AP Physics C Electricity and Magnetism: Relativistic Kinetic Energy Questions

📚 Quick Study Guide

• ⚛️ Relativistic Kinetic Energy: The kinetic energy of a particle moving at relativistic speeds.
• 📏 Lorentz Factor: $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $v$ is the velocity of the particle and $c$ is the speed of light.
• ⚡ Total Energy: $E = \gamma mc^2$, where $m$ is the rest mass of the particle.
• 💡 Rest Energy: $E_0 = mc^2$, the energy equivalent of the mass of the particle when it is at rest.
• 🚀 Kinetic Energy: $K = E - E_0 = (\gamma - 1)mc^2$
• 📐 Important Note: When $v << c$, the relativistic kinetic energy approaches the classical kinetic energy $K = \frac{1}{2}mv^2$.

Practice Quiz

1. A particle has a rest mass of $m$ and is moving at a speed of $0.8c$. What is its relativistic kinetic energy?
   1. $0.25mc^2$
   2. $0.67mc^2$
   3. $0.75mc^2$
   4. $1.67mc^2$
2. An electron has a kinetic energy of $0.511 \text{ MeV}$. What is its total relativistic energy, given that its rest energy is $0.511 \text{ MeV}$?
   1. $0.511 \text{ MeV}$
   2. $1.022 \text{ MeV}$
   3. $1.533 \text{ MeV}$
   4. $2.044 \text{ MeV}$
3. A proton has a kinetic energy equal to its rest energy. What is the Lorentz factor $\gamma$ for this proton?
   1. 0
   2. 1
   3. 2
   4. 3
4. A particle's kinetic energy is twice its rest energy. What is the particle's speed in terms of $c$?
   1. $\frac{\sqrt{3}}{2}c$
   2. $\frac{1}{2}c$
   3. $\frac{\sqrt{2}}{3}c$
   4. $\frac{1}{3}c$
5. What is the kinetic energy of an electron moving at $v = 0.9c$, given its rest energy $E_0 = 0.511 \text{ MeV}$?
   1. $0.415 \text{ MeV}$
   2. $0.511 \text{ MeV}$
   3. $0.668 \text{ MeV}$
   4. $1.179 \text{ MeV}$
6. A particle has a relativistic kinetic energy of $3mc^2$. What is its total energy?
   1. $2mc^2$
   2. $3mc^2$
   3. $4mc^2$
   4. $5mc^2$
7. If the kinetic energy of a particle is 4 times its rest energy, what is the value of the Lorentz factor $\gamma$?
   1. 2
   2. 3
   3. 4
   4. 5