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Lesson #1 – Introducing Energy
Pre-Lesson Notes
Unit: Energy Read textbook 7.4, 7.5, 7.6
Homework: pg 160 Q1-2, pg 163 Q1-6 and worksheet #3 (attached)
Date:
Concept: What is Energy
Definitions:
Energy
Types of Energy
Equations:
Gravitational Potential Energy equation:
Kinetic Potential Energy equation:
1
SPH3U: Introducing Energy!
Recorder: __________________
Manager: __________________
Speaker: _________________
Energy is never created or destroyed; it just moves around and is
stored in various ways. This investigation introduces you to energy
conservation and its connection to the concept of work.
0 1 2 3 4 5
Here are some basic definitions, phrased informally:
 Kinetic energy: The energy stored in the motion of an object. The heavier or faster something is, the
more kinetic energy it has. Thus, Ek is basically the energy due to an object’s speed, v.
 Gravitational potential energy: The energy stored in an object because it has been lifted. The energy is
“potential” because it has the potential to turn into kinetic energy—for instance, if the object gets
dropped. The heavier or higher an object is, the more potential energy is stored up. So Eg is basically
energy due to an object’s height, h.
A: Work and Gravitational Potential Energy
v
FBD
1. A student holds a book of mass m in her hand and raises the book
vertically at constant speed through a displacement Δh. Sketch a
free-body diagram for the book. Is the force exerted by the student
on the book greater than, less than, or equal to m·g? Explain
briefly.
B.
v
A.
2. Suppose the student uses 15 units of energy while lifting the book from position A to position B. Note that the
book always has the constant speed, v.
(a) What quantities of energy change while the student lifts the book? Explain.
(b) By how much did the potential energy of the book change? Explain.
(c) Complete the energy storage
diagram for the book. Why is
the total energy of the system
changing?
Moment A
Ek
Eg
Energy is
inputted
into the
system by
your hand
Moment B
Ek
Eg
The energy of a system can change due to a force acting on it during a displacement. The energy change of the
system due to a force is called work. When the force, F, points in the same direction as the object’s
displacement, ∆d, the amount of work is positive and is given by W = Fa∙∆d.
2
3. Now let’s study this system again using the idea of work.
(a) Use the definition of work to determine the amount of work the student does in raising the book through
a vertical displacement, or height. Express your answer using the symbols m, g, and Δh. (Hint: according to
your FBD in #1 above, what is your Fa equal to?)
(b) Explain how you could use the result from question A#3a to figure out how much the potential energy
has increased.
The gravitational potential energy of an object of mass, m, located at a vertical position, h, above a reference
position is given by the expression, Eg =mgh. The reference position is a vertical position that we choose to help
us compare gravitational potential energies. At the reference position, the gravitational potential energy is
chosen to equal zero. Note that the units for work and gravitational potential energy are Nm. By definition, 1
Nm = 1 J, or one joule of energy. In fundamental units, 1 J = 1 kgm2/s2. In order to get an answer in joules, you
must use units of kg, m, and s in your calculations!
1. What does it mean when we say that a book has, for example, 27 J of gravitational potential energy relative
to a table (the reference position)?
When we say that the “book has” 27 J of potential energy we always mean the earth-book system. Energy is
stored gravitationally due to an interaction between two objects, the book and earth. The book doesn’t really
“have” the energy.
B: The Ball Drop and Kinetic Energy
Next, you will drop a tennis ball from a height of your choice (between 1 and 2 m)
and examine the energy changes.
1.
Draw a diagram of a ball falling and indicate two moments in time A and B at
the start and end of its trip down (just before impact - JBI!) Draw a dashed
horizontal line at the bottom which represents your vertical reference
position. Label this “h = 0”. Indicate the starting height you chose.
2.
Calculate how much gravitational potential energy the ball initially has with
respect to the reference line. What measurement do you need to make? (use
m = 57 g)
3
Moment A
Moment B
Ball falls
down
toward
the earth
3. Draw an energy storage
bar
to
4.
Ek
Eg
Ek
Eg
graph for the earth-ball
system from moments A
B.
Exactly how much kinetic energy do you predict the ball will have just before it reaches the ground? Explain.
The kinetic energy of an object is the energy stored in the motion of the object. The more mass or the more
speed the object has, the greater its kinetic energy. This is represented by the expression, Ek = ½mv2. Energy is
measured in units of joules (J) and is a scalar quantity since energy does not have a direction. m must be in kg
and v must be in m/s.
5.
Use the new equation for kinetic energy to determine the speed of the ball just before it hits the ground.
6.
If you have time, u se the motion detector set up by your teacher to measure the speed of the ball just
before it hits the ground. How do the two results compare?
Gravitational potential and kinetic energy are two examples of mechanical energy. When the total mechanical
energy of a system remains the same we say that the mechanical energy is conserved. Mechanical energy will be
conserved as long as there are no external forces acting on the system and no frictional forces. If mechanical
energy is conserved, we can write an energy conservation equation which equates the sum of kinetic and
potential energies at two moments in time: Emech = EkA + EgA = EkB + EgB
7.
Keeping in mind the experimental errors, was mechanical energy conserved during the drop of the ball?
Explain.
8.
Write down the energy conservation equation for ball drop example. If a quantity equals zero, leave it out.
4
Lesson #2 – Doing work or hardly working?
Pre-Lesson Notes
Unit: Energy 7.1
Homework: pg 151 Q1-4 and worksheet #2 (attached)
Date:
Concept: What is work
Definitions:
Work
Joule
Equations:
Work Equation:
Explanation:
5
SPH3U: Doing work?
A: Working Hard or Hardly Working?
In this section we’ll clarify the meaning of work. Remember: W = F∆d
1. A student pushes hard enough on a wall that she breaks a sweat. The wall, however, does not move; and
you can neglect the tiny amount it compresses. Does the student do any work on the wall? Answer using:
a. your intuition.
b. the physics definition of work.
Apparently, some reconciliation is needed. We’ll lead you through it.
2. In this scenario, does the student give the wall any kinetic or potential energy?
3. Does the student expend energy, i.e., use up chemical energy stored in her body?
4. If the energy “spent” by the student doesn’t go into the wall’s mechanical energy, where does it go? Is it just
gone, or is it transformed into something else? Hint: Why does your body produce sweat in a situation like
this?
5. Intuitively, when you push on a wall, are you doing useful work or are you “wasting energy”?
6. A student says:
“In everyday life, ‘doing work’ means the same thing as ‘expending energy.’ But in physics, work corresponds
more closely to the intuitive idea of useful work, work that accomplishes something, as opposed to just
wasting energy. That’s why it’s possible to expend energy without doing work in the physics sense.”
In what ways do you agree or disagree with the student’s analysis?
The net work is the sum of all the work being done on the system. When the net work is non-zero, the kinetic
energy of a system will change. If the net work is positive, the system gains kinetic energy. If the net work is
negative, the system loses kinetic energy. This is called the kinetic energy - net work theorem and is represented
by the expression: Wnet =EkB – EkA = Ek .
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Lesson 3: Gravitational Potential Energy
We have had a brief introduction to energy stored due to an object’s
position, that is, gravitational potential energy. Today we will explore
this idea in depth.
A: The Ramp Race - Predictions
Your teacher has two tracks set up at the front
of the class. One track has a steep incline and
the other a more gradual incline. Both start at
the same height and end at the same height.
Friction is very small and can be neglected.
A
1. Use energy transfers to describe what will
happen as a ball travels down an incline.
Recorder: __________________
Manager: __________________
Speaker: _________________
0 1 2 3 4 5
Ball
1
B
Ball
2
2. How will the speeds of each ball compare when they reach the bottom of their ramps? Why?
3. Each ball travels roughly the same distance along the tracks between points A and B. Which one do you
think will reach the end of the tracks first? Use energy arguments to support your prediction.
B: The Race!
1. Record your observations of the motion of the balls when they are released on the tracks at the same time.
2. Record your observations of the speeds of the balls when they reach the end of the track.
3. Marie says, “I’m not sure why the speeds are the same at point B. Ball 1 gains energy all the way along a
much longer incline. Surely more work is done on it because of the greater length of the incline. Ball 1
should be faster.” Based on your observations and understanding of energy, help Marie understand.
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4. Albert says, “I don’t understand why ball 2 wins the race. They both end up traveling roughly the same
distance and ball 2 even accelerates for less time!” Based on your observations and understanding of
energy, help Albert understand.
5. According to your observations, how do the kinetic energies of the two balls compare at point B? Where did
this energy come from?
6. The distance the balls travel along each incline is different, but there is an important similarity. Compare the
horizontal displacement of each ball along its incline (you may need to make measurements). Compare the
vertical displacement of each ball along its incline. Illustrate this with vectors on the diagram on the previous
page. Which displacement will help determine the change in gravitational potential energy? Also, calculate
the expected speed of ball 2 at the bottom.
The amount of energy stored in, or returned from gravity does not depend on the path taken by the object. It
only depends on the object’s change in vertical position (displacement). The property is called path
independence – any path between the same vertical positions will give the same results. This is a result of the
fact that gravity does no work on an object during any kind of horizontal motion.
C: The Vertical Reference Position
When making calculations involving gravitational energy, we must choose a vertical reference line from which
we measure the vertical position of the object. What effect does this choice have on the results of our
calculations? Let’s see! In the following work, if there are any quantities you need to know, make a
measurement of the equipment at the front of the room.
Vertical positions above the reference line have positive values, while vertical positions below the reference line
have negative values. This is our energy-position sign convention.
Using the measurements from the ramp demo in the previous 2 sections, answer the following questions:
1. In the diagram to the right, draw and label the vertical reference line, h
= 0 at the bottom level of the track. What is the gravitational potential
energy of the ball at positions A and B?
EgA =
Eg =
EgB =
8
2. In the diagram to the right, draw and label the vertical reference line h =
0 at the top level of the track. What is the gravitational potential energy
of the ball at positions A and B? Remember, we need to consider the
new h here as negative.
EgA =
Eg =
EgB =
3. As the ball rolls down the track, there is a transfer of energy stored in gravity to energy stored in motion.
Draw a vector representing the vertical displacement of the ball in each diagram. How do these two vectors
compare?
4. How does the change in gravitational potential energy, Eg, compare according to the two diagrams? How
much kinetic energy will the ball gain according to each diagram?
Only changes in gravitational potential energy have a physical meaning. The exact value of the GPE at one
position does not have a physical meaning. That is why we can set any vertical position as the h = 0 reference
line. The vertical displacement of the object does not depend on the choice of reference line and therefore the
change in GPE does not depend on it either. So it is not significant if an object has a negative GPE.
9
Lesson # 4 – Conservation of Energy – Rollercoasters!
Pre-Lesson Notes
Unit: Energy Read textbook 7.7
Homework: pg 168 Q1-3 and worksheet #1 (attached)
Date:
Concept: What is Energy
Definitions:
Energy
Types of Energy
Equations:
Gravitational Potential Energy equation:
Kinetic Potential Energy equation:
Work Energy Theorem:
Conservation of Energy Equation:
10
SPH3U: The Conservation of Energy – Roller Coasters!
A: The Behemoth
A rollercoaster at Canada’s Wonderland is called “The Behemoth” due to its 70.1 m tall starting hill. Assume the
train is essentially at rest when it reaches the top of the first hill. We will
A
compare the energy at two moments in time: A = the top of the first hill and
B = ground level after the first hill.
B
1. Draw an energy bar graph for the train. Write down the energy
conservation equation.
Moment B
Moment A
∙
∙
The sum of all E’s before equals
the sum of all E’s after…
Equation
Ek
Eg
Ek
Eg
2. Use the energy conservation equation to find the speed of the rollercoaster at moment B (& convert to
km/h.)
3. The official statistics from the ride’s website give the speed after the first drop as 125 km/h. What do you
suppose accounts for the difference with our calculation?
4. Draw a new energy storage bar graph for the train and its surroundings. Write down a new energy
conservation equation. Use the symbol Ediss for the energy dissipated (lost) due to friction.
Moment B
Moment A
Equation
Ek
Eg
Ek
Eg
Ediss
5. Use the train mass, mt = 2.7 x 103 kg to determine the energy dissipated on the first hill. (Hint: use the
difference between the energy at the top and the actual energy at the bottom, using the actual speed -- in
m/s.)
The dissipated energy is stored in heat, sound and vibrations. Energy stored in these forms are not mechanical
forms of energy since it is very difficult to transfer energy stored this way back into kinetic or potential energy.
B: The Bluevale Flyer
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Rumour has it that a rollercoaster is going to be built
in the Bluevale field. Plans leaked to the media show
a likely design. The train starts from rest at point A.
For all our calculations, we will assume that the
energy lost to friction is negligible.
1. Point B is located partway down the first hill.
Complete the diagrams and determine the
rollercoaster’s speed at that moment in time.
Moment A
Moment B
Equation
Ek
Eg
Ek
Eg
2. Point D is the top of the loop-de-loop and is located 70 m above the ground. Complete the diagrams and
determine the rollercoaster’s speed at that moment in time. (Hint: We can usually create and solve our
equation by comparing Etot at 2 different points. The 2nd point is D. Does it matter which point is 1st?)
Moment ____
Moment D
Equation
Ek
Eg
Ek
Eg
The loop-de-loop involves some very complicated physics, the details of which are much beyond high school
physics. Yet using energy techniques, we did not have to consider those complications at all! When the
mechanical energy of a system is conserved, we can relate the total mechanical energy at one moment in time
to that at any other moment without having to consider the intermediate motion – no matter how complex.
12
Lesson #5: The Conservation of Energy – Cars
A: Pendulum practice
Before considering cars, let’s first practice these energy bar diagrams with something fairly simple like a
pendulum. Complete these diagrams. Let’s call the lowest point of the swing h = 0. Keep in mind that a
pendulum stops for an instant at the top of its swing.
A (top of swing)
Ek
Eg
C (part way up)
B (bottom)
Ek
Eg
Ek
Eg
D (top of swing)
Ek
Eg
A student says: “Ya, this looks pretty good, but a pendulum eventually comes to a stop. So shouldn’t our A and
D diagrams be a little different from each other?” Do you agree or disagree?
Is there any way you can think of to change the diagrams so that they make perfect sense and truly show the
conservation of energy?
Let’s now practice some energy bar diagrams for simple situations with cars.
B: Regular gas guzzlers
1. A car is coasting at low speed on
a flat road and then heads down
a steeply inclined hill to reach
another flat road at the bottom
with a higher speed even though
the driver didn’t push on the gas
pedal the entire time. Complete
a rough energy storage bar
diagram for this car:
A (top of hill)
Ek
Eg
13
Car coasts
downhill
unassisted
B (bottom)
Ek
Eg
2. Without slowing much on the way,
the same car approaches an uphill
incline, about half as high as the
other hill. Complete another set
of diagrams for this car as it goes
up this smaller hill:
(a) How will the speed of the
car compare at spots A, B
and C?
3. Now the car is on a flat road going
a moderate speed and the driver
sees a red light ahead. They slow
the car gradually by braking until
they come to a complete stop.
Let’s say h = 0. Complete yet
another diagram. We need to
start considering more than just
Ek and Eg now, so let’s make
room for other mystery energy
forms.
B (ground)
Ek
Car coasts
up smaller
hill
unassisted
Eg
Ek
A (coasting)
Ek
C (top of small hill)
Eg E
B (stopped)
Car
gradually
comes to
a stop
E
Eg
Ek
Eg E
E
(a) Since the height and the speed are both zero at the red light (B), then what values do we expect for kinetic
and gravitation energy?
A car gets its energy from chemical energy in the fuel tank. Let’s label it on the above diagram as Echem. It
doesn’t really change, from A to B, does it?
If the Ek went down but the Eg and the Echem stayed the same, a fourth form of energy must have increased. They
say you shouldn’t “ride the brakes” when you go down a big hill, since it can melt your brake pads or even catch
them on fire! This is a clue that the energy must have gone into heat. Let’s label it above as Eheat. Like Eg, it is
relative; what’s important is how much it changed. So it’s ok to show some Eheat in diagram A if you want, but
you have to make it much higher in diagram B since the brake pads would have heated up a lot to dissipate the
energy the car had (or if the car skidded to a stop, the road and the tires would heat up a lot!)
4. How will the car get energy again to get up to speed when the light turns green?
(a) Show this on one more energy bar
diagram. Do this one in pencil, just in
case, since adjustments may be needed
after the next question.
A (at rest)
B (going fast)
Car
speeds up
from rest
(If we want to keep it real here to some
extent, keep in mind that internal
Ek Eg E E
Ek Eg E E
combustion engines are horribly inefficient.
Most cars convert only about 25% of
chemical energy into kinetic energy; that is, about 75% of the energy you get from “burning” gasoline goes to
14
useless, problematic heat energy that does no useful work. That’s why cars need radiators to get rid of all this
troublesome heat!)
(b) With the bad efficiency in mind, let’s try to add some numbers and put a scale on the diagrams in (a) above.
Let’s say you have 80 mL of gas left in your tank only. This is worth about 2 million Joules of chemical energy
(or 2 MJ). So you start your car from rest, with the engine cool (we can say Eheat = 0). Calculate how much
kinetic energy your 1200 kg car will have after getting up to a speed of 25 m/s.
(c) Since only ¼ of the energy went to your Ek, then ¾ went to Eheat. Multiply your answer in (b) by 3, and this
would then be the amount that went to heat. Show your calculations here:
Eheat =
ΔEchem = Ek + Eheat =
(d) Add the appropriate scale to your energy diagram above.
C: Hybrid cars
Similar to regular cars, hybrid cars have gasoline engines (often smaller ones) but they also have electric motors
and a lot of extra batteries. Batteries are a form of chemical energy, but to distinguish this from fossil fuel Echem,
let’s call battery energy Ebatt. When a hybrid goes downhill or when it slows down, the motion of the car is used
to spin-up the electric motor which acts as a generator to charge the batteries, in an attempt to save that kinetic
energy in a different form so that it can be used again. (Most hybrid cars don’t need to be plugged in.)
1. A hybrid car is coasting at low
B (bottom)
A (top of hill)
speed on a flat road and then
Hybrid coasts
heads down a steeply inclined
downhill
hill to reach another flat road at
unassisted, but
the bottom. Unlike the last time
doesn’t speed up.
that we considered this scenario,
this driver wants to maintain a
constant speed. Complete a
rough energy storage bar
Ek Eg Eheat Echem Ebatt
Ek Eg Eheat Echem Ebatt
diagram for this car. If you’re
unsure how it will look, the questions below may give you some hints. Fuel (Echem) is not used, nor is it
gained of course.
(a) With a regular car, it starts with a lot of Eg at the top of the hill. This converted to what kind of energy
in section B, question 1?
(b) This time Eg went down again, yet the car didn’t speed up, that is, Ek stayed constant. Where did this
energy go?
Although battery technology has come a long way in our lifetime, keep in mind that it has a long way to go still.
One reason it took a long time for hybrid cars to become mainstream, is that a lot of the energy is lost on its way
to charging the battery. It’s unfortunately not remotely close to 100% of energy transfer to the batteries. For
example, the wires heat up, so that’s energy lost to heat again. But recovering even a fraction of the kinetic
energy can be worth it, saving significant amounts of energy, fuel, and carbon emissions.
15
B (stopped)
2. Now the hybrid is on a flat road going
A (coasting)
Car
a moderate speed and the driver sees
gradually
a red light ahead. They slow the car
comes to
gradually by “braking”, thus charging
a stop
the batteries, until they come to a
complete stop. Let’s say h = 0.
Complete another E bar diagram.
(Remember: since the height and the
Ek Eg Eheat Echem Ebatt
Ek Eg Eheat Echem Ebatt
speed are both zero at the red light
(B), then we know that Ek and Eg are
both zero too.) You can be somewhat realistic here and show that some of the energy was “lost” to heat.
3. Green light, go! What happens
when you get the hybrid back up
to speed from rest? Here too, a
little energy is probably lost to
heat. Fill in the diagrams:
A (stopped still)
Car speeds
up from rest
B (going fast)
Hint: if Eheat goes up,
a little Echem must be
used-up (go down) to
compensate.
(FYI: you may be interested to look up
“KERS” online. It’s a cool system to
Ek Eg Eheat Echem Ebatt
Ek Eg Eheat Echem Ebatt
store the kinetic energy in a spinning
flywheel instead of a battery. Apparently this type of mechanical system is much more efficient than using a
battery.)
D: Summary comparison
Summarize here to compare a regular car to a hybrid. Let’s keep it simple: no hills, so Eg will always be zero.
Start with only a little heat energy for both cars.
B (stopped)
A (medium speed)
C (back up to speed)
1. Normal Car:
Ek Eg Eheat Echem
Ek Eg Eheat Echem
16
Ek Eg Eheat Echem
A (medium speed)
B (stopped)
C (back up to speed)
2. Hybrid Car:
Ek Eg Eheat Echem Ebatt
Ek Eg Eheat Echem Ebatt
Ek Eg Eheat Echem Ebatt
Remember that when the normal car stopped, it couldn’t store any of the kinetic energy that it had, but the
hybrid can use that energy to charge the battery, so it’s not lost. Generating electrical energy for the batteries
this way while slowing a vehicle is sometimes called “regenerative braking”. A hybrid car can then use this
stored energy in the batteries to help it get back up to speed without using much gasoline. Thus, overall, we
should see in step C, when they are back up to speed, that Echem (gasoline) lowered more for the normal car than
for the hybrid. This fuel saving usually saves a driver enough money after a few years to pay for the extra
purchase cost of a hybrid car, making hybrid cars a more and more practical and popular choice for consumers.
And let’s not forget the bonus of greatly reduced harmful emissions, such as greenhouse gases!
E. Back to simple mechanical energy
Time to get back to simpler examples, with just two type of energy: Ek and Eg, so that we can begin to make
some calculations. Unless otherwise stated, we will assume that virtually no heat is lost in most of our
examples. So the total mechanical energy (Ek + Eg) will be constant; the total value will be the same before and
after an event.
Consider a 4.0 kg bowling ball going 5.0 m/s on the flat ground. If it rolls up a hill, up to what height will it roll?
1. Calculate Ek now:
A (ball at bottom)
B (ball at max. h)
Ball rolls
up a hill
2. What is the speed when it reaches its max. h?
3. Consider these points:
- Etotal at the bottom is just Ek (h = 0 so Eg = 0)
- Etotal at the top is just Eg (stopped so Ek is zero)
Thus, Ek (bott.) = Eg (top) !
Ek
Eg
Etotal
Ek
Eg
Etotal
4. Use this to solve for the max. height! (You may find it helpful to put a scale on your energy bar graph.)
17
Lesson #6 – POWER
Pre-Lesson Notes
Unit: Energy Read textbook 7.2 and 7.3
Homework: pg 153 Q1-6, pg 154 Q1-3
Date:
Concept: What is Power
Definitions:
Power
Watt
Equations:
18
SPH3U: Power
Winning a race is all about transferring as much energy as possible in the least amount of time. The winner is the
most powerful individual.
Power is defined as the ratio of the amount of work done, W, to the time interval, t, that it takes to do the
work, giving: P=W/t. The fundamental units for power are joules/second where 1 joule/second equals one
watt (W).
A: The Stair Master (Recall: what are the 2 equations we have for work? Write them here:
)
Let’s figure out your leg power while travelling up a set of stairs.
1. Describe the energy changes that take place while you go up the stairs
at a steady rate (we will assume v = const., roughly).
Diagram
2. Explain what you would measure in order to determine the work you do
while travelling up a set of stairs. Sketch a diagram of this showing all
the important quantities. (Hint: either one of the equations you wrote
above will work!)
3. To calculate your power, you will need one other piece of information.
Explain.
4. Gather the equipment you will need. Travel up a flight of stairs at a quick pace (but don’t run, we don’t want
you to fall!) Record your measurements on your diagram.
5. Compute your leg power in watts (W) and horsepower (hp) where 1 hp = 746 W. How does this compare to
your favourite car? (2011 Honda Civic DX = 140 hp; Tesla Roadster = 248 hp.)
19
B: Back to the Behemoth!
1. The trains on the Behemoth are raised from 10 m above ground at the loading platform to a height of 70.1
m at the top of the first hill in 60 s. The train (including passengers) has a mass of 2700 kg and is lifted at a
steady speed. Ignoring frictional losses, how powerful should the motor be to accomplish this task?
Complete the energy diagrams below for the earth-train system. In the energy equation, include a term, Wm,
for the work done by the motor.
Moment A
Moment B
Equation
Ek
Eg
Ek
Eg
20
Lesson #7 – Nuclear Energy
Pre-Lesson Notes
Unit: Energy Read textbook 27.1 – 27.4 and 27.6-27.8
Homework:
Date:
Concept: Nuclear energy
Definitions:
Nuclear Fission
Nuclear Fusion
Chain Reaction
Nuclear Reactors
21
WEP Worksheet #1 - Conservation of Energy Problems
1.
A 4.0 kg block falls 8.0 m from rest. Assuming a conservative system (that is, that no energy is lost to heat) what
speed does it reach?
2.
A 6.0kg rock falls from rest, gaining a speed of 8.0 m/s. Assuming a conservative system, how far did it fall?
3.
A 2.0 kg ball is thrown upwards at 8.0 m/s. Assuming a conservative system, how far does it rise? (Use energy
approach. Check with acceleration approach)
4.
A 4.0 kg ball is thrown upwards at l2.0 m/s. Assuming a conservative system, how far must it rise to slow to 4.0 m/s?
5.
A 2.0 kg ball is moving at 3.0 m/s. Assuming a conservative system, how fast is it going after falling 20.0 m?
6.
A 6.0 kg rock is thrown upward at 12.0 m/s. Assuming a conservative system, how fast is it going after rising 4.0 m?
7.
How much work is needed to get a stationary 6.0 kg block moving at 15 m/s? Assume the block is on a horizontal
frictionless surface.
8.
How much work must be done to increase the speed of a 4.0 kg ball from 3.0 m/s to 9.0 m/s? Assume the motion is
horizontal and that the friction is negligible.
9.
80.0 J of work are done on a 3.0 kg ball moving at 4.0 m/s. Assume its height does not change and that there is no
friction. What speed does it reach?
10.
How much work is needed to raise a 6.0 kg object 14.0 m at constant speed? Assume that friction is negligible.
11.
What is the minimum work that must be done to raise a 30.0 kg object from h = 7.0 m to h = 11.0 m?
12.
How much work is needed to raise a 6.0 kg object 4.0 m while increasing its speed from 2.0 m/s to 6.0 m/s? Assume
that friction is negligible.
13.
How much work must be done to increase the speed of a 4.0 kg ball from 3.0 m/s to 7.0 m/s while raising it 3.0 m?
Assume that the friction is negligible.
14.
How much work is required to push a 168 kg crate 7.0 m at constant speed across a horizontal floor for which the
coefficient of friction is 0.40?
15.
800 J of work are done pushing a 40.0 kg crate 6.0 m along a horizontal surface with μ = 0.30. If the crate started at
rest, what speed does it reach?
16.
A 600 kg crate slides 12 m down a ramp on which the force of friction is 700 N. If the vertical drop is 6.0 m, what
speed does the crate reach?
1. 1.3 x 101 m/s
2. 3.3 m
3. 3.3 m
4. h = 6.5 m
5.
6. 8.1 m/s
7. 6.8 x 102 J
8. 1.4 x 102 J
9. 8.3 m/s
10. 8.2 x 102J
11. 1.2 x 103J
12. 3.3 x 102J
13. 2.0 x 102J
14. 4.6 x 103J
15. 2.2 m/s
16. 9.5 m/s
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20 m/s
WEP Worksheet #2 - Work Problems
1. A 75 kg boulder rolled off a cliff and fell to the ground below. If the force of gravity did 6.0 x
104 J of work on the boulder, how far did it fall?
2. A student in a physics lab pushed a 0.100 kg cart on an air track over a distance of 10.0
cm, doing 0.0230 J of work. Calculate the acceleration of the cart (hint: since the cart was
on an air track, you can assume that there was no friction).
3. With a 3.00 x 102 N force, a mover pushes a heavy box down a hall. If the work done on the
box by the mover is 1.90 x 103 J, find the length of the hallway.
4. A 200 kg hammer of a pile driver is lifted 10.0 m at an acceleration of 0.57 m/s2. Calculate
the work done on the hammer (a) by using ΔE; and (b) by using Fa and Δd.
5. A large piano is moved 12.0 m across a room. Find the average horizontal force that must
be exerted on the piano if the amount of work done is 2.70 x 102 J.
6. A crane lifts a 487 kg beam vertically at a constant velocity. If the crane does 5.20 x 104 J
of work on the beam, find the vertical distance that it lifted the beam.
7. A 2.00 x 102 N force acts horizontally on a bowling ball over a displacement of 1.50 m.
Calculate the work done on the bowling ball by this force.
8. Ralph pushes an empty train car (of mass 1100 kg) 12.0 m [E] along a horizontal track with
a force of 800 N. The forces of friction (bearings, track, air, drag etc.) acting against the car
are 740 N. How much work does Ralph do?
9. Erica pushes a 15 kg crate [E] with a force of 200 N. William pushes the crate [W] at 80
[N]. The force of friction between the crate and the floor is 60 N. Initially at rest, the crate
moves 3.0 m [E] . How much work does Erica do?
10. Erica pushes a 800 kg crate along the floor with a force of 2000 N [E]. The force of friction
from floor acting against the crate is 1800 N. Initially at rest, the crate reaches a speed of
1.5 m/s while it moves 6.0 m [E]. How much work does Erica do?
ANSWERS:
1. 82 m
2. 2.3 N/kg
3. 6.30 m
4. 2.1x104 J (both ways!)
5. 22.5 N
6. 11.0 m
7. 300 J
8. 9.6 x 103 J [E]
9. 6 x 102 J [E]
10. 1.2 x 104 J [E]
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WEP Worksheet #3 - EK and Eg
1. In the sport of pole vaulting, the jumper’s centre of mass must clear the pole. Assume that a 59 kg
jumper must raise the centre of mass from 1.1 m off the ground to 4.6 m off the ground. What is the
jumper’s gravitational potential energy at the top of the bar relative to where the jumper started to
jump?
2. A 485 g book is resting on a desk 62 cm high. Calculate the book’s gravitational potential energy
relative to:
a) the desk top
b) the floor
3. Rearrange the gravitational potential energy equation to obtain an equation for:
a) m
b) g
c) h
4. The elevation at the base of a ski hill is 350 m above sea level. A ski lift raises a skier (total mass = 72
kg, including equipment) to the top of the hill. If the skier’s gravitational potential energy relative to the
base of the hill is 9.2 x 105 J, what is the elevation at the top of the hill?
5. The spiral shaft in a grain auger raises grain from a farmer’s truck into a storage bin. Assume that the
auger does 6.2 x105 J of work on a certain amount of grain to raise it 4.2 m from the truck to the top of
the bin. What is the total mass of the grain moved? Ignore friction.
6. A fully dressed astronaut, weighing 1.2 x 103 N on Earth, is about to jump down from a space capsule
which has just landed safely on Planet X. The drop to the surface of X is 2.8 m and the astronaut’s
gravitational potential energy relative to the surface is 1.1 x 10 3 J.
a) What is the magnitude of the gravitational field strength on Planet X?
b) How long does the jump take?
c) What is the astronaut’s maximum speed?
7. Calculate the kinetic energy of:
a) 7.2 kg shot put that leaves an athlete’s hand during competition at a speed of 12 m/s.
b) a 140 kg ostrich (the fastest 2 legged animal on earth!) that runs at 14 m/s
8. Rearrange the kinetic energy equation to solve for:
a) m
b) v
9. A softball is traveling at a speed of 34 m/s with a kinetic energy of 98 J. What is its mass?
10. A 97 g cup falls from a kitchen shelf and shatters on the ceramic tile floor. Assume that the maximum
kinetic energy obtained by the cup is 2.6 J and that air resistance is negligible.
a) What is the cup’s maximum speed?
b) What do you suppose happened to the 2.6 J of kinetic energy after the crash?
11. A locomotive train with a power of 2.1 MW in 1 minute travels at a speed of 35 m/s. Determine the
mass of the train.
ANSWERS!
1. 2.0 x 103 J
2. a) 0 J
b) 3.0 J
4. 1.7 x 103 m
5. 1.5 x 104 kg
6. a) 3.2 N/kg
b)1.3 s
c) 4.2 m/s
7. a) 5.2 x 102 J b) 1.4 x 104 J
9. 0.17 kg
10. a) 7.3 m/s
11. 2.1 x 105 kg or 210 metric tones (1 tonne = 1000 kg)
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SPH3U: The Conservation of Energy – Bouncing Ball
Complete this activity as a lab in your lab duotang.
Task: Study and analyze the motion and energy transfers in a bouncing ball. Review relationship between d-t, vt, and a-t graphs. Review and understand kinetic and gravitational potential energy.
Equipment: video camera that can play back frame by frame, accurate measurements on the wall, bouncy ball,
students.
Investigation:
Using data previously collected for a bouncing ball, we will now analyze the energy relationships of the ball.
Prepare a new table on a new page, with the following long vertical columns: Height (m), Grav. Pot. Energy (J),
velocity (m/s), Kinetic Energy (J), Total Mech. Energy (J). Weigh the ball to get its mass in kg. Transfer your
position values to the Height column and use them to calculate Eg. Transfer you velocity values (converted to
m/s) and use them to calculate Ek. Add Eg and Ek to get Etotal.
On a large graph, plot three lines: Eg vs time (not Δt), Ek vs time, and Etotal (mechanical energy) vs time. Take care
to choose an appropriate scale that will fit the total energy!
Analysis:
1. Describe what happens to each energy (Eg and Ek) as the ball is on the way down.
2. Describe what happens to each energy (Eg and Ek) as the ball is on the way up.
3. Describe what happened to the total energy over the ball’s entire trip. Was there a general trend, roughly?
4. Give an explanation for any change in the total energy.
5. Discuss whether or not energy is conserved in this system.
6. Google the phrase “isolated system” and comment whether or not the system in this lab is isolated.
7. When the ball is in contact with the ground, both Eg and Ek would be zero or close to zero. This would imply
that the total energy (as seen on your graph) is suddenly zero or close to zero. But then an instant later, the
total energy jumps back up. The real total energy should be constant. Thus, during the bounce a different
type of energy must increase for a moment. What type of energy could this be? Explain your reasoning.
8. Calculate the % change in total energy from the beginning to the end.
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