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Why Energy is conserved

The main idea of this page is to elaborate a little more on why energy is conserved and to understand it is a more simplified way. The thought about the fact that energy is neither created nor destroyed can be a mind boggling one simply because energy always seems to be coming from somewhere, so where does it go? The main idea behind why energy is conserved and neither created or destroyed is that it is just transferred to other forms. The first law of Thermodynamics states that the amount of energy in the universe is a constant, fixed amount. Is doesn’t go away and it doesn’t appear randomly.

A Mathematical Model

The mathematical equations that are used to model this topic include many different equations, but they all relate back to the energy principle, ΔEsystem = WSurr +Q. W is the work cone by the surroundings and Q is the thermal energy. The change in energy will be always zero because energy is transferring to other forms of energy within the system or surroundings. Other Important equations include: K = ½mv2, ΔUg = mgΔh, E = K + U, Ei = Ef, Ki + Ui = Kf + Uf, W = F̅Δs cos θ.

A Computational Model

This video shows how energy in conserved in a variety of situations. http://study.com/academy/lesson/first-law-of-thermodynamics-law-of-conservation-of-energy.html

Examples

Simple

Question: State the law of conservation of energy and explain the law by taking an oscillating simple pendulum as an example.

Answer: The law of conservation of energy says that energy can neither be created nor destroyed but can be transformed from one form to another. In the case of the simple pendulum when the bob is as far to the left as it can be, it has maximum potential energy as it is raised with respect to the mean position, but its kinetic energy is zero as the bob stops oscillating for a fraction of a second before moving towards the right. When the bob reaches the mean position, it has a zero potential energy but maximum kinetic energy (maximum velocity too). When the bob of the pendulum swings to extreme right, it has the maximum potential energy but zero kinetic energy.

Middling

Question: A nail becomes warm when it is hammered into a plank. Explain why.

Answer: A raised hammer has potential energy due to its position above the ground, gravity acts as acceleration. When the hammer comes down and strikes the head of the nail, the potential energy is transformed into kinetic energy. If we continue hitting the nail to secure it, the kinetic energy of the hammer is transferred to the molecules of the material of the nail. The heat content of the body is the total energy that the body possesses (Q in the equation above). As the heat content of the body increases, the nail becomes warm.

Difficult

Question: A stone of mass 10 g placed at the top of a tower 50 m high is allowed to fall freely. Show that law of conservation of energy holds good in the case of the stone. Answer: In this case we have to prove that total energy at A, B and C is the same.

Height = 50 m Potential energy at A = mgh = 0.01 x 9.8 x 50 = 0.01 x 98 x 5 = 4.9 J

= 0

Total energy at A = potential energy + kinetic energy= 4.9 + 0 Total energy at A = 4.9 J ...(1) At B Height from the ground = 40 m Potential energy = mgh = 0.01 x 9.8 x 40 = 0.01 x 98 x 4 Potential energy at B = 3.92 J

To calculate v we make use of III equation of motion,

Here, u = 0, a = 9.8 m/s2 and S = 10 m

= 0.98 J Total energy at B = potential energy + kinetic energy

= 3.92 + 0.98 Total energy at B = 4.90 J (2) At C Height from the ground = 0 Potential energy at C = mgh

To calculate v we use III equation of motion,

Here, u = 0, a = 9.8m/s2 and S = 50 m

= 4.9 J Total energy at C = potential energy + kinetic energy = 0 + 4.9 Total energy at C = 4.9 J (3) The total energy at A, B and C is 4.9 J. This means that law of conservation of energy holds good in the case of a stone falling freely under gravity.

References

http://study.com/academy/lesson/first-law-of-thermodynamics-law-of-conservation-of-energy.html http://www.tutorvista.com/content/science/science-i/work-energy/question-answers-2.php#question-21