State the equation for the total energy of a particle of rest mass m₀ moving at speed v.

E = m₀c²/√(1 − v²/c²), where m₀ is the rest mass, v is the speed of the particle and c is the speed of light.

What is the rest mass m₀ of a particle?

The mass of the particle measured in a frame of reference in which it is at rest.

How is the kinetic energy of a particle found from its total energy in special relativity?

Kinetic energy = total energy − rest energy, so Eₖ = m₀c²/√(1 − v²/c²) − m₀c².

What does mass-energy equivalence imply happens to the mass of a particle when it gains kinetic energy?

Its mass increases, because any increase in energy E corresponds to an increase in mass of E/c².

AQA A-Level Physics 7408

Measurements and Their Errors

Topic overview Use of SI units and their prefixes Limitation of physical measurements Estimation of physical quantities

Particles and Radiation

Topic overview Constituents of the atom Stable and unstable nuclei Particles, antiparticles and photons Particle interactions Classification of particles Quarks and antiquarks Applications of conservation laws The photoelectric effect Collisions of electrons with atoms Energy levels and photon emission Wave-particle duality

Waves

Topic overview Progressive waves Longitudinal and transverse waves Principle of superposition of waves and formation of stationary waves Interference Diffraction Refraction at a plane surface

Mechanics and Materials

Topic overview Scalars and vectors Moments Motion along a straight line Projectile motion Newton's laws of motion Momentum Work, energy and power Conservation of energy Bulk properties of solids The Young modulus

Electricity

Topic overview Basics of electricity Current–voltage characteristics Resistivity Circuits Potential divider Electromotive force and internal resistance

Further Mechanics and Thermal Physics

Topic overview Circular motion Simple harmonic motion (SHM)Simple harmonic systems Forced vibrations and resonance Thermal energy transfer Ideal gases Molecular kinetic theory model

Fields and Their Consequences

Topic overview Fields Newton's law Gravitational field strength Gravitational potential Orbits of planets and satellites Coulomb's law Electric field strength Electric potential Capacitance Parallel plate capacitor Energy stored by a capacitor Capacitor charge and discharge Magnetic flux density Moving charges in a magnetic field Magnetic flux and flux linkage Electromagnetic induction Alternating currents Transformers

Nuclear Physics

Topic overview Rutherford scattering α, β and γ radiation Radioactive decay Nuclear instability Nuclear radius Mass and energy Induced fission Safety aspects

AstrophysicsOptional topic

Topic overview Astronomical telescope consisting of two converging lenses Reflecting telescopes Single dish radio telescopes, I-R, U-V and X-ray telescopes Advantages of large diameter telescopes Classification by luminosity Absolute magnitude, M Classification by temperature, black-body radiation Principles of the use of stellar spectral classes The Hertzsprung-Russell (HR) diagram Supernovae, neutron stars and black holes Doppler effect Hubble's law Quasars Detection of exoplanets

Medical PhysicsOptional topic

Engineering PhysicsOptional topic

Topic overview Concept of moment of inertia Rotational kinetic energy Rotational motion Torque and angular acceleration Angular momentum Work and power First law of thermodynamics Non-flow processes The p–V diagram Engine cycles Second Law and engines Reversed heat engines

Turning Points in PhysicsOptional topic

Topic overview Cathode rays Thermionic emission of electrons Specific charge of the electron Principle of Millikan's determination of the electronic charge, e Newton's corpuscular theory of light Significance of Young's double slits experiment Electromagnetic waves The discovery of photoelectricity Wave–particle duality Electron microscopes The Michelson-Morley experiment Einstein's theory of special relativity Time dilation Length contraction Relativistic mass and energy

ElectronicsOptional topic

Topic overview MOSFET (metal-oxide semiconducting field-effect transistor)Zener diode Photodiode Hall effect sensor Difference between analogue and digital signals LC resonance filters The ideal operational amplifier Inverting amplifier configuration Non-inverting amplifier configuration Summing amplifier configuration Real operational amplifiers Combinational logic Sequential logic Astables Principles of communication systems Transmission media Time-division multiplexing Amplitude (AM) and frequency modulation (FM) techniques

Turning Points in Physics

Relativistic mass and energy

3 things to know
Paper 3, section B

Overview

The relativistic equations for total energy, rest energy and mass, how mass and kinetic energy vary with speed, why a particle with mass never reaches the speed of light, and Bertozzi's direct test of kinetic energy against speed.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Process

Calculate the total energy and kinetic energy of an electron moving at 0.80c (rest energy of electron = 0.511 MeV).

Process

State the equation for the rest energy of a particle.

Process

State the equation for the relativistic mass of a particle moving at speed v.

Questions from this subtopic

Each one with the model answer underneath.

1
State the equation for the total energy of a particle of rest mass m₀ moving at speed v.
Model answer
E = m₀c²/√(1 − v²/c²), where m₀ is the rest mass, v is the speed of the particle and c is the speed of light.
2
What is the rest mass m₀ of a particle?
Model answer
The mass of the particle measured in a frame of reference in which it is at rest.
3
State the equation for the rest energy of a particle.
Model answer
E₀ = m₀c².
4
State the equation for the relativistic mass of a particle moving at speed v.
Model answer
m = m₀/√(1 − v²/c²).
5
How is the kinetic energy of a particle found from its total energy in special relativity?
Model answer
Kinetic energy = total energy − rest energy, so Eₖ = m₀c²/√(1 − v²/c²) − m₀c².
6
What does mass-energy equivalence imply happens to the mass of a particle when it gains kinetic energy?
Model answer
Its mass increases, because any increase in energy E corresponds to an increase in mass of E/c².

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