Yatayyat
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#1
Report Thread starter 1 year ago
#1
I need help on some parts of this question.

https://imgur.com/Dqr8QLR
https://imgur.com/2WkoCoq
https://imgur.com/S4tgNoV

For part a i) I've been asked to calculate the extension of the rope.

Knowing that extension is the change in length between the unstretched length and stretched length I did the following:

31m - 19 m = 12m

However this is wrong and the mark-scheme just simply states 11m. How did they get that?

For part a ii) to work out the resultant force, my idea was that resultant force is the maximum tension from the rope minus the weight of the bungee jumper. So this is what I did:

tension can be found from 'F = kx', this gave 380*12 = 4560 N

weight force is mg, so 75 * 9.8 = 735 N

So resultant force is 4560 - 735 = 3825 N

But the answer in the markscheme says 3400 N is the resultant force

part b) was fairly straightforward, to find the extension I simply equated mg = Kx

This mean that x (extension) was mg/k, so (75 * 9.8)/380 = 1.93

so extension was 1.9 m which is right.

Part c was also okay and to find the speed when extension is 5m and has fallen a distance of 25m is:

Gravitational potential energy is mgh --> (75 * 9.8 * 25) = 18375 J

Elastic potential energy in rope is 1/2 k(x)^2 --> (0.5) * (380) * (5)^2 = 4750 J

This means that the change is these 2 energies is converted into kinetic energy, hence I get:

18375 - 4750 = 1/2 m v^2

and solving for v I got a speed of 19.06 ms^-1

For part d) I'm not exactly sure how to answer this.

All I know is that if the bungee rope is more stiff than before, more energy has to be transferred to stretch the rope to some extension compared to the rope with a smaller stiffness.

If anyone can help me with parts a i), a ii), b and d. That would be really helpful because I have no idea what I'm doing wrong.

Thanks!
Last edited by Yatayyat; 1 year ago
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Yatayyat
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username3442196
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#3
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ai) the centre of mass starts 1m above platform.
aii) I think your method is fine, but you should have used 11m as the extension. You'd get ecf.
b) you're happy with?
d) I find it hard to do as the question instructs! Intuitively I'd say, stiffer -> stretches less -> jumper's velocity brought to zero over a much shorter time -> much greater force on the person, possibly breaking things! However, to get the marks we have to use energy.
? stretches less far to store the person's KE as elastic PE ... I'll let someone else come up with this one!
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Eimmanuel
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(Original post by Yatayyat)
I need help on some parts of this question.

https://imgur.com/Dqr8QLR
https://imgur.com/2WkoCoq
https://imgur.com/S4tgNoV

For part a i) I've been asked to calculate the extension of the rope.

Knowing that extension is the change in length between the unstretched length and stretched length I did the following:

31m - 19 m = 12m

However this is wrong and the mark-scheme just simply states 11m. How did they get that?

For part a ii) to work out the resultant force, my idea was that resultant force is the maximum tension from the rope minus the weight of the bungee jumper. So this is what I did:

tension can be found from 'F = kx', this gave 380*12 = 4560 N

weight force is mg, so 75 * 9.8 = 735 N

So resultant force is 4560 - 735 = 3825 N

But the answer in the markscheme says 3400 N is the resultant force

part b) was fairly straightforward, to find the extension I simply equated mg = Kx

This mean that x (extension) was mg/k, so (75 * 9.8)/380 = 1.93

so extension was 1.9 m which is right.

Part c was also okay and to find the speed when extension is 5m and has fallen a distance of 25m is:

Gravitational potential energy is mgh --> (75 * 9.8 * 25) = 18375 J

Elastic potential energy in rope is 1/2 k(x)^2 --> (0.5) * (380) * (5)^2 = 4750 J

This means that the change is these 2 energies is converted into kinetic energy, hence I get:

18375 - 4750 = 1/2 m v^2

and solving for v I got a speed of 19.06 ms^-1

For part d) I'm not exactly sure how to answer this.

All I know is that if the bungee rope is more stiff than before, more energy has to be transferred to stretch the rope to some extension compared to the rope with a smaller stiffness.

If anyone can help me with parts a i), a ii), b and d. That would be really helpful because I have no idea what I'm doing wrong.

Thanks!

For (d), I think old_teach had already mentioned most of the points except for the following where certain exam board would be very particular:

Since both have same unextended length, the kinetic energy of the bungee jumper will be the same when the rope begins to stretch.
As the rope is stiffer, the work done by the elastic force per unit extension would be more and the bungee jumper would come to stop in a shorter distance.
Since more work was done by the elastic force per unit extension, more force would exert on the jumper to stop in a shorter distance which may result in injury or increase the risk of getting injured.
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Yatayyat
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#5
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(Original post by Eimmanuel)
For (d), I think old_teach had already mentioned most of the points except for the following where certain exam board would be very particular:

Since both have same unextended length, the kinetic energy of the bungee jumper will be the same when the rope begins to stretch.
As the rope is stiffer, the work done by the elastic force per unit extension would be more and the bungee jumper would come to stop in a shorter distance.
Since more work was done by the elastic force per unit extension, more force would exert on the jumper to stop in a shorter distance which may result in injury or increase the risk of getting injured.
Thank you that was helpful!
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