# A metal ball of mass 2 kg moving with speed of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after collision both the balls move as a single mass, what will be the loss in kinetic energy due to collision?

1
by m8ukh4vankaussonim
You mean the loss of velocity?
For the 5kg mass?

2016-04-08T16:52:35+05:30
Let us suppose the following things,
Mass of smaller ball,              m₁ = 2kg
Mass of larger ball,                 m₂ = 3kg
Combined mass of two balls, m₃ = 5kg

Initial Velocity of Smaller Ball, u₁ = 36 km/h = 10m/s
Initial Velocity of Larger Ball,   u₂ = 0 m/s
Final Velocity of both balls combined, v = (?)

By, Law of Conservation Of Momentum, (For this case)

m₁u₁ + m₂u₂ = m₃v
∴2 * 10 + 3 * 0 = 5 * v
∴20 + 0 = 5v
∴5v = 20
v = 4 m/s

Thus, the final velocity of both the balls moving as a single mass should be 4 m/s.

Now, let us suppose the following,

Initial combined velocity, v₁ = 10 m/s (Larger ball was at rest)
Final combined velocity, v₂ = 4m/s
Combined Mass,            m  5kg
Initial Kinetic Energy,      K₁
Final Kinetic Energy,       K₂

Change in Kinetic Energy, ΔK = K₂ - K₁
= 1/2 mv₂² - 1/2 mv₁²
= 1/2 m (v₂² - v₁²)
= 1/2 * 5 (4² - 10²)
= 5/2 * (16 - 100)
= 5/2 * (-84)
= 5 * (-42)
∴ΔK = -210 J

Thus change in Kinetic Energy is 210 J.