[Problem] Elastic potential energy

[AmirT]

Hi, I'm a second year Design Engineering student. This year we're having some basic physics class. We're doing projects on potential energy at this moment. I'm having a problem with the following;

The assignment:
The teacher assigned us that only 6 Joules of potential energy may be used to make a contraption move as far as possible, this can be anything, a car, a paper plane, etc..

1. Homework Statement

I connected 5 rubber bands in series with on one side a weight (15 grams), on the other side some duct tape.
The duct tape sticks to the ground while the weight is being tentioned. I let loose of the weight and the whole contraption (including rubber bands and duct tape) shoots away.

I need to get to know the potential energy of a shot.

Homework Equations

[/B]
I calculated the spring constant by hanging a bottle of with water (545 grams) to the rubber bands in series, the rubber bands stretched out 25cm (50cm - 25cm)
F= kx
k= F/x
k= 5,5N/0,25
k= 22Nm

The Attempt at a Solution

[/B]
Then I calculated the PE. This is my ACTUAL PROBLEM, I'm very sceptic about this one because it's seems too little.. (I'm not the best with physics or maths)

PE= 1/2*k*x²
PE= 0,5*22Nm*(0.25m)²
PE= 0,6875 J

A picture of the setup

Is this a realistic/plausible result?

Am I doing this right?

The rubber bands I'm using are the typical office rubber bands.
It would be nice if someone could help me out with this one.Thank you.

 

[haruspex]

Where you wrote Nm for the spring constant units, you mean N/m. Other than that, your working looks correct. The result is reasonable. In descending 0.25m the bottle lost a bit over 1J of gravitational PE. If allowed to fall freely it would have had some KE at the equilibrium point, so the PE in the elastic at that point must be less than 1J (in fact, half the lost gravitational PE).

 

[AmirT]

Where you wrote Nm for the spring constant units, you mean N/m. Other than that, your working looks correct. The result is reasonable. In descending 0.25m the bottle lost a bit over 1J of gravitational PE. If allowed to fall freely it would have had some KE at the equilibrium point, so the PE in the elastic at that point must be less than 1J (in fact, half the lost gravitational PE).

Hi,

Thanks for your answer, I really appreciate it!Another thing popped up in my head now.
Does the fact that the rubber bands are in series makes any difference?

I'm also wondering if there's any way to calculate the the best ratio of maximum travel distance and amount of rubber bands?
Adding more bands gives the contraption more power, but also adds lots of friction.

Perhaps I should stay with 5 ~ 7 bands and stretch it as far as I can?

Thank you

 

[haruspex]

Does the fact that the rubber bands are in series makes any difference?

It affects the spring constant. You should be able to work out in what way.

Adding more bands gives the contraption more power, but also adds lots of friction

It doesn't simply store more energy. It also affects the rate at which the energy is transferred to the projectile and the distance over which it happens.
Do you think the same total energy is transferred from a given amount of energy stored by one band or N bands?
Explain a bit more your thoughts on how it affects frictional losses.

 

[AmirT]

It affects the spring constant. You should be able to work out in what way.

It doesn't simply store more energy. It also affects the rate at which the energy is transferred to the projectile and the distance over which it happens.
Do you think the same total energy is transferred from a given amount of energy stored by one band or N bands?
Explain a bit more your thoughts on how it affects frictional losses.

Hi,

You have very good points there!
I didn't thought about that..

Isn't the serie of rubber bands acts as one big band?
Did I made a mistake when calculating the spring constant with a bottle of water?

About the friction;

I had this feeling that if there's more loose material, there's more friction.

 

[haruspex]

Isn't the serie of rubber bands acts as one big band?

Yes, but the spring constant changes. If I put two springs of constant k in series and apply a tension T, what will the total extension be? What does that make the spring constant for the combination?

Did I made a mistake when calculating the spring constant with a bottle of water?

No, it was about right, though it could be a little more accurate. I guess you took g = 10ms^-2, not 9.8. Keep at least 3 significant figures through the working.

About the friction;

I had this feeling that if there's more loose material, there's more friction.

That's possible - not sure. How will you prevent the object from snagging on the bands ahead of it?
Some things to think about:
When the object loses contact with the elastic bands, you want as much of the energy as possible in the KE of the object. Where else will there be energy?
More bands means a slower but longer acceleration. How will that affect losses due to drag?

Do you have the opportunity to experiment?

 

[AmirT]

Yes, but the spring constant changes. If I put two springs of constant k in series and apply a tension T, what will the total extension be? What does that make the spring constant for the combination?

No, it was about right, though it could be a little more accurate. I guess you took g = 10ms^-2, not 9.8. Keep at least 3 significant figures through the working.

That's possible - not sure. How will you prevent the object from snagging on the bands ahead of it?
Some things to think about:
When the object loses contact with the elastic bands, you want as much of the energy as possible in the KE of the object. Where else will there be energy?
More bands means a slower but longer acceleration. How will that affect losses due to drag?

Do you have the opportunity to experiment?

I took g=10ms because the docent told us that we "have" to use it. At high school I've learned it's 9,81 but for some reason we may just use 10.

Today I've had the chance to experiment at school before the lesson began (my hall at home is not long enough). This assignment was due today (we had to work it out in the weekend).

I was able to shoot this contraption about 25m (?) which surprised me, as well as the others. The other students made cars with mousetrap or weights. 90% didn't even get the half of my distance for some reason (a lot more weight + friction)

I've also seen that at the beginning of the movement, the weight flew in the air for a bit and made the bands fly along. So there was not much friction, although it landed almost halfway and deaccelerated from then.

All in all the teacher said it was okay!

I've did look up some information regarding the rubber bands in series. There was this article saying that you have to calculate this in a simillar manner as you would do with resistors in a electrical circuit.

All in all, thank you very much for your replies! I really do appreciate it!