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Energy: Basics
Definitions
Energy - the ability to do work
Work - the transfer of energy by applying a
force through a distance
But what is a “force”?
Position
Position - orientation and distance an object
is from some origin; measurement of
position requires a coordinate system
If the position does not change, the object is easily found
Displacement - change in position; if position is designated
with the vector r, then displacement is Dr
Velocity
Defn. - time rate of change of
displacement; is a vector
quantity; SI unit = m/s
Displacement
Dr
Average velocity =
=
Elapsed time
Dt
Instantaneous velocity = limit (average velocity)
Dt0
What is the average velocity of a dragster that takes 5.5 seconds
to go the 400 meters down the dragstrip?
Speed
Some books say that velocity is speed + direction. WRONG!
Average speed =
Distance traveled
Elapsed time
Displacement = Distance traveled
Displacement on racetrack is 0,
while distance travelled is not
Acceleration
Defn. - time rate of change of velocity;
is a vector quantity; SI unit is
m/s2
Dv
Average acceleration =
Dt
Accelerations can occur without
changing the magnitude of velocity;
Ex. Object going in circle at constant
rate
Newton’s First Law
Really, Galileo’s
“An object at rest, or in a state of constant motion,
will continue in that state unless acted upon by an
unbalanced force.”
Inverse of statement is very important: if an object is acceleration,
then a net force is operating on it, even if you cannot see the
reason for the force.
Is there a force operating in this picture,
and if so, from what direction?
Newton’s Second Law
F = ma
Relates kinematic variables to dynamic ones
Can measure accelerations  calculate forces
Note: SI unit is newtons, English is pounds
Incorrect to say that X pounds = Y kilograms
Not all forces are constant
What force is needed to accelerate a 1000 kg car to 5 m/s2?
Newton’s Third Law
“For every force, there is an equal and opposite
reaction force.”
Often misunderstood; actually means that one object acting
on a second object will have the second object act on it
Mule pulls on cart. Cart pulls back on
mule with equal and opposite force.
“Why pull?”, says mule, if force will
be negated.
Get Back To Work
Work - the transfer of energy by applying a
force through a distance
W=Fxd
DW = Fn x Dd
if F is constant
if F varies
Lifting box: F = mg
Distance lifted = h
W = mg x h = mgh
Work Example
How much work is done by lifting a 10 kg
box 2 meters from the floor to a shelf?
m = 10 kg
h=2m
Lifting box: F = mg = (10 kg)(9.8 m/s2) = 98 N
Distance lifted = h = 2 m
W = mg x h = (98 N) (2 m) = 196 J
Potential energy
Energy stored within the force between two
objects separated by a distance; if objects
are allowed to move, force is applied through
distance = work done
TYPES OF POTENTIAL ENERGY:
Gravitational
Chemical
Nuclear
Example: Gravitational
potential energy
Potential energy due to gravity
EXAMPLES:
Water behind a dam
A rock at the top of a
steep hill
If the water or rock drops, gravity
operates over a distance, thereby doing work. This work converts
the potential energy to kinetic energy.
Kinetic energy
ENERGY OF MOTION
A moving object has momentum. If it hits
another object, it will transfer energy to it by
applying a force through a distance, i.e. work
Some of the bullet’s kinetic
energy is transferred to the
apple during the collision
Kinetic energy of falling water is
converted to motion of turbines
when water falls on them
Kinetic Energy (cont.)
The kinetic energy of an object depends only
on its mass and its velocity
K.E. = ½ m v2
Example: A .03 kg bullet is moving at 300 m/s right before it hits
an apple. How much kinetic energy does it have?
K.E. = ½ (.03 kg) (300 m/s)2 = (.015 kg)(90000 m2/s2) = 1350 J
1st law of thermodynamics
Energy may be converted to different forms, but it is
neither created nor destroyed during transformations
Energy from chemical
bonds is converted to
kinetic energy and heat
(body and friction from
tires)
ENERGY
Heat
Amount of energy before and after transformation is the
same, only the form of the energy has changed
st
1
Law (Contd.)
Another way to state the 1st law is mathematically.
DE = Q + W
This equation says that the only way to change the energy of a
system is to add heat to it (Q) or to do work on it (W)
Example: Can make
wood hotter by
applying fire or hitting
Conservation of Energy
If no external work is done on a system, or if
no heat is exchanged with its surroundings,
then the total energy of a system will not
change, i.e. the total kinetic plus the total
potential energy will remain constant
Energy can be converted from one form to the other (potential to
kinetic or vice-versa), but the total will remain the same.
Simple Machines
Allow for the same amount of work
to be done, but with smaller forces
Trade-off of using a smaller force is
that the force is applied through a
longer distance
Box lifted straight up a height h, force supplied is F = mg
Force of gravity down inclined plane is F = mg sinq = mgh/L
Distance pushed up plane = L
Power
Power = DE = rate of energy usage
Dt
Can deliver the same amount of energy to a system using less
power, but it takes a longer amount of time
Our Western mindset usually screams for more power
Ex. SUV’s require more powerful engines; larger homes
require more powerful a.c.
How much power do you expend by climbing 3 flights of
stairs (10 m) in 10 seconds?
If you have a mass of 70 kg and each flight is 5 m, then the power is
P = (mgh)/dt = (70 kg)(9.8 m/s2)(15 m)/(10 s) = 1029 W