Help needed in this problem involving a spring and energy balances

[hello478]

Homework Statement

need help in part c of the questions
see question attached below
i dont understand how gpe can be equal to strain energy
in fig 5.2
it is in equillibrium so it wont have gpe or strain energy
but as it moves down it gains gpe and strain energy
then the total energy of system should be zero
thinking about it another way
will the gpe it gain be negative??
so this way the total=gpe+strain energy
and because initial = 0 the final would also be zero
so 0=1/2kx^2 - 0.024
and then 0.025=1/2kx^2
am i right??please correct me
what if in this question kinetic energy is also involved???

Relevant Equations

energy equations... mgh, 1/2kx^2

i do know how to do the working but i dont understand the concept stated above...

 

[PeroK]

According to the homework help guidelines, you need to show some effort. It's not good enough just to say you don't know.

 

[haruspex]

it is in equillibrium so it wont have gpe or strain energy
but as it moves down it gains gpe and strain energy

GPE is relative to some defined zero. The text only refers to changes in GPE, so it does not matter where you set the zero.
As it moves down it loses GPE, so if you define it as zero at the relaxed position then it is going negative, which is fine.
But you are wrong to call 5.2 the equilibrium position; it is the relaxed position. 5.1 is equilibrium.

The question asks for the "change" in GPE. I would take that as a signed value, so negative.
Please explain how you arrived at 0.024 (or is it 0.025?) and state the units.

 

[hello478]

According to the homework help guidelines, you need to show some effort. It's not good enough just to say you don't know.

please read the whole question, im sorry if you didnt get it, i did try to attempt and solve it above... but i solved it in the homework statement part, sorry about that, please read it from there

 

[hello478]

GPE is relative to some defined zero. The text only refers to changes in GPE, so it does not matter where you set the zero.
As it moves down it loses GPE, so if you define it as zero at the relaxed position then it is going negative, which is fine.
But you are wrong to call 5.2 the equilibrium position; it is the relaxed position. 5.1 is equilibrium.

The question asks for the "change" in GPE. I would take that as a signed value, so negative.
Please explain how you arrived at 0.024 (or is it 0.025?) and state the units.

mgh = 0.094*9.81*(2.6/1000) = 2.39 * 10^-3 J
but for part c... we are not looking at figure 5.1 so when it is stopped by a hand/ force so cant we say its in equilibrium?

 

[Lnewqban]

in fig 5.2
it is in equillibrium so it wont have gpe or strain energy
but as it moves down it gains gpe and strain energy

What is it for you, the spring or the mass?

If it refers to the spring, "as it moves down it gains gpe" means (to me at least) that the spring gains or accumulates elastic potential energy (not gpe) as it gets stretched by gravity.

If it refers to the mass, "as it moves down it gains gpe" would be incorrect because the mass loses gravitational potential energy as it falls down.

 

[haruspex]

mgh = 0.094*9.81*(2.6/1000) = 2.39 * 10^-3 J

1000?

but for part c... we are not looking at figure 5.1 so when it is stopped by a hand/ force so cant we say its in equilibrium?

I suppose you could argue that while it is being held it is in equilibrium, but then it is released, so it depends exactly what point in time you mean. Usually, if you describe a spring+mass system as being in equilibrium you mean without any forces on the mass except the spring and gravity.
Besides, you wrote:
"it is in equillibrium so it wont have gpe or strain energy"
If you meant while it is being held, the GPE and strain energy could be anything at all.
In position 5.2, it will indeed have no strain energy, but that is because the spring is relaxed, not because of any equilibrium.

 

[hello478]

1000?

I suppose you could argue that while it is being held it is in equilibrium, but then it is released, so it depends exactly what point in time you mean. Usually, if you describe a spring+mass system as being in equilibrium you mean without any forces on the mass except the spring and gravity.
Besides, you wrote:
"it is in equillibrium so it wont have gpe or strain energy"
If you meant while it is being held, the GPE and strain energy could be anything at all.
In position 5.2, it will indeed have no strain energy, but that is because the spring is relaxed, not because of any equilibrium.

thank you soo much, makes a little sense now :)

 

[hello478]

What is it for you, the spring or the mass?

If it refers to the spring, "as it moves down it gains gpe" means (to me at least) that the spring gains or accumulates elastic potential energy (not gpe) as it gets stretched by gravity.

If it refers to the mass, "as it moves down it gains gpe" would be incorrect because the mass loses gravitational potential energy as it falls down.

yeah ill keep both views in mind
but the answer with both would be the same??

 

[Lnewqban]

yeah ill keep both views in mind
but the answer with both would be the same??

Please, see both links:
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/15-1-simple-harmonic-motion/

https://courses.lumenlearning.com/s...hapter/15-2-energy-in-simple-harmonic-motion/