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Lesson 5.2
Energy
Essential Question: How do you
calculate potential and kinetic
energy?
You go to an amusement park and wait in line to
ride your favorite roller coaster. What happens
when you go from the start of the ride to the
bottom of the first hill?
What is energy?
Energy is the ability to do work.
What is kinetic energy?
• The energy of an object
that is due to the
object’s motion
What determines kinetic energy?
• The speed and mass determine an object’s
kinetic energy.
• It’s a scalar quantity and is measured in joules.
• When solving problems, the mass must be
measured in kilograms and the speed measured
in meters per second.
How do you calculate kinetic
energy?
1
2
𝐾𝐸 = 𝑚𝑣
2
The kinetic energy of an object is equal to onehalf the mass times the velocity squared.
A 6.0 kg cat runs after a mouse at 10.0 m/s.
What is the cat’s kinetic energy?
What is the speed of an 8.0 × 104 kg airliner
with a kinetic energy of 1.1 × 109 J?
What is the speed of a 0.145 kg baseball if its
kinetic energy is 109 J?
A car has a kinetic energy of 4.32 × 105 J when
traveling at a speed of 23 m/s. What is its mass?
A 7.00 kg bowling ball moves at 3.00 m/s. How
fast must a 2.45 g table-tennis ball move in order
to have the same kinetic energy as the bowling
ball? Is this speed reasonable for a table-tennis
ball in play?
What is the relationship between
work and energy?
Recall 𝑣𝑓 2
So 𝑎∆𝑥 =
𝑊𝑛𝑒𝑡 = 𝐹∆𝑥 = 𝑚𝑎∆𝑥
= 𝑣𝑖 2 + 2𝑎∆𝑥
𝑣𝑓 2 −𝑣𝑖 2
2
𝑊𝑛𝑒𝑡
Therefore 𝑊𝑛𝑒𝑡 =
𝑣𝑓 2 − 𝑣𝑖 2
=𝑚
2
1
𝑚𝑣𝑓 2
2
−
1
𝑚𝑣𝑖 2
2
Work-Kinetic Energy Theorem
The net work done by all
the forces acting on an
object is equal to the
change in the object’s
kinetic energy.
Wnet  KE
• When you use the work-kinetic energy
theorem, you must include all the forces that
do work on the object in calculating the net
work done.
• It allows us to think of kinetic energy as the
work that an object can do while the object
changes speeds or as the amount of energy
stored in the motion of the object.
On a frozen pond, a person kicks a 10.0 kg sled, giving
it an initial speed of 2.2 m/s. How far does the sled
move if the coefficient of kinetic friction between the
sled and the ice is 0.10?
A student wearing frictionless in-line skates on a
horizontal surface is pushed by a friend with a constant
force of 45 N. How far must the student be pushed,
starting from rest, so that her final kinetic energy is 352
J?
A 2.0 × 103 kg car accelerates from rest under the
actions of two forces. One is a forward force of 1140 N
provided by the traction between the wheels and the
road. The other is a 950 N resistive force due to various
frictional forces. Use the work-kinetic energy theorem
to determine how far the car must travel for its speed to
reach 2.0 m/s.
A 75 kg bobsled is pushed along a horizontal surface by
two athletes. After the bobsled is pushed a distance of
4.5 m starting from rest, its speed is 6.0 m/s. Find the
magnitude of the net force on the bobsled.
What is potential energy?
• It is stored energy; an object that has the
potential to move because of its position
relative to some other location.
• It is the energy associated with an object
because of the position, shape or condition of
the object.
Potential energy depends
not only on the properties
of an object but also on the
object’s interaction with
its environment.
What is gravitational potential
energy?
The potential energy stored in the gravitational
fields of interacting bodies.
Gravitational potential energy depends on height
from a zero level.
How do you find gravitational
potential energy?
𝑃𝐸𝑔 = 𝑚𝑔ℎ
Gravitational potential energy is equal to the
mass times free fall acceleration times the height.
Gravitational potential energy is measured in
joules.
It is a result of the object’s position, so it must be
measured relative to some zero level.
This zero level is arbitrary and is the vertical
coordinate at which gravitational potential
energy is defined to be zero.
What is elastic potential energy?
The energy available for use when a deformed
elastic object returns to its original configuration
Elastic potential energy depends on distance
compressed or stretched.
It is stored in any compressed or stretched
object, such as a spring or the stretched strings of
a tennis racket or guitar.
The relaxed length is the length of a spring when
no external forces are acting on it
When an external force compresses or stretches
the spring, elastic potential energy is stored in
the spring.
The amount of energy depends on the distance
the spring is compressed or stretched from its
relaxed length.
How do you find elastic potential
energy?
𝑃𝐸𝑒𝑙𝑎𝑠𝑡𝑖𝑐
1 2
= 𝑘𝑥
2
Elastic potential energy is equal to one half times
the spring constant times the distance squared.
What is the spring constant (k)?
A parameter that is a measure of a spring’s resistance to
being compressed or stretched
– For a flexible spring, the spring constant is small.
– For a stiff spring, the spring constant is large.
Spring constants have units of newtons divided by
meters (N/m).
A 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge
spanning a river from a height of 50.0 m. When he
finally stops, the cord has a stretched length of 44.0 m.
Treat the stuntman as a point mass, and disregard the
weight of the bungee cord. Assuming the spring
constant of the bungee cord is 71.8 N/m, what is the
total potential energy relative to the water when the man
stops falling?
When a 2.00 kg mass is attached to a vertical spring, the
spring is stretched 10.0 cm such that the mass is 50.0
cm above the table.
a) What is the gravitational potential energy associated
with this mass relative to the table?
b) What is the spring’s elastic potential energy if the
spring constant is 400.0 N/m?
c) What is the total potential energy of this system?
A spring with a force constant of 5.2 N/m has a relaxed
length of 2.45 m. When a mass is attached to the end of
the spring and allowed to come to rest, the vertical
length of the spring is 3.57 m. Calculate the elastic
potential energy stored in the spring.
The staples inside a stapler are kept in place by a spring
with a relaxed length of 0.115 m. 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?
A 40.0 kg child is in a swing that is attached to ropes
2.00 m long. Find the gravitational potential energy
associated with the child relative to the child’s lowest
position under the following conditions:
a) When the ropes are horizontal
b) When the ropes make a 30.0° angle with the vertical
c) At the bottom of the circular arc
How do you calculate kinetic and potential
energy?