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# Elastic and Inelastic Collisions

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## Ernest Ching

on 25 June 2014

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#### Transcript of Elastic and Inelastic Collisions

KE before
E(S) = (
½
) x 100000 x 100^2
E(S) = 500000000 J
E(M) = (
½
) x 10000 x 0
E(S) = 0
E(S) + E(M) = 500000000 J

KE after
E(S + M) = (
½
) x 110000 x 90^2
E(S + M) = 400000000 J (in 1.sig.f)

KE loss = 500000000 - 40000000
= 100000000 J

Kinetic Energy Loss
Elastic and Inelastic Collision
Elastic Collisions
An elastic collision is a collision in which both
Momentum
and
Kinetic Energy
are conserved.
Elastic Collisions Problem
A ball with a mass of 10 kg moves in constant velocity of 5 ms^-1 collides with a stationary ball with a mass of 10 kg. If an elastic collision occurs as the two balls collide, what is the velocity of the two balls after the collision?
Inelastic Collisions
An inelastic collision is a collision in which Kinetic Energy is not conserved, while the momentum is conserved. The loss of energy are transformed from kinetic energy into other energy forms, for example: heat and sound.

In a totally inelastic collision, the two bodies stick together after colliding.
In a partially inelastic collision, the two bodies do not stick together after colliding.
Totally Inelastic Collisions Example
Vincent, with a mass of 75 kg, is running at a velocity of 7 ms^-1 westward. Charles, who has a mass of 100 kg, is standing stationary in the west direction of Vincent. If a totally inelastic collision occurs as Vincent runs into Charles, and they stick together. What is the resultant velocity? What is the Kinetic Energy loss?

Partially Inelastic Collisions Example
Ernest, with a mass of 50 kg, runs in a velocity of 10 ms^-1 down the road. A bus with the mass of 11980 kg follows behind Ernest with a velocity of 25 ms^-1. If a partially inelastic collision occurs as the bus hit Ernest, what is the velocity of Ernest when the velocity of the bus is 24.9 ms^-1 after the collision?
Q&A
Solution
Since after an elastic collision, the velocity of the two objects with the same mass will swap, therefore:

Ball with a mass of 10 kg: 5 - 5 = 0 ms^-1
Ball with a mass of 10 kg: 0 + 5 = 5 ms^-1
P = m x v

P(v) = 75 x 7 = 525 kgms^-1
P(c) = 100 x 0 = 0 kgms^-1

P(v)+P(c) = 525 kgms^-1

525 = (100 + 75) x V
V = 3 ms-1
Kinetic Energy Loss
KE = (½) m x v^2

KE loss = KE before - KE after
= (½) x 75 x 7^2 + (½) x 100 x
0^2 - (½) x (100+75) x 3^2
= 1837.5 + 0 - 787.5
= 1050 J
Example
A ball with a mass of 5kg, with a velocity 5 ms^-1, impacts with a stationary ball with a mass of 5kg. If an elastic collision occurs, what is the velocity of the original stationary ball after the collision?
Solution
Since the energy is conserved totally within an elastic collision, therefore:

KE = (1/2) x m x v^2

KE before = KE after
KE before = (1/2) x 5 x 25 = 62.5 J
KE after = (1/2) x 5 x v^2 = 62.5 J
v = 5 ms^-1
Solution
P(e) = 50 x 10 = 500
P(b) = 11980 x 25 = 299500
P(e) + P(b) = 300000

P(b)2 = 11980 x 24.9 = 298302
P(e)2 = 300000 - 298302 = 1698
V = 1698 / 50 = 33.96 ms^-1
Conclusion
In an Elastic Collision, where the mass of the two bodies are equal, the velocity of the two bodies will swap.
Resultant Velocity
Totally Inelastic Collision Problem
STAR, with a mass of 100,000 kg, is traveling at a velocity of 100 ms^-1 eastward. MOON, which has a mass of 10,000 kg, is standing stationary in the east direction of STAR. If a totally inelastic collision occurs as STAR collides into MOON, and they stick together. What is the resultant velocity? What is the Kinetic Energy loss?
Resultant Velocity
P(S) = 100000 x 100 = 10000000
P(M) = 10000 x 0 = 0
P(S) + P(M) = 10000000 kgms^-1

P(S+M) = 10000000 = 110000 x v
v = 10000000/110000
v = 90 ms^-1
(in 1 sig. fig.)
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