Question

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?

Answer 1

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