- #1

Nexus99

- 103

- 9

- Homework Statement
- A homogeneous rod of lenght L and mass M translate with a constant velocity ##\vec{v_0}## on a smooth plane. At the time ##t = t_0## the rod is hit simultaneously by 2 bodies of mass ##m_1## and ##m_2## that are moving with velocity ##\vec{v} = - \vec{v_0}## The collision is completely anaelastic. Determine;

1) The position of the center of mass of the system after the collision (consider a reference system with origin in the center of the rod)

2) The final speed of the system after the collision

3) the angular velocity after the collision

4) How much should the magnitude of ##\vec{v}## so that the system composed by the rod and the masses stop after the impact?

- Relevant Equations
- center of mass, conservation of linear and angular momentum

1) I found:

##x_{CM} = z_{CM} = 0 ##

##y_{CM} = \frac{L}{2} \frac{m_1 - m_2}{M + m_1 + m_2} ##

2) Applying the conservation of linear momentum:

##M v_0 - m_1 v_0 - m_2 v_0 = (M + m_1 + m_2) v_f ##

##v_f = \frac{M - m_1 - m_2 }{M + m_1 + m_2} v_0 ##

The velocity should have been found also calculating the velocity of the center of mass of the system, that isn't changed after the collision because there are no external impulsive forces that act on the system.

3) ## \omega = \frac{v_f}{y_{CM}} ##

4)

##M v_0 + m_1 v+ m_2 v = 0 ##

## v = -\frac{M v_0}{m_1 + m_2} ##

Is it correct?

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