A 3.0-kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M?
A) 7.5 kg
B) 5.0 kg
C) 6.0 kg
D) 4.2 kg
E) 8.0 kg

Question

Quizplus · Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved. The conservation of momentum for the system can be expressed as $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$, where $m_1$ and $m_2$ are the masses of the two objects, $v_{1i}$ and $v_{2i}$ are their initial velocities, and $v_{1f}$ and $v_{2f}$ are their final velocities. Given that the second object (mass = M) is initially at rest, $v_{2i} = 0$, and the equation simplifies to $m_1v_{1i} = m_1v_{1f} + Mv_{2f}$.Substituting the given values, we have $3.0 \, \text{kg} \cdot 8.0 \, \text{m/s} = 3.0 \, \text{kg} \cdot (-2.0) \, \text{m/s} + M \cdot 6.0 \, \text{m/s}$. Solving for $M$, we find that $M = 5.0 \, \text{kg}$.

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