If a body is at rest at Earth's surface, can we say that its kinetic and potential energy are $0$ simultaneously?

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Solution 1

Yes, absolutely.

Potential energy is not a measurable physical quantity. What can be measured are differences in potential energy. So, if you compare the potential energies of a given mass at the Earth's surface and $100 \, \mathrm{m}$ above the surface, you cannot choose their difference, because that is governed by the laws of physics. However, you can freely choose to assign any point in space a specific potential energy (for the mass $m$). You could define that $m$'s potential energy at the surface is $0$, or $1234 \, \mathrm{J}$, or any other value.

Kinetic energy of a point particle of mass $m$ is defined by $\frac{mv^2}{2}$, where $v$ is the velocity. "The velocity with respect to what," you may ask. The choice is, again, yours to make; for different frames of references, you get different speeds and kinetic energies, and different notions of "rest". However, as long as $m$ is not accelerating (and $m\ne 0$), there is always a reference frame in which $v=0$ and thus $E_{\textrm{kin}}=0$.

So yes, for a body at rest (with regard to an inertial frame) at the surface (or any other point), you could very well claim that it has zero potential and kinetic energy.

Solution 2

It all depends on where you have set your coordinate system. If it is on the earths surface then yes but if you set it say on the sun then no.

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Updated on August 03, 2020

Comments

  • Qmechanic
    Qmechanic over 3 years

    If a body is at rest at Earth's surface, can we say that its kinetic energy $E_{\textrm{kin}}=0$, and its potential energy $E_{\textrm{pot}}=0$ also? Because its velocity $v$ and height above ground $h$ are zero.

  • RQM
    RQM over 8 years
    The choice of coordinate system does not influence the potential energy at all. The choice of a reference point and reference value for the potential energy, which is unrelated to the coordinate system is what matters. However, the choice of the inertial frame does influence the kinetic energy's value.
  • SAKhan
    SAKhan over 8 years
    If you attach your coordinate system to the sun you are in fact letting the earth have a kinetic energy and thus it would not be zero. As regards potential energy this too will change since the earth distance from the sun does not remain constant. The potential energy difference from a point on the surface of the earth to another point a height h will however not be effected. Philosopher is not asking for the difference of potential energy but the exact value.
  • RQM
    RQM over 8 years
    We do agree on the kinetic energy being dependent on the inertial frame it is measured in. However, the potential energy still does not depend on the choice of the coordinate system. If you, suddenly, include the Sun and its gravitational field into the scenario, of course a point fixed at Earth's surface will undergo a change in potential energy as that point moves towards or from the Sun. However, that would also be true if you chose a coordinate system fixed at Earth's surface. What makes the difference is you altering the problem, not you choosing a specific coordinate system.
  • ACuriousMind
    ACuriousMind about 7 years
    What does this add over the already existing answers?
  • Sanya
    Sanya about 7 years
    Welcome on Physics SE :) While we certainly all appreciate your eagerness to contribute, posting answers on old threads should however be restricted to cases in which a substantial new contribution is made.
  • Mitchell
    Mitchell over 6 years
    What do mean by "a stable body" ?