Elastic Collision Formula and Sums

Elastic Collision Formula :

The Elastic Collision formula  is the mass of 1st body m1(kg/s) in kilogram per second multiply the initial velocity of 1st body u1(m/s) in meter per second multiply mass 2nd body m2(kg/s) in kilogram per second multiply  the initial velocity of the second body  u2 (m/s)  in meter per second is equal to the  mass of the 1st body  m1(kg/s)  in kilogram per second and multiply final velocity of the first body V1 (m/s) in meter per second and addition of mass of the 2nd body m2(kg/s) in kilogram per second final velocity of second body V2(kg/s) in kilogram per second. Hence  Elastic collision formula can be written as,

m1(kg/s)* u1(m/s) +m2(kg/s)  *u2 (m/s) =m1(kg/s)*  V1 (m/s) +m2(kg/s)*   V2(kg/s)

Where,

m1→ mass of 1st body in kg/s

m2→ mass of 2nd body in kg/s

u1→ initial velocity of 1st body in m/s

u2 → initial velocity of the second body in m/s

v1 → final velocity of the first body in m/s

v2 i→ final velocity of the second body in m/s

Sample Sums :

Sum1 :

Calculate the velocity of the ball of mass 8 Kg ball after the collision? If the ball has a mass 6 Kg and moving with the velocity of 15 m/s collides with a stationary ball of mass  9 kg and comes to rest.

Solution :

Given parameters are

Mass of 1 st ball m1 is 6kg

The initial velocity of the first ball u1 is 15m/s

The mass of the second ball m2 is 9kg

The initial velocity of the second ball u2 is 8

The final velocity of the first ball v1 is 0

Final Velocity of the second ball v2 =?

1/2 m1* u12 +1/2m2* u22=1/2m1* V12 +1/2m2 *V22

(1*6×*(15)2)/2+(1*9*8)/2=(1*6*0)/2+(1*9)/2* V22

4086=4.5

=908

V2= 908

V= √908

= 30.13 m/s

Sum 2 :

Calculate the final velocity of first body ? In a 20 Kg block is moving with an initial velocity of 25 m/s with 9 Kg wooden block moving towards the first block with velocity 9 m/s. The second body comes to rest after the collision.

Solution :

Given parameters are

Mass of 1 st ball m1 is 20kg

The initial velocity of the first ball u1 is 25m/s

The mass of the second ball m2 is 9kg

The initial velocity of the second ball u2 is 9 m/s

The final velocity of the first ball v1 is 0

Final Velocity of the second ball v2 =?

m1* u1 +m2* u2=m1* V1 +m2* V2

(20 *25)+(9 *9)=(20 *v1)+(9 *0)

581=20V1 +0

V1=29.05

V1=29.05 m/s

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