Mass and energy (A-level only) Flashcards – AQA A-level Physics (7408)

What equation expresses mass–energy equivalence, and what does $c$ represent?

$E = mc^2$, where $c$ is the speed of light in a vacuum.

What is the rest energy of a stationary body with rest mass $m_0$?

$E_0 = m_0c^2$

How are a change in a system’s energy and its corresponding change in mass related?

$\Delta E = \Delta m c^2$

What is the Lorentz factor $\gamma$ for a body moving at speed $v$?

$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

What is the total relativistic energy of a body with rest mass $m_0$ and Lorentz factor $\gamma$?

$E=\gamma m_0c^2$

In the relativistic-mass convention, how is mass $m$ related to rest mass $m_0$?

$m=\gamma m_0$

In the relativistic-mass convention, how is total energy related to relativistic mass $m$?

$E=mc^2$

What is the relativistic kinetic energy of a body with rest mass $m_0$ and Lorentz factor $\gamma$?

$E_k=(\gamma-1)m_0c^2$

How do relativistic mass and kinetic energy behave on graphs against speed, from $v=0$ to $v$ approaching $c$?

Mass starts at $m_0$ and kinetic energy at zero. Both rise increasingly steeply and tend to infinity as $v$ approaches $c$.

What is the approximate relativistic mass of a body when $v\ll c$?

$m\approx m_0$

What is the approximate kinetic energy of a body with rest mass $m_0$ when $v\ll c$?

$E_k\approx\frac{1}{2}m_0v^2$

Can a body with nonzero rest mass be accelerated to $c$ by supplying a finite amount of energy?

No; its required energy tends to infinity as its speed approaches $c$.

How was electron speed determined in Bertozzi’s experiment?

From the time taken to travel a known distance.

How was the energy delivered by the electrons checked in Bertozzi’s experiment?

By measuring the heating of a target.

How did the observed relationship between electron kinetic energy and speed differ from the classical prediction in Bertozzi’s experiment?

As kinetic energy increased, speed approached the speed of light, rather than increasing without limit as the classical expression predicts. This supported the relativistic relationship.