PHY205H1F Summer
Physics of Everyday Life
Class 3: Energy & Rotation
•
•
•
•
•
•
•
•
Energy
Power
Potential and Kinetic
Conservation of
Energy
Efficiency
Recycled Energy
Energy for Life
Sources of Energy
•
•
•
•
Circular Motion
Rotational Inertia
Torque
Centre of Mass and
Centre of Gravity
• Centripetal Force
• Centrifugal Force
• Angular Momentum
Work
• involves force and distance.
• is force  distance.
• in equation form: W 
Two things occur whenever
work is done:
• application of
•
of something by
that force
Unit of work:
newton-meter (N·m)
or
( )
Work can be positive, zero or
negative
• When the force and the distance are in the same
direction, you are helping the motion with the
force, so the work done on the object is
.
• The force is
to the object +
environment.
• Maybe this force
is speeding the
object up.
F
d
Work can be positive, zero or
negative
• When the force and the distance are at right
angles, you are not helping the motion with the
force, so the work is
.
• This force is
the energy of the
object.
• This force won’t
speed the object
up or slow it
down.
F
d
Work can be positive, zero or
negative
• When the force and distance are in opposite
directions, you are hindering the motion with the
force, so the work done on the object is
.
• This force is
the energy of the object.
• Maybe this
force is
slowing the
object down.
F
d
Discussion Question
• Justin is doing a bench press, and he slowly
pushes the bar up a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the upward push, how much work does
Justin do on the bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Discussion Question
• Justin is doing a bench press, and he slowly
lowers the bar down a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the downward lowering, how much work
does Justin do on the bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Discussion Question
• Justin is doing a bench press, and he slowly
lowers the bar down a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
He then pushes it up slowly the same distance of
0.30 m back to its starting position, also pushing
upwards on the bar with a force of 200 N.
• During the complete downward and upward
motion, how much total work does Justin do on
the bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Power
• Measure of how fast work
is done
• In equation form:
work done
Power =
time interval
Unit of power
• joule per second, called the
watt after James Watt,
developer of the steam
engine
• 1 joule/second  1
• 1 kilowatt  1000
Power
• The unit of power is the
watt, which is defined as
1 watt = 1 W = 1 J/s
• Energy is measured by
Ontario Hydro in kWh
“kiloWatt hours”.
• 1 kWh is the amount of energy used by a
power of
over
• 1 kWh = 1000 J/s * 60 min/hour * 60 s/min
• 1 kWh =
Joules
[Chart downloaded from http://www.ontario-hydro.com/index.php?page=current_rates ]
• Example: Your clothes dryer uses 5000 Watts and you
need to run it for 1 hour to dry your clothes.
• If you run it during “on peak” time, such as between 7 and
11am on a weekday, the cost is 12 cents/kWh.
• If you run it during “off peak” on the weekend the price for
Ontario Hydro electricity is 6 cents/kWh.
• How much money do you save per load by doing your
laundry on the weekend?
Elastic Potential Energy
Stored energy held in readiness with
a potential for doing work
Examples:
• A stretched bow has stored energy
that can do
on an arrow.
• A stretched rubber band of a slingshot
has stored energy and is capable of
doing
.
• Demonstration: A mousetrap that is
“set” has elastic potential energy that
is capable of killing the mouse!
Gravitational Potential Energy
Potential energy due to elevated position
Example:
• coffee mug on the top
shelf
• In equation form:
Potential energy
 mass  acceleration due to
gravity  height
𝑈𝑔 =
Demonstration
A rectangular solid such as a domino has more
gravitational potential energy when it is tipped up on
its edge, because its centre of mass is higher
The energy is added to
the domino by the
work you do in
.
𝑈𝑔 = 𝑚𝑔ℎ
[image retrieved Jan.23 2013 from http://www.decodedscience.com/a-quick-explanation-of-mathematical-induction/1420 ]
Gravitational Potential Energy
Kinetic Energy
• Energy of motion
• Depends on the mass of the object and square of
its speed:
If object speed is doubled  kinetic energy is
quadrupled.
History Question
1
𝐾 = 𝑚𝑣 2
2
• Chapter 7 opens with a story about the physicist
who first advocated the correct equation for kinetic
energy. Who was this physicist?
A. Du Châtelet
B. Einstein
C. Galileo
D. Leibniz
E. Newton
Work and Kinetic Energy
• If an object starts from rest and there is a net
force doing work on it, the work done will be
equal to the
of the object.
• In equation form:
1
𝐹𝑑 = 𝑚𝑣 2
2
Work-Energy Theorem
Work-energy theorem
• Gain or reduction of energy is the result of work.
• In equation form: work  change in kinetic
energy (W  K).
• Doubling speed of an object requires times
the work.
Work-Energy Theorem
• Applies to decreasing speed:
– reducing the speed of an object or bringing it
to a halt
Example: Applying the brakes
to slow a moving car, work is
done on it (the friction force
supplied by the brakes 
distance).
Work-Energy Theorem
CHECK YOUR NEIGHBOR
The work done in bringing a moving car to a stop is the
force of tire friction  stopping distance. If the initial speed
of the car is doubled, the stopping distance is
A.
B.
C.
D.
actually less.
about the same.
twice.
None of the above.
Chapter 7 big idea:
“Conservation of Energy”
• A system of particles has a total energy, E.
• If the system is isolated, meaning that there
is no work or heat being added or removed
from the system, then:
• This means the energy is “conserved”; it
doesn’t change over
.
• This is also the first law of thermodynamics;
“You can’t get something for nothing.”
v
Discussion Question on
Conservation of Energy
• An object is flying through the air with
nothing touching it.
• Neglect air resistance.
• Is energy of the object conserved?
A. Yes
B. No
Discussion Question
• A 1 kg object is dropped from rest a height
of 3 m above the ground.
• Just before it hits the ground, what is its
kinetic energy? [Neglect air resistance.]
A. 3 J
B. 15 J
C. 30 J
D. 90 J
E. 150 J
v
A situation to ponder…
CHECK YOUR NEIGHBOR
Suppose the potential energy of a drawn bow is 50 joules
and the kinetic energy of the shot arrow is 40 joules. Then
A.
B.
C.
D.
energy is not conserved.
10 joules go to warming the bow.
10 joules go to warming the target.
10 joules are mysteriously missing.
Machines
Principles of a machine:
• Conservation of energy concept:
input 
output
• Input force  input distance 
Output force  output distance
• (Force  distance)input  (force  distance)output
Simplest machine:
• Lever
– rotates on a point of support called the
fulcrum
– allows
force over a large distance and
force over a short distance
Efficiency
• Percentage of work put into a machine that is
converted into useful work output
• In equation form:
Efficiency 
Discussion Question
• When the useful energy output of a machine is
100 J, and total energy input is 200 J, what is the
efficiency?
A. 25%
B. 50%
C. 75%
D. 100%
E. 200%
Recycled Energy
• Re-employment of
energy that otherwise
would be wasted.
• Edison used heat from
his power plant in New
York City to heat
buildings.
• Typical power plants waste about
of their
energy to
because they are built away from
buildings and other places that use heat.
Sources of Energy
Example:
• Photovoltaic cells
on rooftops catch
the solar energy
and convert it to
electricity.
More energy from the Sun hits Earth in 1 hour than all of
the energy consumed by humans in an entire year!
Sources of Energy
Concentrated energy
• Nuclear power
– stored in uranium and plutonium
– doesn’t pollute our atmosphere
– creates radioactive waste which, if stored
near humans, can be toxic.
PHY205H1S
Physics of Everyday Life
Chapter 8: Rotation
•
•
•
•
Circular Motion
Rotational Inertia
Torque
Centre of Mass and
Centre of Gravity
• Centripetal Force
• Centrifugal Force
• Angular Momentum
Circular Motion –
Rotational Speed
• Rotational (angular) speed
is the number of radians of
angle per unit of time
(symbol ).
• All parts of a rigid merry-go-round or turntable turn
about the axis of rotation in the same amount of
time.
• So, all parts have the same
.
Tangential speed
 Radial Distance  Rotational Speed
Discussion Question
• The rotational speed on the outer edge of a
rotating roulette wheel is
A. less than toward the centre.
B. the same as toward the centre.
C. greater than toward the centre.
Roulette wheel image from http://yourfamilyfinances.com/2012/09/01/payday-loans-debt-trap/ ]
Discussion Question
• The tangential speed on the outer edge of a
rotating roulette wheel is
A. less than toward the centre.
B. the same as toward the centre.
C. greater than toward the centre.
Roulette wheel image from http://yourfamilyfinances.com/2012/09/01/payday-loans-debt-trap/ ]
Rolling Without Slipping
 Under normal driving
conditions, the portion of the
rolling wheel that contacts
the surface is stationary, not
sliding
 In this case the speed of
the centre of the wheel is:
𝐶
𝑣=
𝑇
where C = circumference [m]
and T = Period [s]
 If your car is accelerating or decelerating or turning,
it is
of the road on the wheels that
provides the net force which accelerates the car
Discussion Question
• The circumference of the tires on your car is
0.9 m.
• The onboard computer in your car measures
that your tires rotate 10 times per second.
• What is the speed as displayed on your
speedometer?
A. 0.09 m/s
B. 0.11 m/s
C. 0.9 m/s
D. 1.1 m/s
E. 9 m/s
Rotational Inertia
• An object rotating about
an axis tends to remain
rotating about the same
axis at the same
rotational speed unless
interfered with by some
external influence.
• The property of an object to resist changes
in its rotational state of motion is called
(symbol I).
[Image downloaded Jan.10, 2013 from http://images.yourdictionary.com/grindstone ]
Rotational Inertia
Depends upon:
•
of object.
•
of mass
around axis of rotation.
– The greater the distance
between an object’s mass
concentration and the axis,
the greater the rotational
inertia.
Rotational Inertia
Which pencil has the largest
rotational inertia?
A. The pencil rotated around an
axis passing through it.
B. The pencil rotated around a
vertical axis passing through
centre.
C. The pencil rotated around
vertical axis passing through
the end.
Torque
• The tendency of a force to
cause
is called
torque.
• Torque depends upon three factors:
–
of the force
– The
in which it acts
– The point at which it is applied on the object
Image by John Zdralek, retrieved Jan.10 2013 from http://en.wikipedia.org/wiki/File:1980_c1980_Torque_wrench,_140ftlbs_19.36m-kg,_nominally_14-20in,_.5in_socket_drive,_Craftsman_44641_WF,_Sears_dtl.jpg ]
Torque
Consider the common experience of pushing open a door.
Shown is a top view of a door hinged on the left. Four
pushing forces are shown, all of equal strength. Which of
these will be most effective at opening the door?
A. F1
B. F2
C. F3
D. F4
Torque
• The equation for Torque is
Torque  lever arm  force
• The
is the perpendicular
distance between the line along which the
force is applied, and the rotation axis.
Rotational Inertia
CHECK YOUR NEIGHBOR
Suppose the girl on the left suddenly is handed a bag
of apples weighing 50 N. Where should she sit order to
balance, assuming the boy does not move?
A. 1 m from pivot
B. 1.5 m from pivot
C. 2 m from pivot
D. 2.5 m from pivot
• Centre of mass is the average position of all the
that makes up the object.
• Centre of gravity (CG) is the average position of
distribution.
– Since weight and mass are proportional, centre of
gravity and centre of mass usually refer to the same
point of an object.
Centripetal Acceleration
A car is traveling East at a constant speed
of 100 km/hr. Without speeding up of
slowing down, it is turning left, following
the curve in the highway. What is the
direction of the acceleration?
A.North
B.East
C.North-East
D.North-West
E.None; the acceleration is zero.
N
W
E
S
Centripetal Force
• Any force directed toward a fixed
is
called a
force.
• Centripetal means “centre-seeking” or
“toward the centre.”
Example: To whirl a tin can at
the end of a string, you pull
the string toward the centre
and exert a centripetal
force to keep the can
moving in a circle.
Centripetal Force
• Depends upon
– mass of object, m.
– tangential speed of the object, v.
– radius of the circle, r.
• In equation form:
𝐹=
Centripetal Force
CHECK YOUR NEIGHBOR
Suppose you double the speed at which you round a
bend in the curve, by what factor must the centripetal
force change to prevent you from skidding?
A. Double
B. Four times
C. Half
D. One-quarter
Centrifugal Force
• Although centripetal force is centre directed, an
occupant inside a rotating system seems to
experience an outward force.
• This apparent outward force is called
force.
• Centrifugal means “centre-fleeing” or “away from
the centre.”
[Image downloaded Jan.10 2013 from http://www.et.byu.edu/~wanderto/homealgaeproject/Harvesting%20Algae.html ]
Rotating Reference Frames
• Centrifugal force in a
is a force in its own right – feels as
real as any other force, e.g. gravity.
• Example:
– The bug at the bottom of the can experiences
a pull toward the bottom of the can.
Angular Momentum
• The “inertia of rotation” of rotating objects is
called angular momentum.
– This is analogous to “inertia of motion”, which was
momentum.
• Angular momentum
 rotational inertia  rotational velocity
𝐿=
– This is analogous to
Linear momentum  mass  velocity
𝑝 = 𝑚𝑣
Conservation of Angular Momentum
The law of conservation of angular momentum
states:
If no external net torque acts on a rotating
system, the angular momentum of that
system remains constant.
Analogous to the law of conservation of linear
momentum:
If no external force acts on a system, the total linear
momentum of that system remains constant.
Angular Momentum
CHECK YOUR NEIGHBOR
Your professor is rotating at some rotational speed ω
with some rotational inertia set partly by the fact that
he is holding masses in his outstretched arms.
Suppose by pulling the weights inward, the rotational
inertia of the professor reduces to half its original
value. By what factor would his rotational speed
change?
A. Double
B. Three times
C. Half
D. One-quarter
Conservation of Angular Momentum
Example:
• When the professor pulls the weights
inward, his rotational speed
!
Before Class 4 on Monday
• Please read Chapters 13 and 14, or at least watch
the 20-minute pre-class video for class 4
• Pre-class reading quiz on chapters 13 and 14 is due
Monday by 10:00am
• Midterm Test in 1 week: Wednesday 1-3 in EX310 (last
name A-M), EX320 (last name N-Z)
• Test will begin promptly at 1:10 and will be 1 hour and 50
minutes long.
• Please bring a calculator, and, if you wish, a a 8.5x11” aid
sheet upon which you may write anything you wish on both
sides
• Test will cover Hewitt chapters 2-5, 7, 8, 13 and 14, and will
include some multiple choice and some short-answer