Simple Harmonic Motion of a Mass Hanging from a Vertical Spring

[momoneedsphysicshelp]

Homework Statement

A 13.6 kg mass is placed on a vertically hanging spring (k=8.8). The mass is slowly released so it comes to rest. What is the displacement from the natural length of the spring?

Relevant Equations

Gravitational potential energy = m*g*x
Elastic potential energy = (1/2)kx^2

Assuming zero spring mass and zero friction,
At the greatest value of x, the loss in gravitational potential energy should equal the loss in elastic potential energy.

so I did

(1/2)kx^2=mgx

to isolate x in the formula,

x=(2mg)/k

then I plugged in my values so:

(2*13.6*9.81)/8.8= 30.3218

so the displacement is 30.32 m.

Can anyone please check what mistake I made in this problem, when I submit it, it is incorrect.

 

[haruspex]

At the greatest value of x, the loss in gravitational potential energy should equal the loss in elastic potential energy.

You mean the gain in EPE, but this scenario does not conserve work:
"The mass is slowly released"

 

[momoneedsphysicshelp]

You mean the gain in EPE, but this scenario does not conserve work:
"The mass is slowly released"

How come elastic potential energy will not decrease as the mass goes down?

 

[rsk]

It's slowly released until it comes to rest.

What can you say about the forces acting on it at this point, at rest?

 

[momoneedsphysicshelp]

It's slowly released until it comes to rest.

What can you say about the forces acting on it at this point, at rest?

decreasing gravitational potential energy

 

[rsk]

Forces, not energy. What can you say about the forces on an object which is at rest?

 

[haruspex]

How come elastic potential energy will not decrease as the mass goes down?

Elastic potential energy of a spring is at minimum when the spring is relaxed. Compressing or stretching it increases the EPE according to ½kx², where x is the change in length from the relaxed length.

Conservation of mechanical work means that work lost by one aspect (potential or kinetic) is gained by other aspects. There is no law that says the loss in one should equal the loss in another,