What Determines the Velocity of a Falling Chain?

[jessicaw]

Homework Statement

uploaded

Homework Equations

rocket equation

The Attempt at a Solution

i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.

 

[zorro]

The question is not visible.

 

[sr-candy]

try considering rate of change of momentum

 

[Quinzio]

Maybe it's better to remeber that F = ma, but more generally
$$F= {d (m v) \over dt}$$
where
$$m = f(t)$$
$$v = f(t)$$

 

[jessicaw]

Maybe it's better to remeber that F = ma, but more generally
$$F= {d (m v) \over dt}$$
where
$$m = f(t)$$
$$v = f(t)$$

yes i know this but how to apply this to the problem?Is it necessary to consider motion on the ground?

 

[Quinzio]

First step is considering the chain as a static system (as a snapshot of a moving system) and then determining the force acting of the string.

Second step is let the system move and introducing
$$F= {d (m v) \over dt}$$

assuming v as a constant (the problem itself tells you this) and understanding what is "m".

Is it necessary to consider motion on the ground?

It's not clear what you mean here.
Ground plays no force on the chain.

i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.

This is not so clear, too.
Show what you want to calculate by formulas or drawings, but it's not a useful way.

 

[jessicaw]

I think when the chain is released the chain will move toward the ground, right?Help!

 

[jessicaw]

when the chain is release doesn't the chain fall towards the ground continously? why can it obtain uniform speed?

 

[Quinzio]

I think when the chain is released the chain will move toward the ground, right?Help!

Yes, it does. What else could it do ?

Jessica, this doesn't want users to give complete solutions, (I agree) so you'll have a lot of hints but no more.

Start with something simple:
you have a chain over a pulley. The chain is not simmetrically placed over the pulley. Both ends of the chain are far from the ground. The offset between one end and the other is a length "h" = 1 meter.
The total length of the chain is 5 meter and the total mass of the chain is 5 kg.

Calculate the initial acceleration when the chain and the pulley are free to move.

when the chain is release doesn't the chain fall towards the ground continously? why can it obtain uniform speed?

In fact it does reach a uniform speed.

 

[jessicaw]

Yes, it does. What else could it do ?

Jessica, this doesn't want users to give complete solutions, (I agree) so you'll have a lot of hints but no more.

Start with something simple:
you have a chain over a pulley. The chain is not simmetrically placed over the pulley. Both ends of the chain are far from the ground. The offset between one end and the other is a length "h" = 1 meter.
The total length of the chain is 5 meter and the total mass of the chain is 5 kg.

Calculate the initial acceleration when the chain and the pulley are free to move.
In fact it does reach a uniform speed.

why? Is it due to the force by the ground?

 

[Quinzio]

No, jessica, the chain can only be pulled not pushed.
If you push a chain it will fold onto itself.
The ground could at least push the chain, so it doesn't have any effect on the chain.

The only force you have to take in account is the gravity.

Solve the simpler problem I gave you.
You have to be able to solve it, before your problem.

 

[jessicaw]

No, jessica, the chain can only be pulled not pushed.
If you push a chain it will fold onto itself.
The ground could at least push the chain, so it doesn't have any effect on the chain.

The only force you have to take in account is the gravity.

Solve the simpler problem I gave you.
You have to be able to solve it, before your problem.

yes i solved your problem. The initial acceleration is 0.2g for the longer side downward. However the acceleration becomes larger and larger as the longer side becomes longer and thus heavier. So i still do not know when the accelertation is 0 so that the speed is constant...
help.....

 

[Quinzio]

Ok, for my problem.

Your original problem now.
You need to define:
- the mass of the chain which hits the floor.
- the mass of the chain that rises from the table.

How can we define that quantities ? Is it a function of what ?
The part of chain hitting the ground. Where does its energy go ?

The part of chain that rises from the table.
Before rising its speed is ... ? Its energy ?
After rising its speed is ... ? Its energy ?
So ?