It's THAT Equation...

We can make the fairly educated guess that the fuel energy enhancement factor is : the same as the time dilation factor.
Thus,

The value of Erest is given by what is probably the most famous equation in physics! Of course, it was that man Einstein who came up with it! It shows that energy and mass are equivalent:

The rest, as they say, is history!

Thus, when the object is moving with respect to an inertial frame, its energy increases by a factor of . Since energy and mass are equivalent, it makes sense that wherever we see m in a familiar equation, we can replace it with m (as is very close to 1 at the low velocities we are used to).

This means that we can increase the energy of a body by increasing its mass (a fancy way of saying that more massive candles burn for longer!).

Conversely we can also increase the mass of a body by increasing its energy, i.e. by giving it a high velocity with respect to another inertial frame.

Activity 2

Try to work out what the approximate mass change would be when the internal energy of water is increased, say, by boiling a kettle, given that the energy required to heat a litre of water from room temperature to boiling point is approximately 300 kJ. How noticeable is this?

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