# Physics Collision For Class11

## COLLISION

When one body struck another body, the collision is said to occurs in two .

### # ELASTIC COLLISION

A collision in which there is absolute no loss of kinetic energy is called Elastic Collision.

Example- The collision between two Ivary balls is an example of elastic collision.

### CHARACTERISTIC OF ELASTIC COLLISION

• Linear momentum is conserved
• Kinetic energy is conserved
• Total energy is conserved

### # INELASTIC COLLISION

A collision in which there occurs in some loss of kinetic energy is called  Inelastic Collision.

Example – A ball is dropped from a certain height and after collision with the ground it could not reach at the same position then the collision of the ball with ground is an example of Inelastic Collision.

### CHARACTERISTIC OF INELASTIC COLLISION

• Linear momentum is conserved   (Because no external force is acting on the body)
• Kinetic energy is not conserved
• Total energy is not conserved

### # PERFECT INELASTIC COLLISION

A collision in which there   occurs maximum loss of energy is called Perfect Inelastic Collision.

Example- mud is thrown on the wall it will stick to wall is an example of Perfect Inelastic Collision.

### CHARACTERISTIC OF PERFECT INELASTIC COLLISION

• Linear momentum is conserved
• Kinetic energy is not conserved
• Total energy is not conserved

### # COFFICENT OF RESTITUTION (e)

Before relative velocity = U1 – U2
After relative velocity = V2 – V1

Coefficient of restitution is defined as the ratio of relative velocity of separation after collision to the relative velocity of approach before collision.

e = V2 – V1 / U1 – U2

If  e = 1  (Then it is called Elastic Collision)
If  e = 0  (Then it is called Perfectly Inelastic Collision)
If  0 < e < 1  (Then it is called Inelastic Collision)

### #  DERIVITION OF COLLISION OF VELOCITY OF ELASTIC COLLISION

When two body of different mass when two body as moving with different velocity in same straight line and after collision moves in same straight line collision is said to be called Elastic Collision.

Consider two body mass M1  and  M2 moving with the velocity U1 and U2  in same straight line if U1  >  U2   they collide and after collision they move with velocity with V1  and  V2  in a straight same line.
As the collision is elastic , the linear momentum is conserved therefore the

Linear momentum before collision =  Linear momentum after collision

M1 U +  M1 U2  =   M1 V1  +  M1 V2             ----------------------(1)
M1 U -  M1 V1  =   M2 V2  -  M2 U2
M1 ( U -  U2 ) =   M2 (V1  -  V2 )            ---------------------------(2)

As the collision is elastic the kinetic energy is conserved
Kinetic energy before collision = Kinetic energy after collision
½ M1 U12   +   ½  M1 U22  =   ½  M1 V1 2 +   ½  M1 V22
M1 U12   +    M1 V12  =   M2 V2 2 +   M2 U22
M1 ( U12   +  V12 ) =  M2 (V2 2 + U22)
M1 ( U1  +  V1 ) ( U1  -  V1 )  =  M2 (V2  + U2) (V2  - U2)  -----------(3)

Dividing equation ‘3’ by equation ‘2’
M1 ( U1  +  V1 ) ( U1  -  V1 ) / M1 ( U -  U2 )   =  M2 (V2  + U2) (V2  - U2) / M2 (V1  -V)

U1  +  V1  =  V2  + U2
V2  =  U1  +  V1 -  U2 ----------------------------------(4)

Putting the value of V2 in equation ‘1’

M1 V1  +  M2 U1  + M2V1 – M2U2   =  M2U1 + M2U2
M1 V+ M2V1  =  M1U1 - M2U1     +  M2 U2  +  M2 U2
V1 (M+ M2)  = U1( M1 - M2)   + 2 M2 U2
V1 = U1( M1 - M2)/ (M+ M2   + 2 M2 U2/(M+ M2) -----------(5)

Putting the vale of V1 in equation ‘4’

TRICK – In place of 1 write 2 and in place of 2 write 1.

V2 = U2( M2 - M1)/ (M+ M1   + 2 M1 U1/(M+ M1)    --------(6)

### # What happen wen equal mass collide in elastic collision.

M1 =M2
V1 = U1( M1 - M2)/ (M+ M2   + 2 M2 U2/(M+ M2)
V1 = U1( M - M)/ (M  + M)     + 2 M U2/(M  + M)
V1 = 0 + 2 M U2/(M  + M)
V1 = U1

V2 = U2( M2 - M1)/ (M+ M1   + 2 M1 U1/(M+ M1)
V2 = U2( M - M)/ (M  + M1   + 2 M U1/(M  + M)
V2 = 0 + 2 M U1/(M  + M)
V2 = U2
It show before collision and after collision the velocity remain same if the mass is equal.

### # DERIVATION OF INELASTIC COLLISION OF VELOCITY

As the collision is inelastic the linear momentum is conserved
M1 U +  M2 U2  =   M1 V1  +  M2 V2      ----------(1)
Now with the help of coefficient of restoration  e = V2-V1/U1-U2
e( U1- U2) = V2 - V1
eU1- eU2 = V2 - V1
V2=  eU1- eU2 + V--------------(2)

Putting the value of V2 in equation ‘1’

M1 U +  M2 U2  =   M1 V1  +  M2(eU1- eU2 + V)
M1 U +  M2 U2 - M2eU1 + M2eU2 =   M1 V1  +  M2 V1
V1  (M1 +  M2 ) = M1 U- M2eU1 +  M2 U2 + M2eU2
V1  = U1 (M- M2e) /(M1 +  M2 ) +  M2 U2 (1+ e )/(M1 +  M2 )------(3)

Putting the value of V1 in equation ‘2’

TRICK – In place of 1 write 2 and in place of 2 write 1.

V2  = U2 (M- M1e) /(M1 +  M2 ) +  M1 U1 (1+ e )/(M1 +  M2 )------(4)

### # If  e=0 for perfectly inelastic collision

V1  = U1 (M- 0) /(M1 +  M2 ) +  M2 U2 (1 )/(M1 +  M2 )------(5)

V2  = U2 (M- 0) /(M1 +  M2 ) +  M1 U1 (1 )/(M1 +  M2 )------(6)

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