Extra credit (up to 10 bonus points, but won’t count off if you don’t do it!). A
ID: 1427304 • Letter: E
Question
Extra credit (up to 10 bonus points, but won’t count off if you don’t do it!). A collision between two bodies is defined to be elastic if the total kinetic energy before and after the collision is the same. Consider an elastic collision between two identical atoms one which is initially at rest v2 = 0 and the other is moving with velocity v1 not equal to 0. Denoting v1,2 the corresponding velocities after the collision
(a) Write down the vector equations representing the conservation of momentum and the scalar equation representing the conservation of kinetic energy in an elastic collision.
(b) Use this to prove that v1 and v2 are perpendicular.
Explanation / Answer
a) According to the equations of the conservation of momentum as well as conservation of kinetic energy (Elastic collision),
We can write the equations. First for conservation of momentum (Vector equation)
( m1*u1) +(m2*u2) = ( m1*V1) +(m2*V2)
Where u = initial velocity and V = Final velocity
But for elastic collision Final velocity is same for both the atoms
Therefore,
V1=V2=V
( m1*u1) +(m2*u2) = ( m1+m2) V
Here U and V are in vector notation
Equation for conservation of kinetic energy
( m1*u12) +(m2*u22) = ( m1*V12) +(m2*V22)
( m1*u12) +(m2*u22) = (m1 +m2) V2
The above equation is in scalar form
Where V1=V2=V.
b) In this case V1 and V2 are perpendicular to each other because It is given in problem that V1is not 0.
c) Only that time it is prove.
d) Both the velocities are perpendicular to each other.
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