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

To find the speed at which the kinetic energy (KE) of a particle equals its rest energy (E₀), we use the relationship:

$KE = E_{total} - E_{rest}$

In relativistic physics, the total energy can be expressed as:

$E_{total} = \gamma m_0c^2$

Where (\gamma = \frac{1}{\sqrt{1 - (v^2/c^2)}}). Set the kinetic energy equal to the rest energy:

$\frac{1}{2} m v^2 = m_0c^2$

Solving this gives speed (v = 0.87c) or (v = 2 \times 10^8 , m/s).

The mass of a spring is related to energy through the equation:

$E = mc^2$

When an object is stretched, this appears as an increase in observed mass. In the case of a spring gaining elastic potential energy, the observed mass must also increase, as the energy stored in the spring translates into an effective increase in mass due to the added potential energy.