6.3. Energy Conservation http://www.ck12.org
FIGURE 6.17
Mechanical energy transformations on a
skateboarding half-pipe.Mechanical Energy. The total energy- both kinetic and potential- will remain constant as long as there is no friction
and the person does not expend more muscle energy pushing off.
Friction is often referred to as adissipative force. If the skater falls down and skids to a stop, then friction has taken
effect. The friction does negative work, reducing the kinetic energy. The dissipated kinetic energy is turned into
heat energy. This is why rubbing two objects together makes them warmer. Mechanical energy is conserved only
when dissipative forces are absent.
The conservation of mechanical energy can be rephrased as follows: Assuming there aren’t any non-conservative
forces acting upon a system, the initial kinetic and potential energy contained within a closed system equals the final
kinetic and potential energy contained within that system.
Mathematically:
KEi+PEi=KEf+PEf
The initial sum of kinetic energy and potential energy is equal to the final sum of kinetic energy and potential energy.
http://phet.colorado.edu/en/simulation/energy-skate-park
Illustrative Example 1
A 0.145 kg ball leaves the earth with an upward velocity of 15.0 m/s.
a. Qualitatively describe the changes in kinetic and potential energies of the ball during its ascent and descent in
Figure6.18. Take the ground as the point of zero gravitational potential energy.
Answer:At the instant the ball is released, all of its energy is in the form of kinetic energy. As the ball ascends, its
kinetic energy is transformed to gravitational potential energy. When the ball reaches its highest position, its speed is
zero and, therefore, its kinetic energy is zero. All of the energy of the ball is now in the form of gravitational potential
energy. As the ball begins its descent, gravitational potential energy is transformed back into kinetic energy. At all
times the sum of kinetic and potential energy is constant.
b. What is the total energy of the ball at half of its maximum height?
Answer:The total energy of the ball remains constant, so it is irrelevant at which position the total energy of the
ball is found. Therefore: