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Elastic and Inelastic Collisions

AP Physics 1· difficulty 4/5

m1 v1 m2 v2

Object 1 (mass m1m_1, speed v1v_1 along +x+x) collides with object 2 (mass m2m_2, speed v2v_2 along +y+y) and they stick together. What is the speed of the combined object after the collision?

  • A

    vf=(m1v1)2+(m2v2)2/(m1+m2)v_f = \sqrt{(m_1 v_1)^2 + (m_2 v_2)^2}/(m_1+m_2)

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  • B

    vf=(m1v1+m2v2)/(m1+m2)v_f = (m_1 v_1 + m_2 v_2)/(m_1+m_2)

  • C

    vf=v12+v22v_f = \sqrt{v_1^2 + v_2^2}

  • D

    vf=m1v12+m2v22/(m1+m2)v_f = \sqrt{m_1 v_1^2 + m_2 v_2^2}/(m_1+m_2)

Explanation

Momentum components: px=m1v1p_x = m_1 v_1, py=m2v2p_y = m_2 v_2. Total momentum magnitude =(m1v1)2+(m2v2)2= \sqrt{(m_1 v_1)^2+(m_2 v_2)^2}. Divide by total mass m1+m2m_1+m_2 for final speed.

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