Conservation of Linear Momentum Practice

Sample questions

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1. Sample 1difficulty 2/5

   A $4~\text{kg}$ object at $5~\text{m/s}$ collides head-on with a $1~\text{kg}$ object at rest. After collision the $1~\text{kg}$ object moves at $8~\text{m/s}$ in the direction the $4~\text{kg}$ object was moving. The final velocity of the $4~\text{kg}$ object is

   • A

     $8~\text{m/s}$

   • B

     $5~\text{m/s}$

   • C

     $2~\text{m/s}$

   • D

     $3~\text{m/s}$

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   Why

   Momentum: $4(5) = 4 v + 1(8) \Rightarrow v = 12/4 = 3~\text{m/s}$.

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2. Sample 2difficulty 2/5

   A $200~\text{kg}$ cannon fires a $10~\text{kg}$ ball at $80~\text{m/s}$. The cannon's recoil speed is

   • A

     $8~\text{m/s}$

   • B

     $1~\text{m/s}$

   • C

     $4~\text{m/s}$

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   • D

     $2~\text{m/s}$

   Why

   $0 = 200(-v) + 10(80) \Rightarrow v = 800/200 = 4~\text{m/s}$.

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3. Sample 3difficulty 2/5

   A $2.0~\text{kg}$ rifle fires a $0.010~\text{kg}$ bullet at $400~\text{m/s}$. What is the rifle's recoil speed (ignore the shooter)?

   • A

     $4.0~\text{m/s}$

   • B

     $0.50~\text{m/s}$

   • C

     $1.0~\text{m/s}$

   • D

     $2.0~\text{m/s}$

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   Why

   $0 = m_b v_b + m_r v_r \Rightarrow v_r = -m_b v_b / m_r = -(0.010)(400)/2.0 = -2.0~\text{m/s}$ (rearward).

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4. Sample 4difficulty 2/5

   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

     $-1.0~\text{m/s}$

   • B

     $+1.0~\text{m/s}$

   • C

     $+0.2~\text{m/s}$

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   • D

     $+2.0~\text{m/s}$

   Why

   $p_\text{initial} = (2)(+5) + (3)(-3) = 10 - 9 = +1~\text{kg·m/s}$. Final: $v' = p/(m_1+m_2) = 1/5 = +0.2~\text{m/s}$ (slight motion to the right).

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5. Sample 5difficulty 2/5

   Two skaters at rest, masses $40~\text{kg}$ and $60~\text{kg}$, push off each other. The $40~\text{kg}$ skater moves at $3~\text{m/s}$. The $60~\text{kg}$ skater's speed is

   • A

     $3.0~\text{m/s}$

   • B

     $2.0~\text{m/s}$

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   • C

     $1.5~\text{m/s}$

   • D

     $4.5~\text{m/s}$

   Why

   $0 = 40(3) + 60(-v) \Rightarrow v = 120/60 = 2.0~\text{m/s}$.

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