IIT JEE , AIEEE Forum - Physics , Mechanics

akhil_o

Two identical equilateral triangular wedges of mass M rest on a smooth surface
s sphere of mass m falls from a height h strikes the wedges symmetrically
coefficient of resitution=e
find the velocities of spheres and wedges just after collision

jinu.coolboy

iI think we have to apply law of conservation of linear momentum
between the blocks and the ball

akhil_o

well..its not that i cant get it...but just thought u shd try!
so plz post complete solution!

jinu.coolboy

Is it elastic or Inelastic collision.plz give me quick reply.

akhil_o

coeff of restitution=e
so partially inelastic

ganesha1991

can u give the solutions

thevyzz

clearly the two wedges must move with the same velocity in opp directions

let it be v1

let v2 be the velocity of the ball after collision
let u2 be the sphere's vel befrore collison

now ( v1^2 + v2^2 ) ^ (0.5) = u2*e ----- eqn 1

Let T be the force offered by the sphere over a time dt on the wedges

Let @ = 60 deg

now change in momentum of the two wedges = T*cos@*sin@dt/2 ( force offered by sphere normal to wedge = Tcos@, force offered in the direction of motion = Tcos@sin@)

change in momentum of sphere (By 3rd law) = T*cos@

now, v1 = T*dt*cos@sin@/2M

v2 = u2 - T*dt*cos@/m

v2 = u2 - v1 * 2M/msin@

substituting in eqn 1

( v1^2 + v2^2 ) ^ (0.5) = u2*e

v1^2 + (2gh - v1*2M/msin@)^2 = 2gh*e

now solve for v1 and find v2

ganesha1991

is it something like
velocity of sphere = (2mgh) (1-e)/(m+2M) + 2egh
velocity of each wedge = (2mgh) (1-e)/(m+2M)
i'm not sure

BALGANESH

v0 = initial vel of sphere

v1 = vel of sphere after colln

v2 = vel of block after colln

from fbd

2Jcos = mv1 - (-mv0)

therefore

J = m(v1 + v0 ) .....................1

Jsin = mv2 ..........2

subst 1 in 2 we get

2mv2 / root 3 = mv1 + mv0 .....................3

now e = - v2sin - v1cos / -v0cos

on solving ev0 - root3v2 = v1 ...................4

subst 4 in 3 and solving we get

v2 = v0m( 1 + e )root3/2M + 3m

u can rate me if useful

BALGANESH

please download it and keep watching it while reading the soln

akhil_o

Answers:
velocity of block=U=(2eM-3m)(

2gh)/(2M+3m)
velocity of sphere:V=(2eM-3m)(

2gh)/(2M=3m)

BALGANESH

ooooooopsy v0 is not the given thing , will think again but i think whatever i have done is correct , isn't it

akhil_o

well..even if u take v=root(2gh), ur answers arent really matching are they?

anshu_kk

akhil u told its inealstic but confused me ...relative velocity after collsion will b zero in inealstic collison

Ask & Discuss Questions with Community & Experts