Download SPH3U: Work and Energy

Day
1
Lesson
Introducing
Energy
2
Doing Work?
3
Gravitational
Potential Energy
4
The Conservation
of Energy – Part
1
The Conservation
of Energy – Part
2
5
6
Power
7
Heat
8
9
Heat
Nuclear E
10
11
Review
TEST
WORK, ENERGY, POWER Unit Outline
Topics
Homework and Assignments
Work, gravitational
Read: 7.1, 7.4, 7.5, 7.6
potential energy,
Problems: pg 160 Q1-2 and pg 163 Q1-6
kinetic energy,
Lesson:
mechanical energy,
http://physics.wku.edu/phys201/Information/ProblemSolving/
joule, energy flow
EnergyDiagrams.html and
diagram, energy
http://physics.wku.edu/phys201/Information/ProblemSolving/
storage bar graph
energydiagramexample.html
Positive, negative
Read: 7.1, 7.2, 7.3
and net work
Problems: pg 151 Q1-3 and WEP worksheet #1 and #2
Video: www.youtube.com/watch?v=2WS1sG9fhOk
www.youtube.com/watch?v=PD7a1EWjsTc
Path independence, Problems: WEP worksheet #4
energy reference
Video: www.youtube.com/course?list=EC30077BEE77FB6D43
line
Video: www.youtube.com/watch?v=EZNpnCd4ZBo
Conservation of
mechanical energy
Definition of power,
watt
Read: 7.7
Problems: pg 168 Q1-3 and
WEP Worksheet #5
Lesson: Video: Canada’s Wonderland Behemoth
Simulation: Rollercoaster
Simulation: Skateboarding Park
Read: 7.2 and 7.3
Problems: pg 153 Q1-6
Video:
http://www.youtube.com/view_play_list?p=6A1FD147A45EF5
0D
Read Chapter 8
Complete Heat Calculations worksheet (handout)
Complete lab in lab notebook
1
SPH3U: Introducing Energy!
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.
Recorder: __________________
Manager: __________________
Speaker: _________________
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.
 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.
For this investigation you need: one ramp, one large steel ball bearing, and a stopwatch. Set up the ramp with a rise of
between 15 and 20 centimetres.
A: Energy Flows
1.
Roll the ball bearing up the incline and catch when it comes to rest at the top. After it has left your hand and as it goes
up, is it gaining or losing any kind of energy? Explain based on your observations.
A system is a set of objects whose properties we choose to keep track of. An energy flow diagram is an illustration of the
energy that flows into or out of the system. An energy flow diagram consists of a circle that represents the system. Inside the
circle we list all of the objects that are in the system. We draw an arrow going in or out of the circle representing the flow of
energy into or out of the system. On the outside end of the arrow we list the object(s) outside of the system that take part in
the energy flow.
2.
In this example, the ball bearing is our system. Draw an energy flow diagram based on
your answers to questions A#1. What object outside of the system is interacting with the
ball bearing and causing the change in energy?
3.
How could you demonstrate or prove that the ball’s original kinetic energy has transferred into gravitational potential
energy? (Hint: What could you do with the ball?)
B: Work and Gravitational Potential Energy
1.
A student holds a book of mass m in her hand and raises the book vertically
at constant speed through a displacement Δy. 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 mg? Explain briefly.
v
FBD
B.
v
A.
2
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) Consider the earth-book system. 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.
An energy storage diagram has two separate bar graphs which show the amount of energy stored in each mechanism
(gravitational, kinetic, elastic, heat, etc.) at two different moments in time. Unless you know exact values, the exact height of
the bars is not important as long as the changes are clear. In between the two bar graphs we put the energy flow diagram.
(b) Complete the energy storage
diagram and the energy flow
diagram for the earth-book
system. Why is the total energy
of the system changing?
Moment A
Ek
Eg
Flow
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 = F∆d.
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. Express your answer using the symbols m, g, and Δy.
(b) Explain how you could use the result from question B#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!
4.
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)? Think in terms of your answer to question A#3.
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.
3
C: 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 it hits!) 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.
Draw an energy storage bar graph
and an energy flow diagram for the
earth-ball system from moments A
to B.
4.
Exactly how much kinetic energy do
you predict the ball will have just
before it reaches the ground?
Explain.
Moment A
Ek
Flow
Eg
Moment B
Ek
Eg
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.
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
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: how do you feel when you’ve expended lots of energy?
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?
B: Positive and Negative Work
1. A book with a mass of 0.70 kg is initially at rest. Then it is pushed by a hand with
a horizontal force of 10 N along a sheet of ice that has no friction.
(a) Draw vector arrows for the force and displacement. Draw an energy flow
diagram for the system of the book.
(b) After it moves a distance of 0.40 m, how much work has been done on the
book by the external force? Does the external force act in the same or in the
opposite direction as the displacement?
Adapted from Maryland Tutorials in Physics Sensemaking, U. Maryland, open source
5
Vectors
2.
The same book is sliding along a table with an initial velocity of +0.8 m/s and
soon comes to rest. The coefficient of kinetic friction is 0.20.
(a) Draw vector arrows for the force and displacement. Draw an energy flow
diagram for the system of the book.
Vectors
(b) What is the work done by the friction force in bringing the block to rest?
How does the amount of work compare with the original kinetic energy?
3.
Describe the difference between the vectors and the energy flow diagrams you drew for questions B#1 and 2. In each
case, what has happened to the total mechanical energy of the systems?
We need to modify our equation for work, since in the first case, energy was gained by the system and in the second case,
energy was lost. We can cover both these cases with one new equation: W = |F|| d|cos, where  is the angle between the
force and displacement vectors. Positive work is done when the force and displacement vectors are in the same direction,
while negative work is done when these vectors are in opposite directions. From now on, always use this new equation.
4.
In question B#1, what is the angle between the force and displacement vector arrows? Use this in the new work
equation to confirm that positive work was done. What happens to a system experiencing positive work?
5.
In question B#2, what is the angle equal to? Use this in the new work equation to confirm that negative work was done.
What happens to a system experiencing negative work?
C: Total or Net Work
1. The same book as earlier is at rest on the same table as in question B#2. It is pushed through a distance of
0.50 m while experiencing a horizontal applied force of 5 N. What is the work done by the applied force
on the block? Is it positive or negative? What is the work done by the frictional force on the block? Is it
positive or negative? Is the total or net work done on the book positive or negative? Draw an energy flow
diagram for the system of the book.
2.
Overall, is the system gaining or losing energy? Offer two explanations first using the net work and second based on
your understanding of the net force.
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 . Note that this is the same as finding the work done on the system by the net force vector: Wnet = Fnetx cos.
6
SPH3U: 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.
1.
A
Recorder: __________________
Manager: __________________
Speaker: _________________
0 1 2 3 4 5
Ball
1
B
Use energy transfers to describe what will
happen as a ball travels down an incline.
Ball
2
2.
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.
3.
How will the speeds of the two balls compare when they reach the end of the tracks? Why?
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.
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.
7
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?
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.
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 =
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?
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.
8
SPH3U: The Conservation of Energy – Part 1
Complete this activity as a lab in your lab notebook.
Task: Study and analyze the motion and energy transfers in a bouncing ball. Review your understanding
of the relationship between DT, VT, and AT graphs before beginning this investigation. Review and
understand kinetic and gravitational potential energy before beginning this investigation.
Equipment: video camera that can play back frame by frame, accurate measurements on the wall,
bouncy ball, students, Mrs. Meissner
Investigation:
We will use a video camera to record the motion of a bouncy ball when dropped from rest by a student.
The video will capture the motion of the ball. We will use a scale on the wall of the classroom to help us
get accurate measurements. After we record the motion of the bouncy ball with the video camera, we
will record measurements in our observation table by playing the video back frame by frame. The video
camera records 30 frames in 1 second. Therefore, 3 frames is 0.10 seconds.
As part of your results and analysis, you will construct DT, VT, and AT graphs for your bouncy ball.
You will also include a fourth graph: Energy vs time, where you will plot the values of Eg and Ek on the
same graph vs time. You will then add the 2 energies together to record a third energy on your energy vs
time graph. You will need to identify what this is.
Observations:
Create an observations table with the following headings: Δd (m), t (s), v1 (m/s), v2 (m/s), Ek (J), Eg (J)
9
SPH3U: The Conservation of Energy – Part 2
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 compare the
energy at two moments in time: A = at the top of the first hill and B = at ground level
after the first hill.
1. Draw an energy storage bar graph and an energy flow diagram for the earth-train
system. Write down the energy conservation equation.
Moment A
Flow
Moment B
Equation
Ek
Eg
Ek
Eg
2. Choose a convenient vertical position for your energy reference line. Use the energy conservation equation to
find the speed of the rollercoaster at moment B in 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 and an energy flow diagram for the earth-train system. Write down a
new energy conservation equation. Use the symbol Ediss for the energy dissipated (lost) due to friction.
Moment A
Moment B
Flow
Equation
Ek
Eg
Ediss
Ek
Eg
Ediss
5. Use the train mass, mt = 2.7 x 103 kg to determine the amount of energy dissipated on the first hill.
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.
10
B: The Bluevale Flyer
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
Flow
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.
Moment A
Moment D
Flow
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.
11
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
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 as a
steady rate.
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.
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)
Diagram
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
Flow
Equation
Ek
Eg
Ek
12
Eg
Heating/Cooling Curves
Example:
1. How much heat is needed to make 5 kg of ice go from -10°C to water at 20°C?
13
Nuclear Energy
Isotopes –
Example: Carbon can exist the isotopes carbon-12, carbon-13, and carbon-14.
They both have 6 protons (or else they wouldn't be carbon), but a different
number of neutrons.
Isotope Protons Neutrons Calculating
12
6C
13
6C
6
6
You calculate the neutrons by subtracting the bottom
number (atomic number) from the top number (atomic
mass number or isotopic mass). So for carbon-13:
14
6C
13 (#protons & neutrons)
-6 (#protons)
7 (#neutrons)
The atomic mass that appears on the periodic table is a weighted average of all of the
isotopes that are known to exist.
Radioactive nucleus Many isotopes do this naturally. A radioactive nucleus spontaneously changes into a
different nucleus, releasing other particles and energy in the process. This occurs
randomly and without any outside energy.
What happens to the electrons?
14
Nuclear Fission and Nuclear Fusion
Nuclear Fission
Fission is the splitting of a
large atom into two or more
smaller ones.
Critical mass of the
substance and high-speed
neutrons are required.
Nuclear Fusion
Fusion is the fusing of two
Definition:
or more lighter atoms into a
larger one.
High density, high
Conditions:
temperature environment is
required.
Extremely high energy is
required to bring two or
Takes little energy to split
more protons close enough
Energy requirement: two atoms in a fission
that nuclear forces
reaction.
overcome their electrostatic
repulsion.
Natural occurrence Fission reaction does not
Fusion occurs in stars,
of the process:
normally occur in nature.
such as the sun.
Few radioactive particles
are produced by fusion
Byproducts of the
Fission produces many
reaction, but if a fission
reaction:
highly radioactive particles. "trigger" is used,
radioactive particles will
result from that.
The energy released by
fission is a million times
The energy released by
greater than that released in fusion is three to four times
Energy Ratios:
chemical reactions; but
greater than
lower than
the energy released by
the energy released by
fission.
nuclear fusion.
One class of nuclear
One class of nuclear
weapon is the hydrogen
weapon is a fission bomb,
Nuclear weapon:
bomb, which uses a fission
also known as an atomic
reaction to "trigger" a fusion
bomb or atom bomb.
reaction.
15
16
WEP Worksheet #1 - Work Problems
1. 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.
2. 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?
3. 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).
4. 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.
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. 2.1x104 J
2. 82 m
3. 2.3 N/kg
4. 6.30 m
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]
17
WEP Worksheet #2 - Work – Part II - Problems
1. In each of the following cases, state whether you are doing work on your textbook. Explain
your reasoning.
a. You are walking down the hall in your school, carrying your textbook.
b. Your textbook is in your backpack on your back. You walk down a flight of stairs.
c. You are holding your textbook while riding up an escalator.
2. If you push vigorously on a brick wall, how much work do you do on the wall?
3. Describe 2 different scenarios in which you are exerting a force on a box but you are doing
no work on the box.
4. A 160 kg log must be pulled at a constant speed a distance of 56.0 m along a slope inclined
at 9.0°. The force of friction acting against the log is 1200 N. Calculate the work done on the
log.
5. A father is pushing a baby carriage down the street. Find the total amount of work done by
the father on the baby carriage if he applies a 172.0 N force at an angle of 47° with the
horizontal while pushing the carriage 16.0 m along the sidewalk.
6. A farmer pushes a wheelbarrow with an applied force of 124 N. If the farmer does 7314 J of
work on the wheelbarrow while pushing it a horizontal distance of 77.0 m, find the angle
between the direction of the force and the horizontal.
7. Mrs. Meissner is taking her dog Cooper for a walk. Cooper stops to sniff a tree stump and
Mrs. Meissner has to exert a force of 148 N on Cooper’s leash (held 35° above the
horizontal) in order to get him to move 2.0 m away from the tree stump. Calculate the work
done by Mrs. Meissner to get Coop to move.
8. A person pushes a 10 kg cart a distance of 20 m by exerting a 605 N force, 60° above the
horizontal. The frictional resistance force is 50 N. How much work is done by each force
acting on the cart?
ANSWERS:
4. 8.1 x 104 J
5. 1.9 x 103 J
6. 40°
7. 2.4 x 102 J
8. work by Ff = 1 x 103 J (negative work)
work by Fapp = 6.0 103 J
work by Fg and FN = 0 N
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WEP Worksheet #4 - 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 103 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.
1.
2.
ANSWERS!
2.0 x 103 J
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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WEP Worksheet #5 - Conservation of Energy Problems
1.
A 4.0 kg block falls 8.0 m from rest. Assuming a conservative system, 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
7. 6.8 x 102 J
2
x 10 J
13. 2.0 x 102J
15. 2.2 m/s
16. 9.5 m/s
3. 3.3 m
8. 1.4 x 102 J
14. 4.6 x 103J
4. h = 6.5 m
5. 20 m/s
6. 8.1 m/s
9. 8.3 m/s
10. 8.2 x 102J 11. 1.2 x 103J
12. 3.3
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