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URGENT A Level Physics question

A spring is stretched by hanging on it a variable mass m. The mass m is always at rest.
The spring obeys Hooke’s law.
What is the relationship between the elastic potential energy E in the spring and the mass m?
A E m–1
B E m–2
C E m
D E m2

For this question the solution is apparently bc E=1/2F/k^2, but why can't you use E=1/2mgx, is x non constant?
Reply 1
EPE is 1/2 ke^2 where the extension e must satisfy tension = weight
ke = mg
so EPE is proportional to m^2. As you say, the extension is proportional to mass.
(edited 2 months ago)
Original post by mqb2766
EPE is 1/2 ke^2 where the extension e must satisfy tension = weight
ke = mg
so EPE is proportional to m^2. As you say, the extension is proportional to mass.

what about E=1/2Fx, and then saying EPE is proportional to mass from E=1/2mgx?
Reply 3
Original post by efsfsf\\eeeeeee
what about E=1/2Fx, and then saying EPE is proportional to mass from E=1/2mgx?

Not surebwhat you mean as E=1/2Fx is correct, but both the extension x and the force F are proportional to mass.
Original post by mqb2766
Not surebwhat you mean as E=1/2Fx is correct, but both the extension x and the force F are proportional to mass.

Basically im saying im pretty sure you cant form a proportionality relation using E=1/2Fx=1/2mgx, because you have more than 2 variables (E,m,x), which is why im asking if this is the reason that you have to manipulate the equation to get it with only two variables; in this case subbing in F=kx, gets rid of the variable x to allow you to form a proportionality relation.

sorry to drag this out lol
(edited 2 months ago)
Reply 5
Original post by efsfsf\\eeeeeee
Basically im saying im pretty sure you cant form a proportionality relation using E=1/2Fx=1/2mgx, because you have more than 2 variables (E,m,x), which is why im asking if this is the reason that you have to manipulate the equation to get it with only two variables; in this case subbing in F=kx, gets rid of the variable x to allow you to form a proportionality relation.
sorry to drag this out lol

proportional effectively means you have
constant * variable
or some transformation (squared or ...) of the variable and here you can write both the force and extension as
constant * mass
so overall (product of force and extension) you have
constant * mass^2
so EPE is proportional to mass^2

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