Force due to a chain falling on a table

[Suyash Singh]

Homework Statement

a uniform fine chain of length l is suspended with lower end just touching a horizontal table. Find the pressure on the table, when a length x has reached the table..

Homework Equations

Pressure = force/area

The Attempt at a Solution

let mass density, m= mass/l (this gives the mass per unit length)
force= mgx

How do i proceed now?

 

[Baluncore]

A pressure requires knowledge of the area of the table or the width of the chain.

The question only makes sense if the word pressure is replaced with force.

If you use units of pressure = Newtons per square table top, you will get the same answer as finding the force.

 

[haruspex]

Homework Statement

a uniform fine chain of length l is suspended with lower end just touching a horizontal table. Find the pressure on the table, when a length x has reached the table..

Homework Equations

Pressure = force/area

The Attempt at a Solution

let mass density, m= mass/l (this gives the mass per unit length)
force= mgx

How do i proceed now?

I assume the question says, or is supposed to say, that the chain is released. So there is not only the weight of the chain already on the table but some force, perhaps, from the new links arriving.
Consider momentum.

 

[Suyash Singh]

I assume the question says, or is supposed to say, that the chain is released. So there is not only the weight of the chain already on the table but some force, perhaps, from the new links arriving.
Consider momentum.

so how do i do it?

something like mass x velocity? and then calculate pressure (which i can't figure out how)

 

[Suyash Singh]

the answer is 3mgx and no more details are given. From one site i found that m here represents mass density but i am not sure about that.

 

[Arman777]

the answer is 3mgx and no more details are given. From one site i found that m here represents mass density but i am not sure about that.

How the unit of pressure can be $Nm$ (Newtonxmeter) ?

 

[haruspex]

something like mass x velocity?

Sort of.

Consider a short period of time Δt.
At time 0, the end of the chain is just touching the table and x=0.
When there is a length x on the table, what is the velocity of the chain?
How much chain hits the table in time Δt?
What is the change in its momentum ?

found that m here represents mass density

Yes, that m would be the mass per unit length.

 

[Vriska]

Sort of.

Consider a short period of time Δt.
At time 0, the end of the chain is just touching the table and x=0.
When there is a length x on the table, what is the velocity of the chain?
How much chain hits the table in time Δt?
What is the change in its momentum ?Yes, that m would be the mass per unit length.

hey not OP, but I'll try

when s is on the table v^2 = 2gs, let linear density be L, L*x hits the chain in time dt, change in momentum is... m*dv/dt+ vdm/dt
sooo L*x *(d/dt (sqrt(2gs))+ Lv^2 annnnd I think the first term is wrong, it is isn't it?

 

[haruspex]

change in momentum is... m*dv/dt+ vdm/dt

I meant the change in momentum of the piece that hits the table.
You can write the mass of that piece in terms of your other variables.

 

[Vriska]

I meant the change in momentum of the piece that hits the table.
You can write the mass of that piece in terms of your other variables.

Okay momentum of piece is mass *change in velocity. but the mass that'd have fallen in time dt is Lvdt =L(sqrt(2gx))dt but the change in velocity is sqrt(2gx) . dp = 2Lgx dt. 2Lgx, force due to change in momentum is 2Lgx. force on the table due to weight already on it = Lgx, which is 3Lgx. Thanks!

 

[haruspex]

Okay momentum of piece is mass *change in velocity. but the mass that'd have fallen in time dt is Lvdt =L(sqrt(2gx))dt but the change in velocity is sqrt(2gx) . dp = 2Lgx dt. 2Lgx, force due to change in momentum is 2Lgx. force on the table due to weight already on it = Lgx, which is 3Lgx. Thanks!

Good, but since you did not originate the thread you probably should have held off a while before posting the solution.

 

[Suyash Singh]

lol its so complicated that i just learned its answer.