Question

Physics, theoretical question.

Answer 1

I am hanging 5 different mass M(i) on the string.
I have some initial height Yo and some height when
a particular mass M(i) is added.

M(i) are: 100, 200, 300, 400, 500 and grams.
The heights where each mass is located are: Y1, Y2, Y3, Y4, Y5.
The hanger, has a mass of M(h).

I hang the mass with the hanger on the string.
Then I calculate the weight by, W=( M(h)+M(i) )*g.
The elongation (the stretch vertical distance) is: Yo-Y1.

F = k * x
k = F / x
k = W / x
k = [ (M h + M i) * g] / [ Yo - Y1 ]

If I use this, I get unproportional values of k, for each ith mass.

BUT, if I use the law without using the weight of the hanger, i.e.
k = [ M i * g] / [ Yo - Y1 ]

then, I get the proportional k values.

Answer 2

So what should I do to find k,

THIS:
k = [ (M h + M i) * g] / [ Yo - Y1 ]

OR THIS:
k = [ M i * g] / [ Yo - Y1 ]

???

Answer 3

Do you know why you are using F=kx?

Answer 4

If it is a string, not a spring, than you shouldn't be using this equation.

Answer 5

if your start point is with the hanger, measure extensions from that point.

Answer 6

it's a linear relationship.