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Newton's Second Law (Translational Dynamics)

AP Physics 1· difficulty 4/5

m1 m2

Two blocks (m1>m2m_1 > m_2) hang from a massless rope over a frictionless, massless pulley. What is the magnitude of acceleration of each block, and what is the tension in the rope?

  • A

    a=ga = g, T=m2gT = m_2 g

  • B

    a=(m1−m2)g/(m1+m2)a = (m_1 - m_2)g/(m_1 + m_2), T=2m1m2g/(m1+m2)T = 2 m_1 m_2 g/(m_1 + m_2)

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  • C

    a=(m1−m2)g/(m1+m2)a = (m_1 - m_2)g/(m_1 + m_2), T=(m1+m2)g/2T = (m_1 + m_2)g/2

  • D

    a=(m1+m2)g/(m1−m2)a = (m_1 + m_2)g/(m_1 - m_2), T=m1gT = m_1 g

Explanation

Newton's second law on each: m1g−T=m1am_1 g - T = m_1 a and T−m2g=m2aT - m_2 g = m_2 a. Adding gives a=(m1−m2)g/(m1+m2)a = (m_1 - m_2)g/(m_1+m_2). Substitute back to get T=2m1m2g/(m1+m2)T = 2m_1 m_2 g/(m_1+m_2).

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