A steel ball bearing of mass m₁ and speed of magnitude v₁ has a head-on elastic collision with a steel ball bearing of mass m₂ at rest. Rank the speed v₁ of m₁ relative to v₂, the magnitude of the speed of m₂, after the collision when i) m₁ m₂; ii) m₁ = m₂; and iii) m₁ v₂

Question

A steel ball bearing of mass m₁ and speed of magnitude v₁ has a head-on elastic collision with a steel ball bearing of mass m₂ at rest. Rank the speed v₁ of m₁ relative to v₂, the magnitude of the speed of m₂, after the collision when i) m₁ > m₂; ii) m₁ = m₂; and iii) m₁ < m₂. A) v₁ < v₂; v₁ < v₂; v₁ < v₂ B) v₁ < v₂; v₁ = v₂; v₁ > v₂ C) v₁ < v₂; v₁ > v₂; v₁ > v₂ D) v₁ > v₂; v₁ = v₂; v₁ < v₂ E) v₁ > v₂; v₁ > v₂; v₁ > v₂

Quizplus · Accepted Answer

In an elastic collision, when masses are equal (ii), they exchange speeds, so $v_{1} = v_{2}$. If $m_{1} > m_{2}$ (i), $m_{1}$ slows down but is still faster than $m_{2}$ after the collision, hence $v_{1} < v_{2}$. If $m_{1} < m_{2}$ (iii), $m_{1}$ bounces back with a greater speed than $m_{2}$ moves forward, so $v_{1} > v_{2}$.

A Steel Ball Bearing of Mass M1 and Speed of Magnitude

A Steel Ball Bearing of Mass M₁ and Speed of Magnitude