Cart 1 has an initial velocity and hits Cart 2 which is stationary. After a perfectly inelastic collision, the combined carts are traveling with exactly one third the initial velocity of Cart 1, and in the same direction. Which is correct about the mass of Cart 2?
Answer
A
The mass of Cart 2 must be twice the mass of Cart 1.
B
The mass of Cart 2 must have decreased during the collision.
C
The mass of Cart 2 must be one third the mass of Cart 1.
D
The mass of Cart 2 must be the same as the mass of Cart 1.
Explanation
Conservation of momentum gives m₁v = (m₁ + m₂)(v/3), since Cart 2 starts at rest and the carts stick together. Multiplying by 3 and dividing by the nonzero initial velocity gives 3m₁ = m₁ + m₂, so m₂ = 2m₁. Therefore, Cart 2 must have twice the mass of Cart 1.
AI-written and checked against the verified answer.