# M3 Elastic strings on inclined planes

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I'm getting slightly confused with energy conservation questions that involve elastic strings on inclined planes.

The question is from the old Heinemann M3 book (Ex2C Q8):

My Working for the first part

After this I get x=-0.665m, which is correct, except I can't explain why it is negative [should be positive], when my positive direction was down the plane?

To calculate the change in GPE & EPE I'm doing (Final EPE/GPE - Start EPE/GPE) - should it be the other way round?

Also, I have a similar problem with the second part:

The question is from the old Heinemann M3 book (Ex2C Q8):

Spoiler:

A particle P of mass 2 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus 20N. One end of the string is fixed to a point A on a rough plane inclined at 45 degrees to the horizontal. P is held at rest on the plane below A with AP along a line of greatest slope of the plane and AP=0.6 m. The coefficient of friction between P and the plane is 0.2. P is released. Calculate the distance P moves down the plane before coming to instantaneous rest. Calculate also the speed when AP=0.8m.

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A particle P of mass 2 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus 20N. One end of the string is fixed to a point A on a rough plane inclined at 45 degrees to the horizontal. P is held at rest on the plane below A with AP along a line of greatest slope of the plane and AP=0.6 m. The coefficient of friction between P and the plane is 0.2. P is released. Calculate the distance P moves down the plane before coming to instantaneous rest. Calculate also the speed when AP=0.8m.

My Working for the first part

Spoiler:

Show

After this I get x=-0.665m, which is correct, except I can't explain why it is negative [should be positive], when my positive direction was down the plane?

To calculate the change in GPE & EPE I'm doing (Final EPE/GPE - Start EPE/GPE) - should it be the other way round?

Also, I have a similar problem with the second part:

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#3

(Original post by

Anyone?

**ThatPerson**)Anyone?

(very busy)

look at questions 6, 10 and 11 in this link while you are waiting for help

http://madasmaths.com/archive/maths_...gs_springs.pdf

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#4

(Original post by

To calculate the change in GPE & EPE I'm doing (Final EPE/GPE - Start EPE/GPE) - should it be the other way round?

**ThatPerson**)To calculate the change in GPE & EPE I'm doing (Final EPE/GPE - Start EPE/GPE) - should it be the other way round?

Starting energy - work done by system = final energy.

Which rearranges to "Work done = starting energy - final energy".

I note that you have the GPE as positive, although P is below your zero level.

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(Original post by

I think of it as:

Starting energy - work done by system = final energy.

Which rearranges to "Work done = starting energy - final energy".

I note that you have the GPE as positive, although P is below your zero level.

**ghostwalker**)I think of it as:

Starting energy - work done by system = final energy.

Which rearranges to "Work done = starting energy - final energy".

I note that you have the GPE as positive, although P is below your zero level.

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#6

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I was going to put GPE as -ve but then I thought that energy is a scalar so it doesn't matter?

**ThatPerson**)I was going to put GPE as -ve but then I thought that energy is a scalar so it doesn't matter?

In the case of GPE, it arises from work done against a force, in this case gravity. As the amount of work done increases - i.e. you raise the object higher - so its energy increases.

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#7

**ThatPerson**)

I was going to put GPE as -ve but then I thought that energy is a scalar so it doesn't matter?

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(Original post by

It matters.

In the case of GPE, it arises from work done against a force, in this case gravity. As the amount of work done increases - i.e. you raise the object higher - so its energy increases.

**ghostwalker**)It matters.

In the case of GPE, it arises from work done against a force, in this case gravity. As the amount of work done increases - i.e. you raise the object higher - so its energy increases.

Can you see any error in the second part? The way I've interpreted the question, is that the system is still released at AP=0.6, but I need to work out the speed after P has moved to AP=0.8?

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#9

(Original post by

Ah - That gives me the +ve answer. Thanks.

Can you see any error in the second part? The way I've interpreted the question, is that the system is still released at AP=0.6, but I need to work out the speed after P has moved to AP=0.8?

**ThatPerson**)Ah - That gives me the +ve answer. Thanks.

Can you see any error in the second part? The way I've interpreted the question, is that the system is still released at AP=0.6, but I need to work out the speed after P has moved to AP=0.8?

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#10

(Original post by

Also, I have a similar problem with the second part:

[spoiler]

Work done,W, against friction in moving from AP=0.6 to 0.8:

After rearranging I get v=1.63ms^-1 when the correct answer is 1.25.

**ThatPerson**)Also, I have a similar problem with the second part:

[spoiler]

Work done,W, against friction in moving from AP=0.6 to 0.8:

After rearranging I get v=1.63ms^-1 when the correct answer is 1.25.

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(Original post by

For the GPE, the distance moved down the plane is 0.2, not 0.8

**ghostwalker**)For the GPE, the distance moved down the plane is 0.2, not 0.8

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#12

(Original post by

But A is 0 GPE, and P is below A, so when P has moved down the plane by 0.2, isn't it then 0.8m from A?

**ThatPerson**)But A is 0 GPE, and P is below A, so when P has moved down the plane by 0.2, isn't it then 0.8m from A?

Again, this would be negative relative to A.

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(Original post by

True; my mistake. I was assuming that you had the change in GPE there, since you'd only posted one, rather than the initial and final GPEs.

Again, this would be negative relative to A.

**ghostwalker**)True; my mistake. I was assuming that you had the change in GPE there, since you'd only posted one, rather than the initial and final GPEs.

Again, this would be negative relative to A.

I'm equating energy at P with energy at AP=0.8 + Work Done

.

Edit: Never mind, I was being stupid - forgot the g. Thanks for your help.

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#14

(Original post by

Edit: Never mind, I was being stupid - forgot the g. Thanks for your help.

**ThatPerson**)Edit: Never mind, I was being stupid - forgot the g. Thanks for your help.

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