Velocity (v/c)0.00.51.0cEnergy (E)
Relativistic Energy (E) Newtonian Energy Prediction

Live Telemetry & Summary

Observe the divergence of the energy curves. At low speeds ($v < 0.3c$), Newton's prediction matches relativity almost perfectly. However, as speed approaches the speed of light $c$, the relativistic curve shoots up vertically toward infinity, showing why no amount of energy can accelerate a mass to $c$.

Lorentz Factor (ฮณ):1.2500x
Rest Mass Energy (Eโ‚€):2.00 J
Relativistic Kinetic Energy (K_rel):0.500 J
Total Relativistic Energy (E):2.500 J
Newtonian Kinetic Energy Prediction:0.360 J

Variable Adjuster

Velocity (v/c)0.6c
00.99
Rest Mass (mโ‚€)2kg
110

Mass-Energy Equivalence

MEEQ

Mass-Energy Equivalence states that mass and energy are interchangeable. The total energy of a moving object consists of its rest mass energy and its relativistic kinetic energy. As an object's velocity approaches c, its relativistic kinetic energy and total energy approach infinity, making it impossible for massive objects to reach the speed of light.

E=ฮณm0c2=E0+Krel,E0=m0c2E = \gamma m_0 c^2 = E_0 + K_{rel}, \quad E_0 = m_0 c^2

Whiteboard Solver Steps

Step 1

Rest Energy (Eโ‚€)

Every resting object contains an inherent amount of energy proportional to its mass.

E0=m0c2=2.00โ‹…12=2.00E_0 = m_0 c^2 = 2.00 \cdot 1^2 = 2.00
Step 2

Total Relativistic Energy (E)

As speed increases, the total energy of the object increases by the Lorentz factor ฮณ.

E=ฮณm0c2=1.2500โ‹…2.00=2.5000E = \gamma m_0 c^2 = 1.2500 \cdot 2.00 = 2.5000
Step 3

Relativistic Kinetic Energy (K_rel)

At low speeds, this matches classical KE, but approaches infinity as velocity v approaches c.

Krel=(ฮณโˆ’1)m0c2=(1.2500โˆ’1)โ‹…2.00=0.5000K_{rel} = (\gamma - 1) m_0 c^2 = (1.2500 - 1) \cdot 2.00 = 0.5000
Step 4

Classical Kinetic Energy (K_class)

The Newtonian kinetic energy prediction which becomes inaccurate at relativistic speeds.

Kclass=12m0v2=0.5โ‹…2.00โ‹…0.602=0.3600K_{class} = \frac{1}{2} m_0 v^2 = 0.5 \cdot 2.00 \cdot 0.60^2 = 0.3600