**An Elastic Collision**Demonstrate that for a perfectly elastic collision between two objects with masses \( m_1 \) and \( m_2 \) and initial velocities \( v_1 \) and \( v_2 \), the final velocities \( v'_1 \) and \( v'_2 \) are:\[v'_1 = v_1 \left( \frac{m_1 - m_2}{m_1 + m_2} \right) + v_2 \left( \frac{2m_2}{m_1 + m_2} \right)\]and\[v'_2 = v_1 \left( \frac{2m_1}{m_1 + m_2} \right) + v_2 \left( \frac{m_2 - m_1}{m_1 + m_2} \right)\]

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Demonstrate that for a perfectly elastic collision between two objects with masses m1 and m2 and initial velocities vi and v2, the final velocities v and v are: (m1 – m2 2m2 vị = v1 + v2 \m1 + m2. \m1 + m2. and 2m1 m1 (M2 + v2 \m, + m2. v2 = v1 \M1 + m2.

Demonstrate that for a perfectly elastic collision between two objects with masses m1 and m2 and initial velocities vi and v2, the final velocities v and v are: (m1 – m2 2m2 vị = v1 + v2 \m1 + m2. \m1 + m2. and 2m1 m1 (M2 + v2 \m, + m2. v2 = v1 \M1 + m2.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**An Elastic Collision**

Demonstrate that for a perfectly elastic collision between two objects with masses \( m_1 \) and \( m_2 \) and initial velocities \( v_1 \) and \( v_2 \), the final velocities \( v'_1 \) and \( v'_2 \) are:

\[
v'_1 = v_1 \left( \frac{m_1 - m_2}{m_1 + m_2} \right) + v_2 \left( \frac{2m_2}{m_1 + m_2} \right)
\]

and

\[
v'_2 = v_1 \left( \frac{2m_1}{m_1 + m_2} \right) + v_2 \left( \frac{m_2 - m_1}{m_1 + m_2} \right)
\]

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