Question

# Usually the agreement between the theoretical and measured values for momentum is better than the agreement...

Usually the agreement between the theoretical and measured values for momentum is better than the agreement between theoretical and measured values for kinetic energy? Why it this?

I'll try to explain the phenomenon for both large to very small bodies. The momentum for large bodies is measured as:

While the kinetic energy is defined as:

The problem here comes with the velocity measurement, this has a error asociated so the uncertainty for both measurements are:

As you can see the error for kinetic energy is larger because implies much larger quantities.

Another way to look at it is that the kinetic energy depends on the momentum:

So the uncertainty of the kinetic energy depends on the momentum

For relativistic purposes is similar:

The energy depends on the momentum so the uncertainty is this measurement depends on the momentum uncertainty

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