# Kinetic energy of an object

We know that motion is relative. So let an object(o) be moving with a certain velocity with respect to an object (A).If another object (B) is moving with respect to (A) at a given moment and they calculate the kinetic energy of the (same) object(o), they will get different answers.How is that possible?

As others have already said, kinetic energy is reference frame dependent. The same applies to gravitational potential energy.

It should be pointed out, however, we are talking about kinetic energy at the macroscopic level. It is not necessarily the case at the microscopic level.

For example, I have a box resting on a table containing an ideal gas which I define as my system. The gas molecules have some average value of random translational kinetic energy which is reflected by the temperature of the gas. This kinetic energy is the internal kinetic energy of my system.

I set the box in motion. The temperature of the gas does not change. The internal kinetic energy of my system does not change. It is reference frame independent. But macroscopically, the overall mass of the gas (my system) has acquired kinetic energy that is reference frame dependent. We call this the system’s external kinetic energy because it depends on an external frame of reference.

The total energy of the system is the sum of its internal and external kinetic and potential energy. In general the external energy of the system depends on an external frame of reference. The internal energy does not.

Hope this helps.

You have successfully discovered that the kinetic energy depends on the reference frame.

Further to this, is that the fact that kinetic energy is conserved is not reference frame-dependent.

When one balances the conservation of energy equation in separate frames, one would find different absolute values for the total energy, but you will also see that the energy before and after a, say, elastic collision will be that same value.

See the definition of kinetic energy involves the term speed as well as kinetic energy is a reference dependent quantity.The term $$v$$ in the definition of kinetic energy is defined as the speed observed of the concerned body relative to the reference frame.