AP Physics C Questions on the Energy-Momentum Relation with Answers

📚 Quick Study Guide

• 💡 The energy-momentum relation is a fundamental concept in physics, linking a particle's energy ($E$), momentum ($p$), and rest mass ($m$).
• ⚛️ The relativistic energy-momentum relation is given by: $E^2 = (pc)^2 + (mc^2)^2$, where $c$ is the speed of light.
• 📏 For massless particles (like photons), the relation simplifies to: $E = pc$.
• ⏱️ In non-relativistic cases, kinetic energy $K$ can be approximated as $K = \frac{p^2}{2m}$.
• 🔍 Total energy $E$ is the sum of kinetic energy $K$ and rest energy $mc^2$: $E = K + mc^2$.

🧪 Practice Quiz

1. Question 1: A particle has a momentum of $p$ and a rest mass of $m$. If its total energy is $E$, which of the following equations correctly relates these quantities?
   1. $E = \sqrt{p^2c^2 - m^2c^4}$
   2. $E = pc$
   3. $E = \sqrt{p^2 + m^2}$
   4. $E = \sqrt{p^2c^2 + m^2c^4}$
2. Question 2: A photon has an energy of 3 MeV. What is its momentum? (Note: 1 MeV = $1.602 \times 10^{-13}$ J)
   1. $1.6 \times 10^{-21}$ kg m/s
   2. $1.6 \times 10^{-22}$ kg m/s
   3. $1.6 \times 10^{-23}$ kg m/s
   4. $1.6 \times 10^{-20}$ kg m/s
3. Question 3: An electron has a kinetic energy of 0.5 MeV. What is its relativistic momentum? (Electron rest mass = 0.511 MeV/$c^2$)
   1. 0.97 MeV/c
   2. 1.02 MeV/c
   3. 0.5 MeV/c
   4. 0.25 MeV/c
4. Question 4: If the momentum of a particle is doubled, how does its kinetic energy change in the non-relativistic limit?
   1. It doubles.
   2. It quadruples.
   3. It remains the same.
   4. It halves.
5. Question 5: A proton has a total energy of 2 GeV. If its rest mass energy is approximately 1 GeV, what is its kinetic energy?
   1. 1 GeV
   2. 2 GeV
   3. 3 GeV
   4. 4 GeV
6. Question 6: Which of the following is true for a particle with zero rest mass?
   1. Its energy is zero.
   2. Its momentum is zero.
   3. Its energy and momentum are related by $E = pc$.
   4. It cannot exist.
7. Question 7: A particle's energy is 5 mc². What is the kinetic energy of the particle?
   1. 2 mc²
   2. 3 mc²
   3. 4 mc²
   4. 6 mc²