Download Work-Kinetic Energy Theorem (WKET)

607AP Physics
Work-Kinetic Energy Theorem (WKET) & Conservation of Mechanical Energy (COE)
The central ideas that we have covered this year so far and learned how they are reflected in
actual physical situations (i.e., how to use them to solve problems) include:



Newton’s Laws of Motion (NLM) for translation (Fnet = ma) and Kinematics
Work-kinetic energy theorem (WKET),
Conservation of energy (CoE),
Basic Theory
 Work-kinetic energy theorem (WKET),
The theorem states that the total work done by all forces acting on a system changes
the total kinetic energy of the system. If more than one object makes up the system,
the total kinetic energy is the algebraic sum of their individual kinetic energies.

Conservation of Mechanical Energy (COE)
The forces acting on a system can be categorized as Conservative or Nonconservative. Conservative forces are those for which the work done by the force
between an initial position and a final position is independent of the path taken and
depends only on the initial and final positions, e.g gravitational force and spring force.
For such forces, we can define a potential energy (symbol U) associated with the
force:
P.E = U = -W = - ò F(x)dx
U gravity = mgy;
1
U spring = kx 2
2
Potential energy is the energy associated with a specific configuration (how the system is
positioned, how it ‘looks’). The conservation of mechanical energy for a system that also has
non-conservative forces (viz. friction and applied force) acting on it, is:
i
i
f
f
K.E i + Ugravity
+ Uspring
+ Wnon-conservative = K.E f + Ugravity
+ Uspring
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We now need to address when a given physical situation or problem is best described using these
different concepts. Note that these ideas are present in all physical situations and any problem could – in
some sense – be modeled using many different ideas. However, frequently one idea will either best
capture what is happening or will be the simplest way to solve a given problem. You will need to learn how
to find key aspects or indicators that suggest which of these ideas best describe a given problem. Listed
next are some key indicators for WKET or COE type problems.
607AP Physics
Key Indicators
(1)
(2)
A variable force is acting on an object, e.g., a spring or other force that depends on
position/velocity.
The focus is on either an initial or final condition / state and not how rapidly a change
happens. You are given information about an initial or final state (position or velocity)
and/or asked to find about some initial or final state (position or velocity) – but not about
accelerations.
Strategy for WKET
1. Draw a diagram (if only description is provided) of the system. You should be able to
figure out what the system does, how it moves etc.
2. Clearly identify relevant objects and what is known about them: initial/final position and
velocity. Also clearly highlight what is not known and what is to be found.
3. For each object, make a FBD of its interactions with the surroundings and how much
work each Force does on the object – noting that some of these forces will be applied at
right angles to the displacement and will do no work (e.g FN), while others may do an equal
amount of positive and negative work leading to no net work (e.g T in connecting ropes).
Alternatively, it may be possible to compute the net force acting on the object and find
only the net work as
. If several forces are acting at right angles and
especially if their magnitude is not known, then finding the net force may not be useful.
4. With the net work and the initial/final states identified, apply the work-kinetic energy
2
2
theorem: Wnet = DK = 12 mv f - 12 mvi .
Remember to include the work done by all
forces/interactions between an object and its surroundings. In general, the result will
be only one equation with only one unknown which could include one of the following
variables: (a) displacement x, (b) position xf or xi, (c) velocity vi or vf, or (d) the force
needed to explain an observed change.
Strategy for COE
1. Draw a diagram (if only description is provided) of the system. You should be able to
figure out what the system is doing.
2. Identify the initial and final configurations of the system. Has the vertical position of an
object changed? If yes, include gravitational P.E, making sure to capture the entire
change in position. Is the spring compressed/elongated in the initial/final configuration?
If yes, include spring potential energy.
3. If friction or applied force is present, include work done by these forces on the ‘initial’
side of the equation.
4. Only initial and final positions matter, so typically there is no need to break up the
problem into more parts.
Other Important Things to Remember
Whether an object speeds up or slows down depends only on the direction of velocity and
force (if directions same, speeds up; if opposite, slows down). Hence, maximum speed
occurs at the point where the direction of net force on the object changes sign i.e point
where net force is zero.