IIT JEE , AIEEE Forum - Physics , Mechanics - CHALLENGE-3

frenied

Two blocks of masses m1 and m2 are connected by a spring of spring constant k.now forces F1 and F2 start acting on the two blocks in a manner to stretch the spring.Find the max.elongation of the spring.

rooney

Is the answer 2(F₁ + F₂) / k ?

shubham_sachdeva

*post edited*

anit_sahu

maximum elongation is 2(f1m1+f2m2)/k(m1+m2)

karthik2007

*edited*

rooney

@Karthik

I also gave the same answer but it cant be that simple (great if it is! )

@anit_sahu

Please Please and please type your answers in more understandable form. Cant understand whats the numerator and which is the denominator.

rooney

@anit_sahu

I think that might not be the answer because dimensionally its incorrect.Its having the dimensions that of mass/k where as elongation has the dimension that of Force/k

rhd92781

is the answer 2(m1F2+m2F1)/k(m1+m2)

rooney

@rhd92781

Can you post the solution please ?

rhd92781

let F2>F1
acc of system, a=(F2-F1)/(m1+m2)
fbd of m1:
kx1-f1=m1a
solving we get, x1=(m1f2+m2f1)/(k(m1+m2))
fbd of m2:
f2-kx2=m2a
on solving, x2=(m1f2+m2f1)/(k(m1+m2))
so max elongation = x1+x2 = 2(m1F2+m2F1)/(k(m1+m2))

rhd92781

why rated?
i'm not sure of the soln
is this correct

rhd92781

rooney can u post ur soln

rooney

It is same as karthik's.

Energy conservation
Energy stored in string = Work done by F1 + Work done by F2

1/2kx^2 = F1x + F2x
x = 2(F1 + F2)/k

@rhd92781

1 thing in your solution that confuses me is that, the elongation x2 should also be considered while considering the force on m1. The force acting on a mass should be due to the net elongation (I seem to have seen this logic in one of the IIT questions where the spring is inside a circular shell)

frenied

rhd's ans is correct...but his method is wrong...so ill not give him a rate..why have u taken the accn.of both blocks to be SAME???

though ill thnk him for the diag...all u pll who need a diag..that's the correct one.

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