5.2 Energy
DEFINITION OF KINETIC ENERGY
Kinetic energy is the energy of motion
Kinetic energy depends on an objects speed
and mass.
5.2 Energy
DEFINITION OF KINETIC ENERGY
The kinetic energy KE of and object with mass
m and speed v is given by
KE 
1
2
mv
2
Scalar quantity
SI Unit for Kinetic Energy is the Joule
Kinetic Energy
• What are the SI units for KE?
– kg•m2/s2 or N•m or J
Work and Kinetic Energy
• KE is the work an object can do if the speed changes.
• Wnet is positive if the speed increases.
5.2 Energy
Question #8
Calculate the kinetic energy of an 8.0X104kg
airliner flying at 600.0 km/h.
1.1X109 J
5.2 Energy
Question #9
Two bullets have masses of 3.0g and 6.0g,
respectively. Both are fired with a speed of
40.0 m/s. Which bullet has more kinetic
energy? What is the ratio of their kinetic
energies?
– The bullet with the greater mass
– 2 to 1
5.2 Energy
Question #10
Two 3.0g bullets are fired with velocities of
40.0 m/s and 80.0m/s respectively. What
are their kinetic energies? Which bullet
has more kinetic energy? What is the ratio
of their kinetic energies?
– 2.4 J
– The bullet with the more speed
– 4 to 1
5.2 Energy
Question #11
A running student has half the kinetic energy that
his younger brother has. The student speeds up
by 1.3 m/s, at which point he has the same
kinetic energy as his brother. If the student’s
mass is twice as large as his brother’s mass,
what were the original speeds of both the
students and his brother?
– 3.2 m/s
– 6.4 m/s
5.2 Gravitational Potential Energy
DEFINITION OF POTENTIAL ENERGY
~Stored Energy
~Gravitational potential energy depends on the
height from a zero level
PE  mgh
PE  mg  h i  h f 
5.2 Gravitational Potential Energy
DEFINITION OF POTENTIAL ENERGY
The potential energy (PE) is defined by the
mass and height of the object above an arbitrary
zero level.
PE  mgh
PE  mg  h i  h f 
5.2 Gravitational Potential Energy
PE g  mgh
PE gravity  mg hi  h f

Potential Energy
• Energy associated with an object’s
potential to move due to an interaction
with its environment
– A book held above the desk
– An arrow ready to be released from the bow
• Some types of PE are listed below.
– Gravitational
– Elastic
– Electromagnetic
Gravitational Potential Energy
• What are the SI units?
– kg•m2/s2 or N•m or J
• The height (h) depends on the “zero level” chosen where
PEg = 0.
5.2 Gravitational Potential Energy
Example A Gymnast on a Trampoline
The gymnast leaves the trampoline at an initial height of 1.20 m
and reaches a maximum height of 4.80 m before falling back
down. What was the initial speed of the gymnast?
5.2 Gravitational Potential Energy
W 
1
2
mv f 
2
1
2
2
mv i
mg h i  h f   
1
2
2
mv i
W gravity  mgh
vo 
vo 

 2 9 . 80 m s
2
 2 g h o  h f
1 .20 m  4 .80 m   8 .40 m
s

5.2 Elastic Potential Energy
DEFINITION OF ELASTIC POTENTIAL
ENERGY
The energy stored in a spring that is
compressed or stretched
PE elastic 
1
kx
2
2
K = Spring Constant
X= Distance the spring is compressed or stretched
Elastic Potential Energy
• The energy available for use in deformed elastic objects
– Rubber bands, springs in trampolines, pole-vault poles, muscles
• For springs, the distance compressed or stretched = x
5.2 Elastic Potential Energy
DEFINITION OF ELASTIC POTENTIAL
ENERGY
Increasing the spring constant indicates a stiffer
spring
K = Spring Constant
SI unit = N · m
5.2 Elastic Potential Energy
Question #12
Staples inside a stapler are kept in place by
a spring with a relaxed length of 0.115m. If
the spring constant is 51.0 N/m, how much
elastic potential energy is stored in the
spring when its length is 0.150 m?
3.1 X 10-2 J
5.2 Elastic Potential Energy
Question #13
A spring with a force constant of 5.2 N/m
has a relaxed length of 2.45m. When a
mass is attached to the end of the spring
and allowed to come to rest, the vertical
length of the spring is 3.57m. Calculate the
elastic potential energy stored in the
spring.
3.3 J
5.2 Elastic Potential Energy
Question #14
A 40.0kg child is in a swing that is attached
to ropes 2.00m long. Find the gravitational
potential energy associated with the child
relative to the child’s lowest position under
the following conditions:
When the ropes are horizontal.
785 J
5.2 Elastic Potential Energy
Question #15
A 40.0kg child is in a swing that is attached
to ropes 2.00m long. Find the gravitational
potential energy associated with the child
relative to the child’s lowest position under
the following conditions:
When the ropes make a 30.0° angle with
the vertical.
105 J
5.2 Mechanical Energy
DEFINITION OF MECHANICAL ENERGY
The mechanical energy is the sum of potential
energy and kinetic energy.
ME  PE  KE
Mechanical Energy (ME)
• ME = KE + PEg + PEelastic
– Does not include the many other types of
energy, such as thermal energy, chemical
potential energy, and others
• ME is not a new form of energy.
– Just a combination of KE and PE
5.2 Mechanical Energy
Question #16
What forms of energy are involved in the
following situations:
• A bicycle coasting along a level road
– Kinetic
• Throwing a football
– Kinetic and gravitational potential
• Winding a hairspring of a clock
– Elastic potential
5.2 Mechanical Energy
Question #17
A pinball bangs against a bumper, giving the
ball a speed of 42 cm/s. If the ball has a
mass of 50.0g, what is the ball’s kinetic
energy in joules?
4.4 X 10-3 J
5.2 Mechanical Energy
Question #18
A spoon is raised 21.0 cm above a table. If
the spoon and its contents have a mass of
30.0g, what is the gravitational potential
energy associated with the spoon at the
height relative to the surface of the table?
6.18 X 10-2 J
5.2 Mechanical Energy
Question #19
A 65kg diver is poised at the edge of a
10.0m high platform. Calculate the
gravitational potential energy associated
with the position of the diver. Assume the
zero level is at the surface of the pool?
6.4 X 103 J
5.2 Mechanical Energy
Question #20
What is the kinetic energy of a 1250kg car
moving at 45.0 km/h?
9.77 X 104 J
5.2 Mechanical Energy
Question #21
The force constant of a spring in a child’s toy
car is 550 N/m. How much elastic potential
energy is stored in the spring if the spring
is compressed a distance of 1.2 cm?
4.0 X 10-2 J
5.2 Mechanical Energy
Question #22
A 25.0 kg falling object strikes the ground
with a speed of 12.5 m/s. If the kinetic
energy of the object when it hits the
ground is equal to the gravitational
potential energy at some height above the
ground, what is the height ?
7.96 m
Classroom Practice Problems
• Suppose a 1.00 kg book is dropped from a
height of 2.00 m. Assume no air resistance.
– Calculate the PE and the KE at the instant the
book is released.
• Answer: PE = 19.6 J, KE = 0 J
– Calculate the KE and PE when the book has
fallen 1.0 m. (Hint: you will need an equation
from Chapter 2.)
• Answer: PE = 9.81 J, KE = 9.81 J
– Calculate the PE and the KE just as the book
reaches the floor.