Momentum and Energy

Rest Energy Uses the Speed Limit

The toy speed limit makes rest energy an exact hundred joules. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Rest energy uses the speed limit

Mass 4 kg and toy speed limit 5 m/s give rest energy 100 J.

Erest=4⋅52=100E_{\rm rest}=4\cdot5^2=100
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energy

Gamma scales rest energy

Gamma gives total energy 125 J.

100⋅54=125100\cdot\frac{5}{4}=125
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energy