2. What is elastic collision? Explain with reason what will happen when
a). a heavy body collides with a light body at rest.
b). alight body collides with aheavy body at rest.
Let us assume two bodies:
masses : m1 & m2
initial velocity: u1 & u2
final velocity: v1 & v2
Elastic Collision
In collision if the kinetic energy of the collision before collision is equal to kinetic energy after the collision.
or
velocity of approach = velocity of separation
Condition:
masses : m1 & m2
initial velocity: u1 & u2
final velocity: v1 & v2
They undergo collision:
Linear momentum balance:
m1u1 + m2u2 = m1v1 + m2v2
Kinetic Energy balance
1/2 m1u12 +1/2 m2u22 = 1/2 m1v12 + 1/2 m2v22
If collision is elastic
velocity of approach = velocity of separation
u1-u2 = v2-v1
So if collision is elastic and you solve the momentum and energy equations you will get v1 & v2 as:
a). a heavy body collides with a light body at rest.
m1>>>>m2
u2=0
So from the above formula:
v1 = u1
v2 = 2u1
b). a light body collides with a heavy body at rest.
m2>>>>>>m1
u2=0
v1 = -m2/m2 * u1 +0 = -u1
v2=0
masses : m1 & m2
initial velocity: u1 & u2
final velocity: v1 & v2
Elastic Collision
In collision if the kinetic energy of the collision before collision is equal to kinetic energy after the collision.
or
velocity of approach = velocity of separation
Condition:
- No external impulse acting.
- No friction acting.
- Duration of collision small.
masses : m1 & m2
initial velocity: u1 & u2
final velocity: v1 & v2
They undergo collision:
Linear momentum balance:
m1u1 + m2u2 = m1v1 + m2v2
Kinetic Energy balance
1/2 m1u12 +1/2 m2u22 = 1/2 m1v12 + 1/2 m2v22
If collision is elastic
velocity of approach = velocity of separation
u1-u2 = v2-v1
So if collision is elastic and you solve the momentum and energy equations you will get v1 & v2 as:
a). a heavy body collides with a light body at rest.
m1>>>>m2
u2=0
So from the above formula:
v1 = u1
v2 = 2u1
b). a light body collides with a heavy body at rest.
m2>>>>>>m1
u2=0
v1 = -m2/m2 * u1 +0 = -u1
v2=0