Mass on Elastic Rope: Solving for Rope Extension after Collision

[Foemph]

1. The problem statement, all variables and given data
A mass hangs in balance on a elastic rope (k= 800 N/m). The length of the rope in balance is 1m. They pull the mass 25 cm out of balance. The mass colides with the ceiling (restitution coefficient = 0,8). How far extend the rope after the collision. ( Solution: 0,0113m)

Homework Equations

In balance: m*g=k*u
E_k=1/2 m v²
E_p= m*g*h
E_v= 1/2 k u²

The Attempt at a Solution

I have tried different things with using the law of conversation of energy. But I think a have not enough known date. So, I compared the energy of the moment when the mass is pulled 25cm out of balance with the moment it collides with the ceiling:

1/2 k (u+0,25)²=1/2 m v²+ m g 1,25

I want to determine the speed. Then I know that the speed after the collision is equal to 0,8v. Then I would use the law of conversation of energy again to determine the extending of the rope. TO determine v I think have not enough data but maybe I forgot something. Can anyone help me? Thanks a lot!

 

[PeroK]

1. The problem statement, all variables and given data
A mass hangs in balance on a elastic rope (k= 800 N/m). The length of the rope in balance is 1m. They pull the mass 25 cm out of balance. The mass colides with the ceiling (restitution coefficient = 0,8). How far extend the rope after the collision. ( Solution: 0,0113m)

Homework Equations

In balance: m*g=k*u
E_k=1/2 m v²
E_p= m*g*h
E_v= 1/2 k u²

The Attempt at a Solution

I have tried different things with using the law of conversation of energy. But I think a have not enough known date. So, I compared the energy of the moment when the mass is pulled 25cm out of balance with the moment it collides with the ceiling:

1/2 k (u+0,25)²=1/2 m v²+ m g 1,25

I want to determine the speed. Then I know that the speed after the collision is equal to 0,8v. Then I would use the law of conversation of energy again to determine the extending of the rope. TO determine v I think have not enough data but maybe I forgot something. Can anyone help me? Thanks a lot!

You seem to have the right idea: it's all about energy. Energy is always a combination of PE in the rope, gravitational PE and KE. Just keep going with your idea.

 

[PeroK]

Do you know the mass?

 

[Foemph]

Do you know the mass?

No the mass is not given. Otherwise it would be so easy. :-(

 

[PeroK]

No the mass is not given. Otherwise it would be so easy. :-(

Mass is definitely a factor. You could solve the problem for two different masses to show this.

The only other possibility is that the rope has 0 length when unweighted. That would allow you calculate the mass.

 

[Foemph]

Mass is definitely a factor. You could solve the problem for two different masses to show this.

The only other possibility is that the rope has 0 length when unweighted. That would allow you calculate the mass.

Oke I'll try this tomorrow. Hopefully I find the right answer.

 

[PeroK]

Oke I'll try this tomorrow. Hopefully I find the right answer.

The second idea can't work, because then the mass wouldn't hit the ceiling.

You could solve it if you knew the unstretched length of the rope. Either that or the mass is required.