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We know that energy is the ability to do work and we know that the work can be negative as cos theta of the angle in which force is applied can be negative. Moreover we take the units of work and energy as equal. So can we say that there exists negative energy. Tell me if my consideration is wrong.

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To put this simply, the work-energy theorem states that

The work performed by a force $\mathbf F$ over a distance $\Delta \mathbf r$, $W=\mathbf F\cdot\Delta \mathbf r$, is equal to the change in kinetic energy $\Delta E_\mathrm{kin}$ of the relevant object.

If the inner product $\mathbf F\cdot\Delta \mathbf r$ is negative, the force is acting in the opposite direction of the object's velocity $\mathbf v=\Delta \mathbf r/\Delta t$, the change in kinetic energy $\Delta E_\mathrm{kin}$ is negative, and the object's kinetic energy decreases. This is colloquially known as "braking".

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  • $\begingroup$ Thanks for sharing this theorem. I was not about this theorem and didn't now it was change in displacement which even if is negative makes the energy less and not negative. Now I understood and thanks once again to end my confusion. $\endgroup$ Commented Jun 10, 2016 at 10:42
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No, we can't. I assume that you are talking about a moving object and therefore kinetic energy. You Can apply a resistive force, therefore slowing the object and reducing its energy. But as soon as the object reaches zero energy (read: kinetic energy), the body will be at rest. If you continue to apply the same force, from Newton's 2nd principle, the body will accelerate in the same direction of the Force thus leasing to a value

$\cos\theta=\cos0=1$

The work will be now positive and the energy will increase.

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  • $\begingroup$ But what about negative work ? While doing a negative work the energy is what : Negative or Positive? That's what I'm asking. $\endgroup$ Commented Jun 10, 2016 at 10:29
  • $\begingroup$ @AbhinavDhawan The energy of what exactly? $\endgroup$
    – lemon
    Commented Jun 10, 2016 at 10:29

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