigm_for_Rubber_Elasticity.5B7.5D

 

[Sanev]

The only thing preventing the rubber band to crunch is the mass of the ball. So we can say that the energy of the ball is also involve. The whole idea is to construct a formula (or at least to now what is the actual formula) for this case scenarium which is using the energy of the ball as a factor for stretching it the rubber band. Also let's not forget that this thought experiment is developed in empty space without stars, acceleration just empty space

 

[haruspex]

The only thing preventing the rubber band to crunch is the mass of the ball.

The mass is irrelevant. The ball merely has to be sufficiently strong to resist (and could be a lot stronger).

 

[Sanev]

So what is the actual formula for this problem?

 

[haruspex]

So what is the actual formula for this problem?

First, as others have noted, rubber is a bit complicated. Let's change it some unspecified elastic material that obey's Hooke's Law.
What determines the tension in a stretched string or spring, according to Professor Hooke?

 

[Sanev]

The force applied?

 

[haruspex]

The force applied?

I meant, what does Hooke's law state?

 

[Sanev]

Hooke's law states that the force (F) needed to extend or compress a spring by some distance X scales linearly with respect to that distance

 

[haruspex]

Hooke's law states that the force (F) needed to extend or compress a spring by some distance X scales linearly with respect to that distance

So can you use that to answer your original question?

 

[Sanev]

I don't know because i can't define the force, i don't have acceleration. I know the displacement i know the initial state of the elastic think i do not know the K constant so how i can define the force in this case? I have just mass, radius of that mass and somthing elastic aroun it. Also the displacement is equal to the diameter of that mass.

 

[haruspex]

i don't have acceleration

As has been pointed out to you, there is no acceleration.
Tension is not quite the same as force. It is more like a pair of equal and opposite forces.

I know the displacement i know the initial state of the elastic

Good.

i do not know the K constant

Then you have no way to answer the question.

 

[Sanev]

But if i can define what is the force i will find the K constant.

 

[haruspex]

But if i can define what is the force i will find the K constant.

I thought you were trying to find the force.

 

[Sanev]

No I'm trying to find K but i don't know how to define the force.

 

[haruspex]

No I'm trying to find K but i don't know how to define the force.

To find the k you stretch the string, measure the extension and measure the force. That's it.

 

[Sanev]

The situation is this i see ball and string around that ball. I don't know previous state. For example how is stretched the string or what stretched it. I see only this state and i have to define the force.
I believe that it's has to have some correlation between the force needed to stretch and the mass of the object or the mass density or pressure which the object exert and so for. If it doesn't in this case scenario i can't do nothing. Which is look not right for me. Because you have the mass of the object this object has pressure has density that have direction. If i exert pressure on you you will exert the same on me.

 

[haruspex]

has pressure has density

Yes, it has those things, but there's little or no connection between them.
The force the ball exerts on the string will be whatever it needs to be to match the force the string exerts on it. If the ball is fairly rigid this will have very little relationship to the pressure in the ball. If it is very flexible the ball will be deformed into a shape like an hour glass. Either way, I see no prospect of determining the force from these data. The mass is obviously irrelevant.