Name: _______________________
Miss Shea Physics
Date:______
One leader changes everything
Understanding 4.1a All energy transfers are governed by the law of conservation of energy.*
Major Understanding 4.1b Energy may be converted among mechanical, electromagnetic, nuclear, and
thermal forms.
Major Understanding 4.1c Potential energy is the energy an object possesses by virtue of its position or
condition. Types of potential energy include gravitational* and elastic*.
Major Understanding 4.1d Kinetic energy* is the energy an object possesses by virtue of its motion.
Major Understanding 4.1e In an ideal mechanical system, the sum of the macroscopic kinetic and
potential energies (mechanical energy) is constant.*
Major Understanding 4.1f In a nonideal mechanical system, as mechanical energy decreases there is a
corresponding increase in other energies such as internal energy.*
Major Understanding 4.1g When work* is done on or by a system, there is a change in the total energy*
of the system.
Process Skills 4. Energy exists in many forms, and when these forms change energy is conserved.
4.1 Observe and describe transmission of various forms of energy.
i. describe and explain the exchange among potential energy, kinetic energy, and internal energy for
simple mechanical systems, such as a pendulum, a roller coaster, a spring, a freely falling object
ii. predict velocities, heights, and spring compressions based on energy conservation
v. observe and explain energy conversions in real-world situations
Energy is the ability to do work.
Units: Joules (J)
Yes, work and energy are related. Energy is measured by the amount of work an object can
do or actually does.
Types of energy: (1) Potential Energy and (2) Kinetic Energy
1) Potential Energy- the ability to do work
Symbol: PE
Equation: PE=mgh
Unit: Joules (J)
Gravitational field is a conservative field. Therefore, the only quantity causing a change in
the gravitation energy of an object is its change in height. The path of the motion is not
important.
PracticeTeacher: A 155-Newton box is on a ramp. A force causes the box to slide to the top of the
ramp, which is 5.3 m long and 1.8 m high. What is the total amount of gravitational
potential energy gained by the box?
Together: A cart is loaded with a brick and pulled at constant speed along an inclined plane
to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat
top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the
seat-top?
Try: Calculate the potential energy of a 5.2 kg object positioned 5.8 m above the ground.
Tough: A marble beings at an elevated point on top of an inclined ruler and roles down to
the bottom of the ruler, what happens to the potential energy?
Hooke’s Law- states the relationship between the amount of stretch of a spring and the
force applied to the spring is linear.
Symbol: Fs
Equation: Fs=kx
where: k is the spring constant (N/m)- based on the spring itself
x is the displacement from equilibrium (m)
Almost anything that stretches, compresses, or bends obeys Hooke’s Law. Eventually
objects will reach a limit where Hooke’s Law will fail.
PracticeTeacher: A spring has a spring constant of 25 Newton’s per meter. The minimum force
required to stretch the spring 0.25 meter from its equilibrium position is equal to what?
Together: The graph representing the elongation of a spring with different forces added to
it. What is the value of the spring constant?
Try: A 20-newton weight is attached to a spring, causing it
to stretch 0.5 meters from the equilibrium point. What is
the spring constant of the spring?
Tough: On a graph of applied force vs. spring displacement, what is equal to the slope of
the line?
Elastic Potential Energy- The stored energy in a stretched or compressed spring.
Symbol: PE2
Equation: PEs= ½ kx2
where k is the spring constant
x is the change in spring length
PracticeTeacher: Spring A has a spring constant of 140 newtons per meter, and spring B has a
spring constant of 280 newtons per meter. Both springs are stretched the same distanced,
how does the PE of spring A compare to the PE of spring B?
Together: An unstretched spring has a length of 0.4m when at equilibrium. The spring has
a spring constant of k. A weight is hung from the spring causing it to stretch to a length of
0.6 m. How many joules of elastic potential energy are stored in this stretched spring?
Try: What is the elastic potential energy of a spring that is stretched 0.75 m and has a
spring constant of 1 N/m.
Tough: A 0.1 m spring is stretched from equilibrium to 0.15 m then to 0.20 m. Compared
to the spring’s potential energy at the first point, what is the potential energy at the second
point?
2) Kinetic Energy- the energy of motion
Symbol: KE
Equation: KE= ½ mv2
Units: Joules (J)
PracticeTeacher: Calculate the kinetic energy of a 5.2 kg object moving at 2.4 m/s.
Together: Calculate the speed of a 5.2 kg object that possesses 26.1 J of kinetic energy.
Try: What is the kinetic energy of a 980-kilpogram race car traveling a 90 meters per
second?
Tough: A young boy's glider is soaring through the air, possessing 0.80 joules of potential
energy. If its speed is doubled and its height is doubled, then the new potential energy will
be _______.
The Work Energy Theorem- Energy is the ability to do work. If work is done, the total
energy of a system changes. The total energy of a system includes the kinetic energy,
gravitational potential energy, elastic potential energy, and heat (due to friction)
Equation: W=ET
Where w= work done (J)
ET = total energy change (J)
PracticeTeacher: 500 Joules of work were used to bring an object initially traveling at 5 m/s to rest.
What is the mass of the object?
Try: A 15.0 kilogram mass is moving at 7.5 meters per second on a horizontal, frictionless
surface. What is the total work that must be done on the mass to increase its speed to 11.5
meters per second?
Conservation of Energy-The total energy of a system remains constant. Energy can be
transformed from one form to another, and transferred from one object to another, but the
total amount of energy remains constant.
Equation: ET=KE + PE +Q
where: ET= Total Energy (J)
KE = Kinetic Energy
PE = potential energy
Q = internal energy/heat
Mechanical energy is the sum of KE, change in PE, and Elastic potential energy (PEs)
Heat (internal or thermal energy) is only present when there is friction.
PracticeTeacher: Use the law of conservation of energy (assume no friction) to fill in the blanks at
the various marked positions for a 1000-kg roller coaster car.
Together: A student makes a simple pendulum by attaching a mass to the free end of a 1.5
meter length of string suspended from the ceiling of her physics classroom. She pulls the
mass up to her chin and releases it from rest, allowing the pendulum to swing in its curved
path. Her classmates are surprised that the mass doesn’t reach her chin on the return
swing, even though she does not move. Explain why the pendulum does not have enough
energy to return to its starting position.
Try: Calculate the total mechanical energy (TME) of a 5.2 kg object moving at 2.4 m/s and
positioned 5.8 m above the ground.
Try: A ball is dropped from the top of a cliff. Sketch the graph that represents the
relationship between total energy and time elapsed.
Tough: How would you describe the changes in kinetic and total mechanical energy as a
box is pulled up an incline?
Homework Problems
A- Potential Energy
1. A 2.00 kg textbook is lifted from the floor to a shelf 2.10 m above the floor.
a. What is its gravitational potential energy relative to the floor?
b. What is its gravitational potential energy relative to the head of a 1.65 m tall
person?
2. A person weighing 630. N climbs up a ladder to a height of 5.00 m.
a. What is the increase in the gravitational potential energy of the person from the
ground to this height?
b. Where does the energy come from to cause this increase in the gravitational
potential energy?
3. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the
height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is
0.45 m, then what is the potential energy of the loaded cart at the height of the seat-top?
4. Knowing that the potential energy at the top of the tall pillar is 30 J, what is the potential
energy at the other positions shown on the hill and the stairs?
5. Determine the potential energy stored in a spring with a spring constant of 25 N/m
when a force of 2.5 N is applied to it.
B- Kinetic Energy
1. A shot-putter heaves a 7.26 kg shot with a final velocity of 7.50 m/s. What is the
kinetic energy of the shot?
2. A rifle can shoot a 4.20 g bullet at a speed of 965 m/s. Find the kinetic energy of the
bullet.
3. A comet with mass 7.85 x 1011 kg strikes Earth at a speed, relative to Earth, of 25
km/s. Find the kinetic energy of the comet in joules.
4. Determine the kinetic energy of a 1.0 x 103 kg roller coaster car that is moving with
a speed of 20.0 m/s.
5. If the roller coaster car in the previous question were moving with twice the speed,
then what would be its new kinetic energy?
6. Missy Diwater, the former platform diver for the Ringling Brother's Circus had a
kinetic energy of 15,000 J just prior to hitting the bucket of water. If Missy's mass is
50 kg, then what was her speed?
7. A 750 kg compact car moving at 100 km/hr has approximately 290,000 J of kinetic
energy. What is the kinetic energy of the same car if it is moving at 50 km/hr?
8. What is the kinetic energy of a proton traveling at 5.5x106 meters per second?
9. What is the kinetic energy of an electron traveling at 75% the speed of light in a
vacuum?
10. Make a sletch of a graph showing KE vs v.
C- Work-Energy Theorem
1. A shot-putter heaves a 7.26 kg shot. If the shot was initially at rest, how much work
was done on it so that it attains a final velocity of 7.50 m/s?
2. A person weighing 630. N climbs up a ladder to a height of 5.00 m. What work does
the person do?
3. A comet with mass 7.85 x 1011 kg strikes Earth at a speed, relative to Earth, of 25
km/s. Compare the work done with the energy released in exploding the largest
nuclear weapon ever built, equivalent to 100 million tons of TNT, or 4.2 x 1015 J of
energy. Such a comet collision has been suggested as having caused the extinction
of the dinosaurs.
4. A rifle can shoot a 4.20 g bullet at a speed of 965 m/s.
a. What work is done on the bullet if it starts from rest?
b. If the work is done over a distance of 0.75 m, what is the average force on the
bullet?
c. If the bullet comes to rest by pushing 1.5 cm into metal, what is the
magnitude and direction of the average force it exerts?
5. A 1.0 x 103 kg car traveling with a speed of 25 m/s skids to a stop. The car experiences
an 8.0 x 103 N force of friction. Determine the stopping distance of the car.
D- Conservation of Energy
1. In the following descriptions, the only forces doing work on the objects are internal
forces - gravitational and spring forces. Thus, energy is transformed from KE to PE
(or vice versa) and the total mechanical energy is conserved. Read each description
and indicate whether energy is transformed from KE to PE or from PE to KE.
a.
A ball falls from a height of 2 m in the absence of air resistance.
b.
A skier glides from location A to location B across the friction-free ice.
c.
A baseball is traveling upward towards a man in the bleachers.
d.
A bungee chord begins to exert an upward force on a falling bungee jumper.
e.
The spring of a dart gun exerts a force on a dart as it is launched from an initial rest
position.
2. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike
and rider is 85 kg.
a.
Find the kinetic energy of the bike and rider.
b.
The rider coasts up the hill. Assuming there is no friction, at what height will
the bike come to a stop?
c.
Does your answer depend on the mass of the bike and rider? Explain.
3. A large chunk of ice with mass 15.0 kg falls from a roof 8.00 m above the ground.
a.
Find the kinetic energy of the ice when it reaches the ground.
b.
What is the speed of the ice when it reaches the ground?
4. Tarzan, mass 85 kg, swings down from a tree limb from the end of a 20. m vine. His
feet touch the ground 4.0 m below the limb.
a.
How fast is Tarzan moving when he reaches the ground?
b.
Does your answer depend on Tarzan’s mass?
c.
Does your answer depend on the length of the vine?
5. A 60. kg girl and a 70. kg boy swing together on a rope 5.0 m long attached to a tree
over a swimming hole. At the start of the swing, the end of the rope is 10. m above
the surface of the water. At the bottom of the arc, the girl lets go and drops into the
water. The boy remains on the rope. How high does the end of the rope rise at the
top of its swing with the boy alone?
6. Consider the falling motion of the ball in the following two frictionless situations.
For each situation, indicate the kinetic energy and the velocity of the 2 kg ball just
prior to striking the ground.
7. If frictional forces and air resistance were acting on the falling ball in the previous
question, would the kinetic energy of the ball just prior to striking the ground be
more, less, or equal to the value predicted? Explain.
8. The cartoon strip below depicts a pile-driver falling from a high elevation (diagram
A) to a low elevation (diagram B) before it encounters the force of a spike which
ultimately brings it to rest (diagram C). Assume there is no air resistance and that
the spike moves only slightly. Fill in the blanks in the cartoon strip.
Use the following diagram to answer questions 9 and 10. Neglect the effect of friction and
air resistance.
9. As the object moves from point A to point D across the frictionless surface, the sum
of its gravitational potential and kinetic energies ______________________
a.
decreases, only
b.
decreases and then increases
c.
increases and then decreases
d.
remains the same
10. The object will have a minimum gravitational potential energy at point _________