A 2,000 kg truck moving at 10 m/s strikes a car waiting at a traffic light. After collision, the two move together at 8 m/s. The mass of the car is _____.

Question

Question

Answer 1

The correct answer is 500 kg.

CONCEPT:

The type of collision in which there is a loss of kinetic energy and after the collision both the colliding particles move together is called perfectly inelastic collision.
In this type of collision the coefficient of restitution is equal to 0.
Momentum of the system remains constant in this collision.

P1 = m1u1 + m2u2

P2 = m1v1 + m2v2

CALCULATION:

Here, speed of the car is 0 m/s

⇒ After collision speed is 8 m/s

According to "Principle of conservation of momentum"

⇒ So, 8 = (m₁v₁ + m₂v₂)/(m₁ + m₂) where m₁is the mass of truck, v₁ is the velocity of truck, v₂ is the velocity of car and m₂ is the mass of car.

⇒ 8 = (2000 × 10 + m₂ × 0)/(2000 + m₂)

⇒ 16000 + 8 m₂ = 20000

Therefore, mass of the car is 500 kg.