- #1
Quinzio said:Maybe it's better to remeber that F = ma, but more generally
[tex]F= {d (m v) \over dt} [/tex]
where
[tex]m = f(t) [/tex]
[tex]v = f(t)[/tex]
It's not clear what you mean here.Is it necessary to consider motion on the ground?
This is not so clear, too.i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.
jessicaw said:I think when the chain is released the chain will move toward the ground, right?Help!
when the chain is release doesn't the chain fall towards the ground continously? why can it obtain uniform speed?
Quinzio said: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.
Quinzio said: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.
The length of the chain does not affect the time it takes to fall down. According to Galileo's Law of Falling Bodies, the acceleration due to gravity is constant for all objects, regardless of their mass or length.
The chain falls in a uniform manner due to the force of gravity acting on each individual link. This force causes each link to accelerate at the same rate, resulting in a uniform descent.
No, the material of the chain does not affect its falling speed. As long as the chain is uniform in weight and shape, it will fall at the same rate due to the force of gravity.
No, a longer chain will not fall faster than a shorter chain. Again, this is due to the constant acceleration of gravity acting on all objects regardless of their mass or length.
The only factor that can affect the uniformity of the chain's fall is air resistance. In a vacuum, the chain would fall in a perfectly uniform manner. However, in the presence of air, the resistance can cause slight variations in the speed of individual links, resulting in a slightly non-uniform fall.