Energy Conservation bungee jumping

[Jack08]

Kaplan topical Physics waves question 1: woman bungee jumping from a bridge. dmax = max distance from bridge.

1) Why does the woman NOT hit the bridge on her way
back up from dmax?


C . The force of gravity prevents her from reaching
the bridge.
D . Energy is not conserved due to the frictional force
of air resistance.


The back of the book says gravity is a conservative force so C is the incorrect answer. But when I try to logically think about this, even when I assume no friction force of air resistance, I still see C as being a correct answer as well. Gravity is always pulling "down" on the woman. It will aid in her descending downwards and then will fight her on going back upwards. Thus keeping her from ever returning to the original bridge height. Why is C wrong? Or is it actually correct but D was just a better answer? Thanks

---

Members don't see this ad.

 

[justwantanmdphd]

If total energy is conserved, the PE at the highest will all be transformed into KE at the bottom. Regardless of gravity, this KEmax at the bottom will be used to drive the woman to the same position where PE was highest and the woman will hit the bridge.
Think of the bungee cord as a spring. PE max on top, KE max on bottom and PEmax=KEmax. the KE max on bottom causes the spring to go back to the very top where PE is max.
The only reason why the spring will not go to the very top is because some E is lost on the way due to friction. So with frictional force..... PE max on top, KE max on bottom but PEmax > KEmax because some E is lost. This KEmax will be used to drive the woman up to a certain point under the bridge when that PE = KEmax. (check out dampening spring). hope that helps

 

[Jack08]

If total energy is conserved, the PE at the highest will all be transformed into KE at the bottom. Regardless of gravity, this KEmax at the bottom will be used to drive the woman to the same position where PE was highest and the woman will hit the bridge.
Think of the bungee cord as a spring. PE max on top, KE max on bottom and PEmax=KEmax. the KE max on bottom causes the spring to go back to the very top where PE is max.
The only reason why the spring will not go to the very top is because some E is lost on the way due to friction. So with frictional force..... PE max on top, KE max on bottom but PEmax > KEmax because some E is lost. This KEmax will be used to drive the woman up to a certain point under the bridge when that PE = KEmax. (check out dampening spring). hope that helps

Thanks. That is a good explanation for the correct answer D. I'm trying to understand why C would be wrong in real life. If someone were to bungee jump in a frictionless environment where gravity was still around however, they would return 100% to the top? I just can't overcome that thought. Gravity is trying to pull them to the earth, even with no friction of air. So gravity will pull hard on the bungee jumper accelerating her towards earth. Once shes at the bottom and the bungee cord begins to pull upwards on her, gravity is trying to still pull her downwards. Makes no sense to me how she'd ever reach back to the top 100% . What am I missing?

 

[el_duderino]

C is wrong because if none of the energy were lost due to friction from the air and within the rope, she WOULD hit the bridge on the way back up.

Think about it in terms of energy. She has some potential energy x standing on top of the bridge. She jumps off, and as she falls she loses potential energy as it becomes kinetic energy. Then she bounces up, and she is motionless at the very top. Zero kinetic energy. If she hadn't gained back all her original potential energy, where is the rest of it?

 

[justwantanmdphd]

Thanks. That is a good explanation for the correct answer D. I'm trying to understand why C would be wrong in real life. If someone were to bungee jump in a frictionless environment where gravity was still around however, they would return 100% to the top? I just can't overcome that thought. Gravity is trying to pull them to the earth, even with no friction of air. So gravity will pull hard on the bungee jumper accelerating her towards earth. Once shes at the bottom and the bungee cord begins to pull upwards on her, gravity is trying to still pull her downwards. Makes no sense to me how she'd ever reach back to the top 100% . What am I missing?

So the PE=mgh means that you are doing work against gravity. So you are already taking into account the problem of g pulling it down. The Gravitational potential energy is the work needed to apply against gravity. you have already taken into account the pulling down of gravity once you apply GPE (or in short PE) to an object. in another words, think of the all the energy you put into raising something to the top against gravity. once you drop it and once at the bottom all that PE you have put become available to the object. the object can then use it to reach to the top in a frictionless environment. Once at the bottom, some form of E must be present since all the PE is no longer there. This E at the bottom is in the form of KE.

 

[Jack08]

So the PE=mgh means that you are doing work against gravity. So you are already taking into account the problem of g pulling it down. The Gravitational potential energy is the work needed to apply against gravity. you have already taken into account the pulling down of gravity once you apply GPE (or in short PE) to an object. in another words, think of the all the energy you put into raising something to the top against gravity. once you drop it and once at the bottom all that PE you have put become available to the object. the object can then use it to reach to the top in a frictionless environment. Once at the bottom, some form of E must be present since all the PE is no longer there. This E at the bottom is in the form of KE.

Thanks so much. That helped me understand or at least get the idea. Crazy to think that if there is no friction/air resistance, only gravity, and I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity. Thanks for the help though, truly appreciate it!

 

[justwantanmdphd]

Thanks so much. That helped me understand or at least get the idea. Crazy to think that if there is no friction/air resistance, only gravity, and I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity. Thanks for the help though, truly appreciate it!

No problem. Yep. You would be stuck there ........ or you would die of slamming on the bridge 😵

 

[DrknoSDN]

Thanks so much. That helped me understand or at least get the idea. Crazy to think that if there is no friction/air resistance, only gravity, and I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity. Thanks for the help though, truly appreciate it!

Ignoring the original question because that seems to be resolved I still have to correct this.

You would need a bungee cord that has zero length. By that I mean it would need to start building potential energy the moment you were lower than the height of the bridge.
The only way for that to happen would be if it was made of a magical material that compressed to zero length on it's own but had stretching properties that followed a hook's law spring constant relationship.

Otherwise the potential energy required to launch you back up to bridge level would not begin building until you passed the natural rest position and you wouldn't attain enough stored potential energy at the bottom to launch you back up to bridge level. In that aspect, even if you were doing a bungee jump in a vacuum (no air resistance), you still would not bounce back up to bridge level without a bungee made of flubber.

Even without air resistance it can't happen because like you said, it would allow perpetual motion machines to be built anywhere that doesn't have an atmosphere. (the moon etc)

 

[el_duderino]

Ignoring the original question because that seems to be resolved I still have to correct this.

You would need a bungee cord that has zero length. By that I mean it would need to start building potential energy the moment you were lower than the height of the bridge.
The only way for that to happen would be if it was made of a magical material that compressed to zero length on it's own but had stretching properties that followed a hook's law spring constant relationship.

Otherwise the potential energy required to launch you back up to bridge level would not begin building until you passed the natural rest position and you wouldn't attain enough stored potential energy at the bottom to launch you back up to bridge level. In that aspect, even if you were doing a bungee jump in a vacuum (no air resistance), you still would not bounce back up to bridge level without a bungee made of flubber.

Even without air resistance it can't happen because like you said, it would allow perpetual motion machines to be built anywhere that doesn't have an atmosphere. (the moon etc)

I thought about that as I was writing my initial post, but I don't think it's correct.

After all, when you boil it down, you're either losing energy into the system or not. With a frictionless environment and ignoring internal friction in the cord and whatnot, you need to conserve energy. You start with some x of PE and when you bounce back up and are motionless at the top of the bounce, there's zero kinetic energy. There's nowhere else for that PE to have gone, so you must have gotten all the energy back as PE.

And when you think about it logically, you will have some x m/s velocity at the moment the bungee starts to elongate. When you bounce back up and pass the point when the bungee returns to its original length, whatever that was, you will be at -x m/s.

So no matter the length of the bungee, you will end up hitting the bridge (or returning to your original height) if you're not losing any energy due to wind resistance/friction.

 

[DrknoSDN]

I thought about that as I was writing my initial post, but I don't think it's correct.

After all, when you boil it down, you're either losing energy into the system or not. With a frictionless environment and ignoring internal friction in the cord and whatnot, you need to conserve energy. You start with some x of PE and when you bounce back up and are motionless at the top of the bounce, there's zero kinetic energy. There's nowhere else for that PE to have gone, so you must have gotten all the energy back as PE.

And when you think about it logically, you will have some x m/s velocity at the moment the bungee starts to elongate. When you bounce back up and pass the point when the bungee returns to its original length, whatever that was, you will be at -x m/s.

So no matter the length of the bungee, you will end up hitting the bridge (or returning to your original height) if you're not losing any energy due to wind resistance/friction.

The bungee material matters significantly (entirely?). Hypothetically say you used a rope as your bungee and had a slack of 20 meters. You still expect to bounce back to bridge height? (ignore air resistance)

 

[el_duderino]

The bungee material matters significantly (entirely?). Hypothetically say you used a rope as your bungee and had a slack of 20 meters. You still expect to bounce back to bridge height? (ignore air resistance)

Having fallen while climbing using dynamic rope, believe me you can bounce quite a bit falling a long way on a rope!

But in the "real world" if you used static rope you would not bounce, because the human body simply isn't that elastic. Most of the energy will be transferred to things like bones snapping.

But in the idealized world of an MCAT physics problem where you're not losing energy to internal friction in the rope, slop in the ankle fittings, broken bones and torn ligaments, then yes you would bounce back to bridge height.

 

[DrknoSDN]

Having fallen while climbing using dynamic rope, believe me you can bounce quite a bit falling a long way on a rope!

But in the "real world" if you used static rope you would not bounce, because the human body simply isn't that elastic. Most of the energy will be transferred to things like bones snapping.

But in the idealized world of an MCAT physics problem where you're not losing energy to internal friction in the rope, slop in the ankle fittings, broken bones and torn ligaments, then yes you would bounce back to bridge height.

Only if you began building stored potential energy the moment you were lower than the bridge, and in a rope scenario it would mean the rope was zero meters long. You "bounce back" because you never really left.

The force would exceed the elastic limit of the material causing deformation of the bungee.

 

[el_duderino]

Where does the rest of the initial potential energy go, then? I start with mgh. If I don't hit the bridge at the top of the arc on the way back up, I am motionless with a potential energy of mg(h-x) < mgh.

Where is the other mgx?

 

[DrknoSDN]

But in the idealized world of an MCAT physics problem where you're not losing energy to internal friction in the rope, slop in the ankle fittings, broken bones and torn ligaments, then yes you would bounce back to bridge height.

/Agree, yes the only thing I was trying to correct was the comment that in zero atmosphere it would "actually" work like that. Wasn't trying to convince anyone that the question was flawed.
Only correcting this statement --> "I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity."

I suppose you just cant underestimate the loss of energy from the spring material. If you took an idealized bouncy ball and let it go from height H, on an mcat, it would bounce back to height H. That would be a perfectly elastic collision with no air resistance.
In the real world (which is what eJACKulEIGHT was referring to), even without air resistance a material with extremely elastic properties might only reach 80% of it's original height due to transfer of energy into internal energy of the ball.

I probably shouldn't have bothered to make the correction based on his name alone.. 😵

 

[el_duderino]

/Agree, yes the only thing I was trying to correct was the comment that in zero atmosphere it would "actually" work like that. Wasn't trying to convince anyone that the question was flawed.
Only correcting this statement --> "I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity."

I suppose you just cant underestimate the loss of energy from the spring material. If you took an idealized bouncy ball and let it go from height H, on an mcat, it would bounce back to height H. That would be a perfectly elastic collision with no air resistance.
In the real world (which is what eJACKulEIGHT was referring to), even without air resistance a material with extremely elastic properties might only reach 80% of it's original height due to transfer of energy into internal energy of the ball.

I probably shouldn't have bothered to make the correction based on his name alone.. 😵

"Crazy to think that if there is no friction/air resistance, only gravity, and I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity."

This is an accurate statement. In the idealized MCAT world of no friction or air resistance, he would be a self perpetual machine for eternity! Until you introduce something that takes energy from the system, like a generator or internal friction, then you'll just bounce forever. It is crazy.

 

[DrknoSDN]

"Crazy to think that if there is no friction/air resistance, only gravity, and I was lifted 100m in the air, hooked to a bungee cord, then released, that I'd be a self perpetual machine for eternity."

This is an accurate statement. In the idealized MCAT world of no friction or air resistance, he would be a self perpetual machine for eternity! Until you introduce something that takes energy from the system, like a generator or internal friction, then you'll just bounce forever. It is crazy.

Yes, I suppose the point I was trying to make was that there are forms of energy transfer outside of just air resistance. And it would require some non-existent material to be able to ignore all outside forms of energy transfer. Zero air resistance alone isn't enough.