A pivoted beam has mass m_1 suspended from one end and an Atwood\'s machine susp

Question

A pivoted beam has mass m_1 suspended from one end and an Atwood's machine suspended from the other with masses m_2 and m_3 suspended on either side. The frictionless pulley has negligible mass and size. Find the relation between. Find the relation between m_1, m_2, m_3, l_1, and l_2 which will ensure that the beam has no tendency to rotate just after the masses are released. What would you predict the relation would be in the case that all three masses are equal? Does your answer from part (a) agree with that prediction?

Explanation / Answer

Consider the Atwood machine is wrapped in a box .. Then independent of what's going on side what we feel is just the weight of the two masses (m2 +m3 )g

A) to satisfy A, the torques must be equal and balanced

m1g * l1 = (m2 +m3 )g * l2

m1 * l1 = (m2 +m3 ) * l2

l1 /  l2 = (m2 +m3 ) / m1

b) yes absolutely , it agrees

we can simplify it much more my taking m1 = m2 = m3 = m

l1 /  l2 = (2 m  ) / m

l1 /  l2 = 2

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