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Old Mar 12th 2018, 12:28 AM   #1
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Don't understand this question about strain energy in a bungee jumping rope

Question is:
An 80kg student jumps from a bridge on a bungee rope. If the 100m rope stretches by 10%, calculate the spring constant of the rope.

I looked at the solutions and I don't understand why gravitational potential energy, mgh, = 80 x 9.8 x 110 = strain energy
Why is height 110m? Isn't height supposed to be height above ground? Also why does gravitational energy = strain energy?
Thanks!
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Old Mar 12th 2018, 05:46 AM   #2
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The "height" in your equation should more correctly be called "change in height".

A lot of examples using this equation operate from a "height" to the ground
thus "height" becomes synonymous with "change in height".

However, if you think about the ground level, it also has "height", above sea level (for example).
Thus the "change in height" is always a more correct (if a bit wordy and long winded) way of referring to "h" in the equation.
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Old Mar 12th 2018, 07:16 AM   #3
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Originally Posted by Jasnah View Post
Question is:
An 80kg student jumps from a bridge on a bungee rope. If the 100m rope stretches by 10%, calculate the spring constant of the rope.

I looked at the solutions and I don't understand why gravitational potential energy, mgh, = 80 x 9.8 x 110 = strain energy
Why is height 110m? Isn't height supposed to be height above ground? Also why does gravitational energy = strain energy?
Thanks!
well, one end of the bungee is tied at the point from which the man jumps ,the other end tied to the man , ....

He jumps , falls 100m at this point the bungee starts to pull him up but he continues for 10 more meters ... this is his maximum distance of fall ...110m.
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Old Mar 12th 2018, 04:30 PM   #4
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Thanks! I see now!
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Old Mar 12th 2018, 04:41 PM   #5
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Originally Posted by oz93666 View Post
well, one end of the bungee is tied at the point from which the man jumps ,the other end tied to the man , ....

He jumps , falls 100m at this point the bungee starts to pull him up but he continues for 10 more meters ... this is his maximum distance of fall ...110m.
It is possibly worth adding a bit more to this short but excellent summary.

During the first 100m of the fall all the potential energy of the man is converted to kinetic energy and he has a maximum velocity at this point.
There is no strain energy developed in the rope up to this point.

At this point the man has the kinetic energy due to the fall plus the potential energy of the final 10 metres of the drop.

In the last 10 metres the rope strains (stretches) and its increasing tension opposes the motion of the man bringing him to a halt after a total of 110 metres.

Since the man is again at rest, he has lost all the kinetic energy which was equal to the potential energy of the first 100 metres fall plus a further potential energy of 10 metres fall, making the figure shown.

This is the work done in stretching the rope and is called the strain energy of the rope since it now resides in the rope.
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Old Mar 14th 2018, 03:08 AM   #6
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Originally Posted by studiot View Post
It is possibly worth adding a bit more to this short but excellent summary.

During the first 100m of the fall all the potential energy of the man is converted to kinetic energy and he has a maximum velocity at this point.
There is no strain energy developed in the rope up to this point.

At this point the man has the kinetic energy due to the fall plus the potential energy of the final 10 metres of the drop.

In the last 10 metres the rope strains (stretches) and its increasing tension opposes the motion of the man bringing him to a halt after a total of 110 metres.

Since the man is again at rest, he has lost all the kinetic energy which was equal to the potential energy of the first 100 metres fall plus a further potential energy of 10 metres fall, making the figure shown.

This is the work done in stretching the rope and is called the strain energy of the rope since it now resides in the rope.
ooooooh, that makes it a lot clearer. Thanks a lot! The detail was very appreciated
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Old Mar 14th 2018, 03:27 AM   #7
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Glad you liked it.

A further matter which confuses many is the reasoning behinf the fact that

the strain energy = Half the Load x the extension (or half the stress times strain).

This appears different from the formula that work = Force times distance because of the factor of a half. But it is not really.


There are mathematical proofs, but here is some reasoning to support it.


I said the tension in the rope increases as the extension grows.
When the rope is first extended the first small bit, very little tension is required.

So the work done = a small tension x a small extension. = a small amount.

In fact the curve starts off at zero since zero extension means zero tension.

When the extension is maximum the tension is also maximum.

So the work done is the average tension times the extension.

The average tension is the average of zero and the maximum tension

Tav = 0.5(0 + Tmax) = 0.5 Tmax

So Work done = W = (0.5Tmax) x (e) where e is the extension.
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