12.3.5

# Mass & Energy

Test yourself

## Mass and Energy Equivalence

Mass and energy can be shown to be equivalent.

### Mass varies with speed

• As an object gains velocity, it also gains mass.
• This is given by the formula:
• $m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$
• m is the moving mass.
• $m_0$ is the mass at rest.
• v is the moving velocity.
• c is the speed of light.

### Einstein's relativity

• Einstein extended relativistic mass to produce:
• $E = mc^2$.
• This shows that mass and energy are equivalent.

## Bertozzi's Experiment

Bertozzi’s experiment sought to provide experimental proof that mass increases with velocity.

### Method

• Bertozzi used linear particle accelerators to accelerate electrons into an aluminium disc.
• He recorded the time taken for the electrons to reach the disc, along with the energy provided to the electron.
• He used the heat generated on the aluminium disc to calculate the final velocity of the electrons.
• He did this by equating heat and kinetic energy.

### Results

• He found that the velocities of the electrons did not continue to increase as he supplied more energy to the electrons.
• Instead, they approached a maximum value of c - the speed of light.
• This is the first evidence of special relativity.