IIT JEE , AIEEE Forum - Physics , Mechanics

magiclko

One end of an ideal spring is fixed at point O abnd other end is attached to a small disc of mass m which is given an initial velocity V perpendicular to its length on a smooth horizontal surface. If the maximum elongation in spring is l_o/4 , (l_o = natural length and k= stiffness of spring)..... then find the velocity at maximum elongation and value of V, in temrs of l_o, m and k.

shubham_sachdeva

what do u wanna know, the valocity with which it rebounds???

velocity at max. elongation ,for an instant ,will be 0 & V=

^{[ ]}

Inot/2{kInot/4m-g}

m i correct??

magiclko

i cudnt get wat u hav written!!!

shubham_sachdeva

i hv written A[KA-4MG]/8M ^1/2

WHERE A = I KE FOOT PE GOLI

& ^ MEANS RAISED TO POWER

fundoonikhil

velocity at max. elongation is zero.
v=(I/4){(k/m)^1/2}
this has been done by equatic initial kinetic energy with the final energy in spring.
i hope i'm right.

magiclko

nopes.... its not the answer... answer given is v = 5l₀ / 12 (k/m)^(1/2)and velocity is 4v/5....

shubham_sachdeva

hey, is the disc given velocity in downward dir. or to the right or left of the disc

i don't completely understand???????

malay

after the initial impulse, the system will attain equilibrium.
Let velocity of disc at equilibrium is w and elongation is I/4(by equlibrium, I mean there is no furhter change in speed and disc will move in a circle)

from law of conservation of energy
m*v*v/2=m*w*w/2 + k*I*I/32

since the disc is in equilibrium
m*w*w/(5I/4)=k*I/4

sudeep.kumar

Well.. nice question... completely physics and no maths in it...

The disc starts moving in a straignt line, the spring is elongated, so it pulls the disc inwards (radially) but the velocity continues to take it outwards, but decelerating. After some time, the radial vel ie vel along the spring, becomes 0, (and only tangential vel remains in the disc)and this is the pt of max extension, cause after this, the spring pulls the disc inwards.

Now, maths,

Angular mom. cons about other end of spring...

mVl₀ = mV_f (l₀ + l_o/4) so, V_f = 4V/ 5

Energy conservation..

m {V² - (4V/5⁾²} = k (l₀/4)²

Solve to get V = 5l₀(k/m)^1/2/12

magiclko

thank u sir

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