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Conservation of Linear Momentum

AP Physics 1· difficulty 2/5

m₁=2 kg m₂=3 kg +5 m/s −3 m/s

Two carts on a frictionless track approach each other as shown. They collide and stick together. What is the velocity of the combined cart immediately after the collision?

  • A

    −1.0 m/s-1.0~\text{m/s}

  • B

    +1.0 m/s+1.0~\text{m/s}

  • C

    +0.2 m/s+0.2~\text{m/s}

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  • D

    +2.0 m/s+2.0~\text{m/s}

Explanation

pinitial=(2)(+5)+(3)(−3)=10−9=+1 kg⋅m/sp_\text{initial} = (2)(+5) + (3)(-3) = 10 - 9 = +1~\text{kg·m/s}. Final: v′=p/(m1+m2)=1/5=+0.2 m/sv' = p/(m_1+m_2) = 1/5 = +0.2~\text{m/s} (slight motion to the right).

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