Remember what this class is all about: the big three:
Force, Energy, and Work. The FEW. When dealing with work and energy, don’t have
to calculate acceleration directly, and don’t have to deal with vectors. Work and energy are magnitudes only, are
scalars.
Work. Simple definition for a constant force. The WORK
done on an object is equal to the constant force, F, applied along
displacement, d, parallel to the direction of the force.
W =
Fd (This is really a “dot product”
or scalar product of the two vectors F and d.)
Force
has what units in mks? Newtons. Distance?
Meters. So, work is newtons times meters, abreviated Nm. This combination of units is important enough
to have a name of it’s own: Joule. James Prescott Joule. His family owned a brewery, don’t know which
one, but he worked in it, experimented in it.
Among his other accomplishments, he invented arc welding.
Examples:
Work
against gravity. Force involved is the weight of the book. Raising a book a certain
height, h, requires an amount of work W= weight x height = mgh. Raise this book one meter. What work is that? (mass of book?)
Work
against friction. Push a book or a box across a
table a distance d. Let the force of
friction be “little f”. Work done =
force x distance = fd.
Mechanical
Energy is either Kinetic Energy or Potential E.
The
concept of energy is a unifying concept, applicable in all areas of physics,
and also in other areas of science. But
it’s strictly a physics concept. Energy
is the ability to do work. Can compare
to money: Energy is the payment for
doing work.
Work
is “the process by which energy is transferred from one object to
another.” Like money from one person or
entity to another.
KE
= ½ mv². It is the energy of motion. It also gives another way of calculating
work: When an object changes its
velocity, the work done is
W =½ mv² - ½ mv².
Example
of work against friction: Stopping distance and school zone; fd = final KE minus initial KE = 0 – ½ mv² .
Negative work is done on car to slow it down. Friction does negative work on objects. Main concept here is stopping distance is
proportional to the square of the velocity. For 20 mph it’s about 26 feet; for 40 mph, is
four times that, about 104 ft. This is
rounded up to 105 in book. Try
calculating it yourself.
Potential
Energy. The energy an object has
because of its position or location.
Same example as before: W = mgh =
PE2 – PE1 = change in potential energy in the gravitational field = work done
on object to raise it by height h in gravity of earth (near earth’s
surface). This is gravitational
potential energy. Water stored behind a
dam is another example of gpe.
Other
standard example in physics is the compressed spring. It has
potential energy that can be converted to work.
Conservation
of Energy: Energy can be neither created nor
destroyed. In changing from one form to
another, it is always conserved. Total
amount in an isolated system is constant.
Is the earth an isolated system? Very much not.
Example of conservation used to calculate speed of object
falling height, h. Draw picture.
½ mv² = mgh
The m’s cancel, come up with same equation as in chapter
2, but this is much easier!
Mass is also a form of potential energy, after Albert
Einiesteinie.
Power is the time rate of doing work. The greater the power of engine or
whatever, the faster it can do work. P =
Work/time or joules/sec in mks, which is called a Watt.
Named for steam engine fellow, James Watt. Where do you see this unit
used? Electrical appliances.
It is also time rate of energy production or energy
usage. Other units of power are BTU per
hour and horsepower. Watt rated steam engines in equivalent horse power.
Now we can find the engine horsepower required to make a
car go from 0 to 60 in 6 seconds.
Gotta
multiply horsepower by seconds to get energy expended…. Also note kWh, or kilowatt-hour, your
electrical bill’s units, are units of energy, not power.
A good exercise in energy understanding is to read your electric and gas meters, and based on your last month's bill, try to set an energy budget--which you try to adhere to by checking your meter every few days. That is a way to gain some power (over your utility costs).
