Question

42.) Consider the Atwood's machine (shown at the right) in free space, far away from any gravitational influence. The block and the massless frictionless pulley are being accelerated upward at 20 m/s2 (a) As measured from a reference frame in which the block and pulley are stationary, find the acceleration of M1 (in other words, find the second time derivative of x) (b) If this seems too difficult, imagine that the block and pulley are not being accelerated and the whole system is near the surface of a planet with acceleration due to gravity of 2g. (c) Are these different interpretations equivalent? Discuss. (d) Prove that if M1>M2 then 2 > 0 T-10,000N 2

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Answer 1

(a) When we analyse with respect to pulley then acceleration of both m_1 and m_2 will have same magnitude. T - m_1 g = m_1 (a_1) T - mg = m_2 (a_2) (a_1 - 10) = -(a_2 - 10) g(m_2 - m_1) = -m_2 a_2 = m_1 a_1 a_1 = 20 - a_2 g(m_2 - m_1) = m_1 a_1 - m_2 (20 - a_1) g(m_2 - m_1) = a_1 (m_1 + m_2) - 20 m_2 a_1 = 20 m_2 + 10 m_2 - 10 m_1/m_1 + m_2 a_1 = 30 m_2 - 0 m_1/m_1 + m_2 \r\n b) Yes if we analyse with respect to pulley then a sudo force 10 m_1 on m_1 and 10m_2 on m_2 will act in downward direction. So this is equivalent to 2g acceleration in downward direction. \r\n (c) Yes similar, But the acceleration we get iww will be in frame of pulley and not in ground frame. We need to find further