Energy
1. Work
2. Kinetic Energy
3. Work-Energy Principle
4. Friction
5. Potential Energy
6. Conservation of Energy
©2013 Robert Chuckrow
1. Work
• Work W is defined as the part of the force in
the direction of the motion multiplied by the
distance moved: W = F// x d. Note: The part
of the force perpendicular to the motion does
no work.
• Question: Can work ever be negative?
Answer to Q. 1, and a new Question
Answer: Yes, work done by a force is
negative if the direction of the force doing the
work is opposite to that of the motion (slowing
the object down).
Question 2: Can a force exerted on a moving
object ever do zero work?
Answer to Q. 2, and a new Question
• Answer: Yes, a force exerted on a moving
object can do zero work if it is perpendicular
to the motion.
• Question 3: Are there other cases in which a
force exerted on an object does zero work?
Answer to Question 3
• Answer: Yes, a force exerted on a stationary
object does zero work.
• Summary: (a) The work done by a force is
negative when the direction of the force is
opposite to that of the motion. (b) A force
does zero work if it is perpendicular to the
motion. (c) A force does zero work if it is
exerted on a stationary object.
2. Kinetic Energy
The Kinetic Energy (KE) of a mass m,
moving with speed v is defined:
KE  mv.
Question: By what factor does the KE
of an object change if: (a) its mass is
doubled, but its velocity remains the
same? (b) its velocity is doubled, but its
mass remains the same?
Answer
Recall, KE  mv.
(a) If an object’s mass is doubled, keeping its velocity
the same, its KE doubles. (b) If an object’s velocity is
doubled, keeping its mass the same, its KE
quadruples.
3. Work-Energy Principle
The Work-Energy Principle: The work done by all
forces on an object equals its change in kinetic
energy.
Worktotal = Change in KE
Think: Check the consistency of the above principle
with Newton’s first and second laws.
4. Friction
When an object moves on a “rough” surface, the direction of the
force of friction is always opposite to that of the motion.
Consequently, friction does negative work. When friction causes
a moving object to slow down, the negative work done by friction
reduces that object’s KE.
It might seem that the energy of the moving object is thereby
totally lost, but actually, it becomes microscopic KE; namely, the
random jiggling of molecules of the object and surface
increases. That is, their thermal energy increases (their
temperature rises). Because it is random, thermal energy is very
hard to retrieve, so as far as mechanical energy is concerned, it
is lost.
5. Potential Energy
• Lift a mass m through a height h. The work I do will
be mg x h. Where did the energy go? Answer: It is
potentially available because, if I drop the mass,
gravity will do mg x h of work on the mass—the same
amount of work that it took to lift it. Therefore, by my
lifting the mass, the energy I expended was not lost
but went into potential energy = mgh.
• Note: The word potential comes from the word potent
(having power), so potential means having power that
has not yet been brought into being.
6. Conservation of Energy
We also say that during its way down, the falling mass lost
potential energy (PE), which was converted into kinetic energy
(KE). Thus, in this case, where gravity is the only force doing
work, mechanical energy (PE + KE) is conserved (not lost).
Example: When you throw a ball vertically upward, the work
done by your hand gives it kinetic energy. As the ball rises, it
loses KE and gains PE. When it comes to a stop at its highest
point, it has only PE. As it start to fall, the PE is converted back
into KE. If there were no air friction, when it reached the level
where it left your hand, it would have the same KE again.