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Conservation of Energy

Sometimes physicists use strange words to mean normal things (They say "scalar" when they mean "number", for example.) Sometimes they use normal words to mean normal things, but they mean it a little differently; for example, force and energy. Sometimes they use normal words to mean something completely different from the standard meaning, and this leads to much confusion.

In common parlance, "conservation of energy" means frugal use of energy, a responsibility of good citizens.

In physics, "conservation of energy" means that energy, by decree of Nature, cannot be created from nothing nor destroyed, but it can flow from one form to another or from one place to another. If we calculate the total energy in a closed system at one time, the total energy some time later will be the same. Energy is conserved.
Energy Conservation
The energy in a closed system is conserved, that is, constant in time.

In the table are listed some of the energy forms which may appear on the MCAT.
type of energy description
kinetic bulk motion
potential object's position
gravitational potential object's position in gravity
mechanical MCAT word for kinetic + potential
chemical batteries, muscles, etc.
electrical moving electrons
nuclear energy in the nucleus, radioactivity, fission reactor
sound pressure waves
light electric, magnetic field waves
heat random motion of particles


The principle of energy conservation in the previous box is the Grand Statement, almost too grand to be useful in most problems. For doing problems it is better if the number of kinds of energy considered are few, like two: kinetic and potential.
Energy Conservation, Simple Statement
If there is no friction, or crunching, or nonpotential forces (except forces perpendicular to the motion), then


Use this principle in problems in which gravity does all the work.


The woman of Section B lets go of the cart at the top of the incline. The cart rolls to the bottom.

  1. What is the final velocity?
  2. Describe the energy flow from start to finish.
  1. First, we DRAW A DIAGRAM (Figure 9-6). We need to check all the forces. Although the normal force is nonpotential, it is perpendicular to the motion, so it does no work. The gravitational force is a potential force. We conclude that the simple version of energy conservation applies. Thus we write

EK1 + EP1 = EK2 + EP2


0 + mgh = 1/2 mv22 + 0


Solving for v2 yields



..\art 9 jpg\figure 9-tf.jpg
Figure 9-6



Note that the mass has dropped out. This should remind you of the situation in which a massive object and a light object are dropped at the same time. They fall at the same rate with the same acceleration and same velocity as each other, all the way down.
  1. The energy flow is chemical (woman's muscles) to potential to kinetic.


A pendulum of length 0.7 meters is pulled so that its bob (0.2 kg) is 0.1 meters higher than its resting position. From that position it is let go.
  1. What is its kinetic energy at the bottom of the swing?
  2. What is its velocity at the bottom of the swing?
  3. What is the work done by the string tension during the swing from start to the bottom?
  1. First, we DRAW A DIAGRAM (Figure 9-7).

..\art 9 jpg\figure 9-tg.jpg
Figure 9-7



We check the forces. The tension is perpendicular to the direction the bob is moving at every moment. This is true even though the bob is moving in an arc and the tension is changing direction during the swing. Thus tension does no work. Gravity is a potential force, so equation (6) applies and we can write
EK1 + EP1 = EK2 + EP2,
0 + mgh1 = EK2 + 0,
EK2 = mgh1
= (0.2 kg)(10 m/s2)(0.1) = 0.2 J
  1. Now, we obtain the final velocity from
  1. We have already decided that the tension does no work.


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