Isaac physics help - desperate

why are you typing 'bump'

so his post consistently pops up in latest discussions and someone sees it- generally seen as not nice until at least a couple days if the issue/ question is important

bump

bump

bump

Ive found that if its not replied to within 30 mins, it doesnt get replied to at all

https://isaacphysics.org/questions/pop_up_toy?board=a0bb7973-83fa-429c-87b9-441ee2997240

lo = 1-x
l1 = 1-y
1 - GPE = mglo, EPE = (mg(1-x))/2
2 - GPE = mgl1, EPE = (mg(1-y))/2
3 - GPE = mg(1-x+h), EPE = (mg(1-x))/2
help pls

https://isaacphysics.org/questions/pop_up_toy?board=a0bb7973-83fa-429c-87b9-441ee2997240

lo = 1-x
l1 = 1-y
1 - GPE = mglo, EPE = (mg(1-x))/2
2 - GPE = mgl1, EPE = (mg(1-y))/2
3 - GPE = mg(1-x+h), EPE = (mg(1-x))/2
help pls

Break the situation down into three sections:
1) The spring-mass system is at rest, Energy(1) = mgl0
2) The spring-mass system is squashed, Energy(2) = GPE + EPE
Total Energy = mgl1 + (1/2)k(l0-l1)^2
3) Due to the conservation of energy, Energy(3) = Energy(1) + Energy(2)

mg(l0 + h) = mgl0 + mgl1 + (1/2)k(l0-l1)^2

Rearrange for h:
h = (l1 - l0) + (k(l0-l1)^2)/(2mg)

I am afraid there is some confusion in your chosen system and using of conservation of energy but I agree with your answer.

In a spring-mass system, there is no gravitational potential energy (a pretty common confusion and misconception).

Please explain to me why there is no GPE in the system, it is oscillating vertically so there must be GPE

I would explain using a simple setup.

Consider a mass m is raised to a height h above the ground on Earth. Find the speed of the mass when it is just about to touch the ground.

If I choose the system to be just the mass, the weight of the mass is an external force and I need to consider work done on the mass.
The system only has kinetic energy, NO GPE.

I would write the conservation of energy as

Change in the energy of the system = Work done on the system
Change in kinetic energy = weight time height
$\frac{1}{2} mv^2 - 0 = mgh$ ------(1)


If I consider the system to mass and Earth, then the system would have KE and GPE. The work done on the system would be zero because the weight of the mass is an internal force NOT external force.

The conservation of energy would be

Change in the energy of the system = Work done on the system
$\Delta K + \Delta U_{gpe} = 0$ ------(2)
$(\frac{1}{2} mv^2 - 0 ) + (0 - mgh)= 0$ ------(3)

GPE arises when there is an interaction between two masses. Potential energy is always associated with a system of two or more interacting objects.

If you rearrange (3), you would get to (1). But you have to know how to interprete them correctly. This is why I say a common confusion.

I understand, however, in the question it states:
"The spring is compressed to length l1 when the pop-up is stuck to the ground"

From this, I made the assumption that the spring-mass system was initially placed on a surface, hence, GPE arises. Is this incorrect?

I am afraid that you do not really understand the issue.

The question does not mention anything about elastic potential energy or gpe, so the choice of the system is arbitrary.

Even if the question mentions about gpe, we are still allowed to choose another system that does not have gpe to solve the problem but it is usually slight more difficult to do it.

What forms of energy is within the system depend on your choice NOT YOUR ASSUMPTION.

If you are not taught of such stuff, your understanding of energy can be a bit shaky.

I didn't know that. I don't remember coming across questions like the one from OP at A Level; the usual questions in the textbooks and exams are always quite precise in what they ask. I guess I have alot to learn

Thanks for explaining.