Question

When negative and positive works cancel, does this mean that the energy has been destroyed? For example if you spend 2 Jules of energy to raise the speed of a particle to 10 m/s and then spend another 2 Jules to stop it, where did the 4 Jules go?

Answer 1

Hey check this

The law of conservation of energy states that energy can not be created or destroyed, it can merely be changed from one form of energy to another. Energy often ends up as heat, which is thermal energy (kinetic energy, really) of atoms and molecules. Kinetic friction, for example, generally turns energy into heat, and although we associate kinetic friction with energy loss, it really is just a way of transforming kinetic energy into thermal energy.

http://physics.bu.edu/~duffy/py105/Energy.html

Answer 2

Energy cannot be transformed,so your 4 joules merely just changed form.

Answer 3

I meant destroyed, energy cannot be destroyed,lol

Answer 4

The 4 Jules did not transform to heat, so what did it turn into?

Answer 5

When you stop the body, you do not SPEND 2 joules, on the contrary, you GAIN two joules.
So you take back again what you have put in the system.

If you do this by using a spring it's a simple exchange between kinetic and potential energy.
If you use your muscles, the energy will eventually be dissipated as heat in your muscles; this is why you have the false impression that your are providing work to the system.
Actually, you are only gaining its energy in order to degrade it into heat.

Answer 6

shayanpn, relate to the concept of mechanical energy, where it is the sum of kinetic and potential energy. Remember that in Physics, the law of conservation of energy states that "energy can be neither created nor be destroyed but transformed," and in an isolated system, total energy remains constant. Therefore, in an isolated system, the equation: \[MEi=MEf\] is relevant. The "i" subscript represents initial mechanical energy while the "f" represents final mechanical energy. HOWEVER, in your given scenario, the system you're asking of is NOT isolated. The equation: \[MEi+Wnc=MEf\] applies. The W represents work, a scalar quantity, while the "nc" subscript represents non-conservative. If it did not transform into heat, it has to be another non-conservative (work) force.