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New user has been reminded to use the Homework Help Template when starting schoolwork threads at the PF

Good evening.

The problem states:

Working out by the principle of forces, where the weight, when equated to the elastic force shows,

Fg= -Fk or Fg + Fk = 0 (in the equilibrium point).

So,

-mg = -Cy, and y = mg/C. (What is different from what would be obtained from the spring paradox).

But i simply dont know how to show that the spring argument is wrong, as well.

Please, help!

Thanks.

The problem states:

**Spring paradox. What is wrong with the following argument? Consider a mass m held at rest at y = 0, the end of an unstretched spring hanging vertically. The mass is now attached to the spring, which will be stretched because of the gravitational force mg on the mass. \Vhen the mass has lost gravitational potential energy mgy and the spring has gained the same amount of potential energy so that mgy = ~ Cy²/2, the mass will come to equilibrium. Therefore the position of equilibrium is given b y=2mg/C.**

Working out by the principle of forces, where the weight, when equated to the elastic force shows,

Fg= -Fk or Fg + Fk = 0 (in the equilibrium point).

So,

-mg = -Cy, and y = mg/C. (What is different from what would be obtained from the spring paradox).

But i simply dont know how to show that the spring argument is wrong, as well.

Please, help!

Thanks.