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, then the loss in K.E. due to collision is
A collision is an event where two or more bodies exert forces on each other for a relatively short time. Collisions can be elastic or inelastic, depending on whether kinetic energy is conserved. They play a crucial role in physics, impacting motion, momentum and energy transfer in various systems.
Chapter 5 of Class 11 Physics covers Work, Energy and Power. It introduces the concept of work done by a force and explains different forms of energy, including kinetic and potential energy. The chapter emphasizes the law of conservation of energy and defines power as the rate of doing work, illustrating its applications in various physical scenarios.
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To calculate the loss in kinetic energy due to the collision, we first calculate the initial and final kinetic energies of the system.
Step 1: Convert initial speed to m/s
Initial speed of the moving ball = 36 km/h
Speed in m/s = (36 × 1000) / (60 × 60) = 10 m/s
Step 2: Calculate the initial kinetic energy (K.E.) of the system
Only the first ball is moving initially, so:
Initial K.E. = (1/2) m₁ v₁²
Where:
– m₁ = 2 kg (the moving ball mass)
– v₁ = 10 m/s (the velocity of the moving ball)
Initial K.E. = (1/2) × 2 × (10)²
Initial K.E. = 100 J
.
Step 3: Calculating the resulting velocity of the merged mass
Immediately after impact, the balls have merged as a single object mass
– Total mass = m₁ + m₂ = 2 kg + 3 kg = 5 kg
Applying the law of conservation of momentum:
Initial momentum = Final momentum
m₁ v₁ + m₂ v₂ = (m₁ + m₂) v
where:
– v₂ = 0 (a stationary ball)
Substitute:
(2 x 10) + (3 x 0) = 5v
20 = 5v
v = 4 m/s
Step 4: Find the final kinetic energy of the system (K.E.)
Final K.E. = (1/2) (m₁ + m₂) v²
Final K.E. = (1/2) × 5 × (4)²
Final K.E. = (1/2) × 5 × 16
Final K.E. = 40 J
Step 5: Calculate the loss in kinetic energy
Loss in K.E. = Initial K.E. − Final K.E.
Loss in K.E. = 100 J − 40 J
Loss in K.E. = 60 J
Final Answer:
Loss in kinetic energy due to collision is 60 J.
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