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 (E) is given by the formula:

$KE = E - ext{rest energy}$

Setting these equal:

rac{1}{2}mv^2 = mc^2

Dividing both sides by m yields:

rac{1}{2}v^2 = c^2

Thus:

$v = c \sqrt{\frac{1}{2}} = 0.707c$

Therefore, the speed is approximately:

$speed = 0.707c ext{ or } 2.1 \times 10^8 m s^{-1}$

The observed mass of the spring changes as it is stretched due to the principle of mass-energy equivalence represented by Einstein’s equation:

$E = mc^2$

When an object is stretched, it gains elastic potential energy, which can be observed as an increase in mass. The difference in observed mass may be negligible, but it is an important concept to understand that mass is related to energy. Thus, when the spring is stretched, the increase in elastic potential energy corresponds to an increase in the observed mass.