Download Mechanical Energy

Mechanical Energy
Where does all this motion come
from?
Where does all this motion come from?
• Insofar as scientists understand our universe,
there are essentially two “substances” that
provide the make up of our existence:
matter & energy
• Thanks in great part to Albert Einstein, perhaps
the wisest scientist the world has known to
date, we know that matter and energy are the
same thing!
• It never ceases to amaze me how the seeming
complexity of nature is in actuality very
simple...
E=
2
mc
Energy
Speed of light
Mass (matter)
Ever heard this? Bet you have, but I bet you never really
knew what it meant...
Let’s analyze the units of this quantity before we go on…
So, back to the question: Where does all
this motion come from?
• Motion is just one manifestation of energy
in our lives.
• Other manifestations include heat, and
electromagnetism, which at the fundamental
level is actually caused by motion (vibration
of charged particles).
• Also, energy can be stored energy via
chemical bonds, springs, gravitational
differentials, and many other sources.
So, energy is movement!
Or, going back and looking at Newton’s
Second Law:
Forces cause accelerations which cause
changes in motion.
This becomes:
Changes in energy result in forces which
change/create motion.
Note: This is glossing over a great deal of complicated physics, but
any physicist will tell you this is the main idea.
The Work/Energy Theorem
Derivation:
W = KE = - PE
What does this mean?
• Well, it sounds crazy, but energy is not
really a real quantity. It is a derived product
of other physical and chemical quantities.
That does not mean that it is not real, it just
means that it is an artificial quantity that we
study because certain properties of this
“energy” variable help us figure stuff out
about the universe.
Types of Energy:
• Kinetic Energy
– Anything moving has kinetic energy.
• Potential Energy
– Stored energy
• e.g., springs, chemical bonds, all matter, objects at
heights, etc…
Kinetic Energy
1 2
KE  mv
2
Potential Energy
• Gravitational PE:
– GPE is understood as the energy difference
caused by the relative heights of different
objects above the ground (at h=0m, GPE = 0 J)
GPE  mgh
• Spring PE:
– Spring PE is the energy stored in a compressed
or stretched spring. It describes the spring’s
tendency to snap back into its original shape.
1 2 Where k, is the spring constant or stiffness of
SPE  kx the spring and x is the displacement of the
2
spring from its neutral position.
The Law of Conservation of
Energy
The total amount of energy in any system is
constant.
Energy can neither be created no destroyed, only
changed to a new form.
This principle is ALWAYS true. There are NO
EXCEPTIONS. (just erroneous assumptions)
Energybefore = Energyafter
Work
Work is the amount of energy used up in a mechanical
process.
W = Fx = KE = - PE
Work-Energy Theorem
Works nicely with the impulse-momentum theorem to
help define a system.
Impulse/Momentum is Newtonian Kinematics (VECTORS)
Work/Energy is Dynamics (SCALAR)
Power
• Power is the RATE at which energy is used.
It has many mathematical forms, but
anytime you see any energy variable
described over a period of time, you are
dealing with power.
• More power does not necessarily mean
more energy…
Units for Energy, etc.
• The SI unit for energy is the Newton-Meter,
also called the Joule (J). It is a
(kg)(m2)/(s2).
• Power is energy over time, so J/s which is
also called a Watt (W) (like a 40 W light
bulb…)
– Be CAREFUL! Capital W is the unit for
power, but as a variable is means work or
energy.
Using conservation of energy to
help solve collision problems:
• New definitions!
– Elastic Collision: A collision where kinetic
energy is conserved.
– Inelastic Collision: A collision where kinetic
energy is not conserved.
– The TOTAL energy, sometimes called the
“mechanical energy” in any system is
conserved in any collision.
Problem:
• How do you solve an elastic collision
system where both objects bounce off of
one another elastically and both objects
continue to move?
• Example:
– Two objects of mass m = 2.4 kg collide in an
elastic collision. The first object is traveling
3.9 m/s to the right and the second is traveling
1.5 m/s also to the right. Find the final
velocities of both objects after an elastic
collision.
How do you solve this?
• Set up your conservation of momentum
equation (m1v1i + m2v2i = …)
– Notice that you have two unknown variables,
v1f and v2f.
• Now set up an equation that indicates
conservation of kinetic energy.
– Notice that you have the same two unknowns.
• Solve the system of two equations either by
substitution, or by elimination.
REMEMBER!
• You may only conserve kinetic energy in an
elastic collision!
• Certain systems in which objects collide
inelastically may be solved using
conservation of energy (all types of E) if
more information is known about what
happens either before or after the collision.
You will not have to evaluate these systems
in this course, but you will be responsible
for using Cons. Of Energy to solve elastic
collisions.