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Can energy be negative? I don't think \(E_k\) will be negative because \(E_k=\frac{1}{2}mv^2\), mass cannot be negative but how about \(E_g\)? it's possible right? \(E_g=mg\Delta y\) because \(\Delta y\) can be negative.. energy is a scalar quantity, so what does it mean if it is negative?

Physics
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Answer this: Is energy a vector quantity?
And I think maybe try dimensional analysis.
Not stating this as if I have more knowledge, but I think maybe that's how you get it.

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Damn right I got this typically we talk about energy as the ability to perform work. The amount of energy something contains depends on many different parameters of the system in question. For example, a container of hot liquid can be hooked up to a heat engine and the heat can be pumped to another reservoir and power the engine in the process, resulting in work. The amount of energy depends on the amount of liquid, the temperature, etc. There is also energy that is accessible by the annihilation of particles and antiparticles. In this case the energy is the sum of the mass of the two particles plus any energy they had in their velocities relative to each other. In the first example, once the two reservoirs of liquid reached equilibrium with each other and the engine, no more energy was available. The engine could perform no more work. Can we say that the energy is negative in any way? Sure, we can say that to get each reservoir back to their initial temperatures would require X amount of energy, and thus the system contains negative energy with respect to our end goal. Does this system have negative mass? Only if you compare the mass of the system before and after. If we measured the mass of the system we would ALWAYS measure a positive amount of mass. The 2nd example is similar. We can say that it would require energy to get 2 photons to interact and create an electron and positron. Again, we can say that a particular way the system can be set up would require an input of energy and thus it would have "negative" energy. But, like the 1st example any measurement of mass would always be positive.
It all depends on how you define energy Potential energy can be negative and usually it is any attractive force has a negative potential energy if you take an electron and positron together, the total energy shrinks as you move them closer together, because the coulomb potential becomes more negative. A bound system will have the sum of potential energy and kinetic energy less than zero. However, the total energy, including the individual masses, is still positive. The total energy of any isolated system should be positive or else these systems could spontaneously appear anywhere and the vacuum would not be stable.
http://www.physicsforums.com/showthread.php?t=607736
Energy can be defined to be negative. Gravitational potential energy is defined as negative because it's a bound state, it'd take energy to remove it from that state.
Something being negative doesn't mean it's a vector. Charge can be negative or positive, but it's not a vector.
aah thanks :)

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