momentum qestion.

a uniform chain of mass m and length L is suspende so that its lower end just touches a smooth inelastic inclined plane with angle=45 .when it is released find the total impusle on the plane and the the force exerted by the chain on the plane at any instant??

8 Answers

1
ujjwalkalra kalra ·

no one to answer

23
qwerty ·

consider an element of chain dx at a distance x from the point of contact of incline and chain.

mass of dx = dm =Mdx/L

let v =vel just b4 hitting

now , the tension in the chain will be zero bcz , wen the element of chain hits the incline , then just after striking, it wont hav n e velocity _|_ to the incline ,and thus it wont give n e impulse( along _|_) to another differential element just above it wich will be striking the incline next , with vel v/√2 _|_ to the incline .

thus the chain is under freefall

thus vel of differenetial element wich was at a height x b4 releasing =√2gx
component of v along _|_ to the incline is changing due to inpulse of incline frm v/√2 to 0 .

thus Ndt = dP = dm(v√2 )=\frac{Mvdx}{L\sqrt{2}}

thus total impulse = \int \frac{M\sqrt{2gx}dx}{L\sqrt{2}}=\frac{M\sqrt{g}}{L}\int \sqrt{x}dx=\frac{2M\sqrt{gL}}{3}

is it correct ?

1
ujjwalkalra kalra ·

nup..nwer is not correct..plz try agin and try for force expression too

1
ujjwalkalra kalra ·

cn u plz explain the point tht after striking why it will nt hve any velocity perpendicular to incline??plz

23
qwerty ·

it is an inelastic collision ...e = 0 = velocity of seperation velocity of approach

23
qwerty ·

force expression is ,

Ndt= \frac{Mvdx}{L\sqrt{2}}

so N = MvL√2 dxdt =Mv2L√2 = 2MgxL√2 ??

1
ujjwalkalra kalra ·

its nt correct an wht abut the impulse...leave the force expression i gt it...u plz solve ffr impulse plz

23
qwerty ·

n e 1 interested here??right ans bata do ?

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