Bertozzi investigated how the kinetic energy of electrons varies with speed - AQA - A-Level Physics - Question 4 - 2022 - Paper 7

The relationship between kinetic energy (KE) and rest energy (E₀) can be given by the equation:

$KE = E - E₀$

To find the speed, we can use the formula:

$KE = \frac{1}{2}mv^2$

At the point where kinetic energy equals the rest energy, we have:

$E₀ = mc^2$

Setting them equal gives:

$\frac{1}{2}mv^2 = mc^2$

From this, we can simplify and solve for speed, leading to:

$v = \sqrt{2c^2} = c$

The observed mass of an object is related to its energy as described by the equation:

$E = mc^2$

When a spring is stretched, its potential energy increases, which can lead to an increase in its observed mass. This is sometimes viewed as an increase in the energy of the system, thereby suggesting that the mass associated with the energy contributes to the total mass observed.

Moreover, when an object is stretched, it appears as an increase in observed mass due to the energy added to the system. Treating this change in mass under relativistic terms reveals that the difference in observed mass is negligible as neutral.