Mechanics
Energy
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· Identify various forms of energy.
· Define gravitational potential energy and kinetic energy.
· Understand the relationship between work and kinetic energy.
· Solve problems to calculate potential energy and kinetic energy.
· State the Law of Conservation of Energy.
· Solve problems using the Law of Conservation of Energy.
Demonstrations and Notes
µ Stretch a large rubber band between two poles. Pull back the rubber band and launch a plastic ball. Observe and explain.
energy (E) – the ability to produce a change in itself or its surroundings; measured in Joules.
There are many forms of energy. However, energy is not a physical thing: you can’t buy a box of energy. Energy is simply the ability to produce a
change.
µ Show examples of the various forms of energy.
chemical energy – energy due to the breaking of bonds between atoms in a molecule; alkaline battery, lithium battery, nickel-cadmium battery, photosynthesis, human body.
sound energy – vibration of air particles; vibrations of a speaker.
light energy – release of photons; photoelectric effect; incandescent light bulb, fluorescent light bulb, the sun, x-rays, radio waves.
nuclear energy – combining of atoms (fusion) or splitting of atoms (fission); nuclear power plant, warheads, plutonium, the sun.
potential energy – stored energy; bow, sling shot, wind-up clock, alkaline battery, lithium battery, nickel-cadmium battery, photosynthesis, human body.
heat energy – thermal energy; usually due to friction; rubbing your hands together, the sun, incandescent light bulb.
Demonstrations and Notes
µ Construct a pendulum by hanging a 10 kg mass from a string. Define the position of the hanging mass at rest as the equilibrium position. Swing the pendulum and observe its motion.
The most common type of energy is actually a combination
of energies. Mechanical energy includes
gravitational potential energy, kinetic energy, and heat energy.
mechanical energy (ME) – energy due to position and motion; sum of potential and kinetic energies, including friction (heat, air resistance, etc.).
gravitational potential energy (PE) – energy of position; any object above the zero line has PE.
point of reference – zero line or lowest point of a system.
Joule (J) – units of gravitational potential energy;
1 
.
= J
Gravitational potential energy is usually referred to as
simply potential energy. When
determining PE, the point of reference is set as the lowest point of the
system. This is done to ensure PE will
always be a positive value. It is
possible for PE to be negative, but it is more convenient for it to always be
positive.
kinetic energy (KE) – energy of motion; anything that
is moving (
) has KE.
Joule (J) – units of kinetic energy; 1 .
= J
Kinetic energy is dependent upon the speed of an
object. If an object is not moving, it
has no KE. The value of KE can be either
positive or negative, depending on the object’s direction. It is more convenient when KE is a positive
value, but that is not always possible.
µ Refer again to the pendulum. Explain how energy is transferred from one form to another.
µ Refer again to the large rubber band stretched between two poles. Explain why the ball is launched through the air.
When you do work on an object, you make the object
move. All objects in motion possess
kinetic energy. Therefore, objects have
kinetic energy due to work.
Work-Energy Theorem – the net work done on an object is equal to its change in kinetic energy.
µ Throw a ball through the air. Explain why the ball moves.
Summary Review – Energy and Mechanical Energy
ü Energy is the ability to produce a change in itself or its surroundings.
ü Mechanical Energy is energy due to position and motion. It is the sum of potential and kinetic energies, including friction.
ü Gravitational Potential Energy is energy of position.
ü Kinetic Energy is energy of motion.
ü The Joule is a unit of energy.
ü When work is done on an object, the object moves. Objects in motion possess kinetic energy. Therefore, objects have kinetic energy due to work. This is known as the Work-Energy Theorem.
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1. Identical twins Pat and Chris are painting a house. Pat is standing on the scaffolding 5 meters above the ground. Chris is standing on the scaffolding 5 meters above Pat. Who has more potential energy? Explain.
2. Jared and Clay are climbing the stairs. Jared gets tired and stops halfway to the fourth floor. Clay makes it to the fourth floor without a problem. If Jared is twice as heavy as Clay, who has more potential energy? Explain.
3. A person weighing 630 N climbs up a ladder to a height of 5 meters. How much work does the person do? Determine the increase in the potential energy of the person from the ground to this height. Where does the energy come from to cause this increase in PE?
4. Calculate the kinetic energy of a 750 kg car moving at 13.9 m/s. What is the kinetic energy of the car if the speed is doubled? How much work must be done to double the speed?
5. A rifle can shoot a 4.2 g bullet at a speed of 965 m/s. Find the kinetic energy of the bullet. What work is done on the bullet if it starts from rest? If the work is done over a distance of 75 cm, determine the average force acting on the bullet.
Demonstrations and Notes
µ Using Pasco low-friction tracks and carts of equal mass with a plunger, place two carts touching side-by-side with the plunger engaged. Release the plunger and observe the motion of the carts before, during, and after the explosion.
Approximately 15 billion years ago, it is theorized that
there was a huge explosion. This
explosion sent particles flying out in all directions. This explosion of enormous proportion, known
as the Big Bang, spawned the creation of everything in our universe.
Since this phenomenon was indeed an explosion, the
particles were pushed apart and traveled through space. Space, being a vacuum, allowed the particles
to travel an infinite distance. If you
apply the Law of Conservation of Momentum to the Big Bang Theory, the traveling
particles would never stop moving away from the explosion. This idea led to the theory that the universe
is continually expanding.
However, after you expand something so far, it reaches
its limit and wants to begin compressing.
The same is believed to be true of our universe. After the Big Bang expanded our universe to
its limit, our universe will begin to compress until it has reached its
compression limit. This is believed to
be a continuous process that has been cycling through for billions of years.
When the Big Bang occurred, energy was released. The total energy released billions of years
ago is believed to be the same amount of energy we have today; energy is a
universal constant.
Law of Conservation of Energy – energy cannot be created or destroyed; it may only be transferred from one form to another but the total amount of energy never changes.
Albert Einstein worked on many things throughout his
career and energy is among the topics he investigated. Einstein found that the amount of energy an
object can possess is proportional to its mass.
From that proportion, Einstein formulated an equation that can be used
to calculate the energy of that object.
There are an infinite number of examples of the Law of
Conservation of Energy. Here are a few.
In the perfect physics world, a pendulum will swing
forever. Energy is constantly
transferred between potential and kinetic energies. In the real world, a swinging pendulum eventually
stops due to friction. However, the
total energy of the pendulum never changes.
The energy is transferred from potential energy to kinetic energy. The friction is shown as a form of heat
energy which includes air resistance and sound energy.
µ Hang a bowling ball from the ceiling. Hold the ball to your nose and release it. Do not push the ball or move after the ball is released. Observe.
In the perfect physics world, a person can jump from a
diving board and hit the water with the same amount of energy as they had
before they jumped. Energy is
transferred from potential energy to kinetic energy until they hit the
water. In the real world, air resistance
would also be a factor, but it is usually ignored to simplify the problem. When the diver hits the water, kinetic energy
is transferred into heat and sound energies.
However, the total energy of the diver never changes. The energy of the system is transferred from
potential to kinetic to heat.
µ Pull back on a toy car until it clicks. Release the car and explain what was done to the car to allow it to move.
µ Place a Hot Wheels track between two poles so the track forms a U-shape. Predict how far up the track a car will travel if released from a specific height. Allow a Hot Wheels car to slide down the track. Explain.
µ Make a Slinky travel down the stairs or a stack of books. Explain how the Slinky works.
µ Cut off the top third of a racquetball. Fold the racquetball inside out and place a ping pong ball on the racquetball. Observe and explain.
µ Pull back one ball on a Newton’s Cradle. Predict what will happen when it is released. Repeat with two, three, and four balls, making a prediction for each case.
ą Have the students research the following question regarding Newton’s Cradle on the internet: Explain why one ball in cannot produce two balls out at half the speed, etc.
To fully understand Newton’s Cradle, you must look at
several aspects of physics. Not only
must you apply the Law of Conservation of Energy, you must also recall the Law
of Conservation of Momentum. By applying
both principles to Newton’s Cradle, a basic, yet satisfactory, explanation is
drawn about the proposed question. For
more information, refer students to http://www.lhup.edu/~dsimanek/scenario/cradle.htm.
Summary Review – Conservation of Energy
ü The Law of Conservation of Energy states that energy cannot be created or destroyed.
ü Energy can only be transferred from one form to another.
ü The total amount of energy in the universe never changes.
ü Energy is never lost, only transferred.
Problem Solving with Conservation of Energy
Notes
The key to success when solving any energy problem is
remembering one thing: energy is always
conserved! Since energy is always
conserved, there is technically only one equation necessary. The equations for potential and kinetic
energies are also needed, but they are simply substituted into the conservation
of energy equation. Once the type of
problem is determined, proper set up and substitution will always lead to the
correct answer. Don’t forget to include
proper units!
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conservation of
energy |
potential energy |
kinetic energy |
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When solving problems, the
following procedures will be used.
- Determine if heat (friction) is included in
the problem.
- Make a sketch of the situation and label all
given and unknown quantities.
- Determine what variables are known and needed.
- Recall that energy is always conserved and set
up the proper equation.
- Substitute the given quantities into the
equation using proper units.
- Solve the equation, carrying units throughout
the problem.
- Check your answer to make sure it makes sense.
Summary Review – Problem
Solving with Conservation of Energy
ü Energy is always conserved. Always!
ü The overall mass of a system does not change.
ü The Problem Solving Strategy is used when solving Conservation of Energy problems.
Classwork – Problem Solving with Conservation of Energy
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1. A large chunk of ice with mass 15 kg falls from a roof 8 meters above the ground. Find the kinetic energy of the ice when it reaches the ground. What is the speed of the ice when it reaches the ground?
2. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and the rider is 85 kg. Find the kinetic energy of the bike and rider. If the rider coasts up the hill, calculate the height at which the bike will come to a stop. (Assume there is no friction.) How would your answer vary if the mass of the bike and rider were doubled?
3. A 2 kg rocket is launched straight up into the air with a speed that allows it to reach a height of 100 meters, even though air resistance performs 800 J of work on the rocket. Determine the launch speed of the rocket. How high would the rocket travel if air resistance is ignored?
4. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations.
Homework – Problem Solving with Conservation of Energy
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1. A 20 kg rock is on the edge of a 100 meter cliff. Calculate the potential energy of the rock. If the rock falls off the cliff, what is its kinetic energy just before striking the ground? What speed does the rock have as it strikes the ground?
2. A physics book is dropped 4.5 meters. What speed does the book have just before it hits the ground?
3. From what height would a compact car have to be dropped to have the same kinetic energy that is has when being driven at 100 km/hr?
4. A 70 kg high jumper leaves the ground with a speed of 6 m/s. How high can he jump?
5. Just before striking the ground, a 900 kg Smart Bomb has 88.2 MJ of kinetic energy. If air resistance is ignored, determine the height from which the Smart Bomb was dropped. Determine the drop height if air resistance performs 8.82 MJ of work against the bomb as it falls towards its target.
6. A 74 kg student, starting from rest, slides down an 11.8 meter high water slide. On the way down, friction does 5600 J of work on him. How fast is he going at the bottom of the slide?
7. Block A with a mass of 12 kg moving at 2.4 m/s makes a perfectly elastic head-on collision with block B, mass 36 kg, at rest. Find the velocities of the two blocks after the collision. Assume all motion is in one dimension.
8. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the ball at the various locations.
CONSERVATION OF ENERGY LAB PACKET
Introduction – What’s Going On?
If an airplane were to lose power, the pilot can go into a controlled descent, giving up altitude (potential energy) in an attempt to gain air speed (kinetic energy) and perhaps make a safe emergency landing. When a roller coaster is pulled to the top of the first hill, it is given potential energy which is converted to kinetic energy as it rolls down the other side. For the rest of the ride, these two energies are constantly being converted, one into the other and back again. When a trucker brings a heavy load down a steep hill, he must realize that potential energy will be converted to kinetic energy (speed) as he comes down the hill, and since the truck can’t go too fast, the brakes must be able to absorb the additional energy.
The Law of Conservation of Energy involve concepts related to kinetic energy, potential energy, work, and heat. To see how these concepts affect one another, various experiments can be performed. One experiment reveals the amount of heat created when bouncing a ball. Another requires you to hit a target with a projectile launched horizontally from a modified pendulum. This lab contains two parts that apply the concepts of kinetic energy, potential energy, work, and heat in an effort to develop a better understanding of the Law of Conservation of Energy.
Important equations used throughout this lab packet are listed below for reference.
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% KELOST
= |
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g = -9.8 m/s2 |
Both experiments in this packet requires you to recall various information pertaining to the Law of Conservation of Energy and the Law of Conservation of Momentum. Read each activity and follow the directions listed on the following pages.
Part I – Setting Up
- Each group needs a meter stick and five different balls selected from the following: basketball, volleyball, softball, tennis ball, lacrosse ball, golf ball, plastic ball, chrome ball.
- In addition, two superballs, superball one (happy) and superball two (sad), are needed. The superballs will be handed out after the first five balls are bounced and data recorded.
Part II – Bouncing Balls
- Using the meter stick with zero at the floor, drop each ball from a height of one meter and measure the height each ball bounces back up after the first bounce.
- Bounce each ball five times to determine an average bounce height for each ball.
- After the first five balls are bounced and data recorded, acquire the two superballs from the teacher.
- Find the mass of the seven balls and convert to kilograms.
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All data must be recorded
in the data table provided. Convert
all data to proper units (see data table headings) before entering it in the
data table. |
Part III – Wrap Up
- Complete the attached data table, using proper units. (16 points)
ţ The first PE and KE refer to the ball as it is dropped. The first v refers to the speed of the ball when it hits the ground.
ţ The second PE and KE refer to the ball after it bounces. The second v refers to the speed of the ball when leaving the ground.
- Answer the following questions. (14 points total)
Ř Discuss how the PE and KE of a falling ball are related.
Ř Explain the results for the velocity of each ball as it falls.
Ř
Using 
, explain why the balls don’t bounce back to their
original drop height.
Ř Explain the physics behind the happy and sad balls.
Ř Show how the values for each column of the data table were calculated.
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Ball |
Mass (kg) |
Average
Release Height (m) |
PE (J) |
KE (J) |
v (m/s) |
Average
Bounce Height (m) |
PE (J) |
KE (J) |
v (m/s) |
DKE [Heat
Due to Bounce] (J) |
KELOST (%) |
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Shooting For Your Grade Revisited
Part I – Calculating Horizontal Launch Velocity
- Each group needs a stand, two clamps, string, a bob, a razor blade, and a meter stick.
- Construct a pendulum using the bob and string. Hang the string from a clamp of the stand so the bob hangs just above the table top.
- Attach the razor blade to the stand using a clamp. Align the razor blade so it will cut the pendulum string when swinging. The razor should be as close to the table top as possible.
- Select a release height, measured from the table top, from which to release the bob.
- Using the Law of Conservation of Energy, calculate the horizontal velocity of the bob.
- DO NOT RELEASE THE BOB. You are only calculating theoretical values!
Part II – Hitting the Target
- Using what you learned about projectile motion, predict the horizontal distance the ball will be launched after the razor blade cuts the pendulum string.
- When you are certain you have accurately calculated the horizontal distance of the bob after being cut by the razor, place the target on the floor and let the projectile fly!
Part III – Wrap Up
- The group grade is based on where the projectile hits the target. (50 possible points)
- Extra credit is awarded for turning in your calculations sheet. (10 possible points)
- No more than 50 total points can be earned.
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1. Jamie lifts her toys into her tree house using a homemade elevator. The elevator has a mass of 2.5 kg and the tree house is 8 meters above the ground. How much work does Jamie do when lifting 5 kg of toys into the house? Determine the power used to lift the toys in 5 sec.
2. Mike pulls a sled across level snow with a force of 225 N using a rope that is angled at 35°. Determine the work done if he pulls the sled 65.3 meters.
3. A 2 kg textbook is lifted from the floor to a shelf 2.1 meters above the floor. Determine the book’s potential energy relative to the floor. What is the book’s potential energy relative to the head of a 1.65 meter tall person?
4. A shot-putter heaves a 7.26 kg shot with a velocity of 7.5 m/s. Determine the kinetic energy of the shot. How much work was done on the shot to give it its kinetic energy?
5. Calculate the kinetic energy of a 750 kg compact car moving at 100 km/hr. How much work must be done to slow the car down to 50 km/hr?
6. Determine the mechanical energy of a 450 kg roller coaster moving at 30 m/s at the bottom of the first dip which is 15 meters above the ground.
7. Julie has a mass of 49 kg. What is her potential energy when standing on the 6 meter diving board? (She is 6 meters above the water.) Julie jumps off the diving board. What is her kinetic energy right before she hits the water? How fast does Julie hit the water?
8. An unfortunate skydiver’s parachute fails to open. If the diver hits the ground going 300 m/s, determine the height from which the ill-fated jump was make.
9. Calculate the potential, kinetic, and mechanical energies, velocity, work, and power of the ball at the various locations.
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1. As everyone should know, bullets bounce from Superman’s chest. Suppose Superman, mass 104 kg, while not moving, is struck by a 4.2 gram bullet moving with a speed of 835 m/s If the collision is elastic, find the speed the bullets bounce from Superman’s chest and the speed that Superman has after the collision. (Assume the bottoms of his superfeet are frictionless.)
2. A pendulum is constructed from a 7.26 kg bowling ball hanging on a 2.5 meter long rope. The ball is pulled back until the rope makes a 45° angle with the vertical. Determine the potential energy of the bowling ball. If the bowling ball is released, calculate the bowling ball’s kinetic energy when it reaches its lowest point (equilibrium). What is the speed of the bowling ball at its lowest point?
3. A dock worker places a 350 N crate on the top of an incline which leads to the warehouse. The incline is 8 meters long and sits 5 meters above the warehouse door. If the force due to friction is 50 N, find the velocity of the crate at the bottom of the incline.
4. The cable of a 4,000 kg elevator snaps when the elevator is at rest on the third floor of an office building, 12 meters above ground level. A safety device clamps the guide rails of the elevator shaft so a constant frictional force opposes the motion of the elevator. If the elevator hits the ground level with a velocity of 10 m/s, find the frictional force exerted by the rails.
5. A 70 kg diver steps off a 10 m tower and drops straight down into the water. If she comes to rest 5 m beneath the surface of the water, determine the resistive force exerted on the diver by the water.