Collision Equations

Reference from the original Physics I textbook.

Collision Equations

For a one-dimensional elastic collision with body 2 initially at rest, all velocities below are signed components along the collision axis.

${\vec{v}}_{1, f} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} {\vec{v}}_{1, i}$
${\vec{v}}_{2, f} = \frac{2 m_{1}}{m_{1} + m_{2}} {\vec{v}}_{1, i}$

If the two masses are equal:

${\vec{v}}_{1, f} = 0$
${\vec{v}}_{2, f} = {\vec{v}}_{1, i}$

If the mass initially at rest is very large:

${\vec{v}}_{1, f} \approx - {\vec{v}}_{1, i}$
${\vec{v}}_{2, f} \approx \frac{2 m_{1}}{m_{2}} {\vec{v}}_{1, i}$

If the mass initially at rest is very small:

${\vec{v}}_{1, f} \approx {\vec{v}}_{1, i}$
$v_{2, f} \approx 2 {\vec{v}}_{1, i}$

$m_{n} = Mass of body n (kg)$
${\vec{v}}_{n, i} = Initial velocity of body n (m/s)$
${\vec{v}}_{n, f} = Final velocity of body n (m/s)$

Related Glossary Terms

Index

Chapter 4 - Elastic Collisions

Reviewed physics notes (1)

These corrections keep the original lesson’s purpose while fixing errors in the source edition.

These collision formulae are not general vector equations for oblique collisions. — Reference 1

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