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- Homework Statement
- Two bodies (see figure) are connected by an ideal rope of length ##l = 0.9 m##. The body with mass ##m_1 = 2 kg## is free to slide without friction along a rigid horizontal rod. The second body has mass ##m_2 = 3 kg##. The bodies are both initially stationary in the indicated position (##\alpha = 60 °##) when they are left free to move. Find:

a) the velocities ##v_1## and ##v_2## of the two bodies when they are vertically aligned;

b) the amplitude ##A## of the motion of ##m_1##.

- Relevant Equations
- ##U_g=mgh, E_i=E_f, E=U+K, P_i=P_f##

1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and ##v_1=-\frac{m_2}{m_1}v_2##

2) For ##m_2## I think that the amplitude should be ##A_2=2l\sin(\alpha)## but I don't see how find out the amplitude of ##m_1## so I would appreciate an hint about how to find it, thanks.

2) For ##m_2## I think that the amplitude should be ##A_2=2l\sin(\alpha)## but I don't see how find out the amplitude of ##m_1## so I would appreciate an hint about how to find it, thanks.

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