Transcript Gravitational Potential Energy

EQ: What type of energy describes
the motion of a system?
The Many Forms of Energy
•
The word energy is used in many different ways in
everyday speech.
•
Some fruit-and-cereal bars are advertised as energy
sources. Athletes use energy in sports.
•
Companies that supply your home with electricity,
natural gas, or heating fuel are called energy
companies.
The Many Forms of Energy
•
Scientists and engineers use the term energy much
more precisely.
•
Work causes a change in the energy of a system.
•
That is, work transfers energy between a system and
the external world.
The Many Forms of Energy
•
When work is done on a system, the energy of that system
increases.
•
On the other hand, if the system does work, then the energy of
the system decreases.
 Mechanical energy is the
energy that is possessed by an
object due to its motion or due
to its position.
 The total mechanical energy of
a system is the sum of the PE
and KE of a system
 Mechanical energy can be
either kinetic energy (energy of
motion) or potential energy
(stored energy of position
What is causing the ball to move in the other direction?
What would happen to the one side of the ball if the other
ball was lifted higher to begin the motion? Why?
https://www.youtube.com/watch?v=OuA-znVMY3I
Hmm?!
https://www.youtube.com/watch?v=GQGYXuSjo-E
https://www.youtube.com/watch?v=OuA-znVMY3I
Kinetic energy exists whenever an object which has
mass is in motion with some velocity. Everything you
see moving about has kinetic energy. The greater
the mass or velocity of a moving object, the more
kinetic energy it has.
Formula:
KE = ½ m
2
v
Quantity
Variable
Unit
Kinetic
Energy
mass
velocity
KE
Joules (J)
m
v
Kilograms (kg)
Meters/second (m/s)
Silvana Cruciata from Italy set a record
in one-hour running by running
18.084 km in 1.000 h. If Cruciata’s
kinetic energy was 694 J, what was
her mass?
Example continuation
Givens:
Δx = 18.084 km = 1.8084 × 104 m
Δt = 1.000 h = 3.600 × 103 s
KE = 694 J
Unknown: mass
Equation(s):
manipulated
Substitution:
v =1.8084 × 104 m/3.600 × 103 s = 5.023 m/s
m = 2(694)/(5.023)2 = 55.0127
Solution:
m = 55.0 kg
Ability to do work by virtue of position or
condition. In other words, the amount of work
the object capable of doing based on its
position.
A suspended weight
A stretched bow
Two Types of Potential Energy:
 Gravitational Potential Energy (GPE): The energy
associated with an object due to the object’s position
relative to a gravitational source.
 Elastic Potential Energy: The energy stored
in a compressed or stretched spring.
Formula:
PE = m g h
Quantity
Potential Energy
Mass
height
gravity
Variable
PE
M
∆y
g
Unit
Joules (J)
Kilogram (kg)
Meters (m)
Meters/second (m/s2)
In 1993, Javier Sotomayor from Cuba set a record in
the high jump by clearing a vertical distance of 2.45
m. If the gravitational potential energy associated
with Sotomayor at the top point of his trajectory was
1.59 x 103 J, what was his mass?
m = 66.2 kg
Formula:
PEelastic = ½
Quantity
Variable Unit
Potential Energy
Spring constant
Distance compressed
or stretched
PE
k
x
2
kx
Joules (J)
Newton/meter (N/m)
Meters (m)
A 70.0 kg stuntman jumps from a bridge that is
50.0 m above the water. Fortunately, a
bungee cord with an unstretched length of
15.0 m is attached to the stuntman, so that he
breaks his fall 12.0 m above the water’s
surface. If the total potential energy
associated with the stuntman and
cord is 3.43 x 104 J,what is the force constant
of the cord?
Example continuation:
Givens:
m = 70.0 kg
h = 12.0 m
x = 50.0 m − 12.0 m − 15.0 m = 23.0 m
PEg = 0 J at river level
PEtot = 3.43 × 104 J
g = 9.81 m/s2
Unknown: k
Equation(s):
PEtot = PEg + PEelastic
manipulated
Petot = mgh + 1/2kx2
•The change in gravitational
potential energy of an object is
equal to the amount of work
needed to change its height
•Therefore:
Work = DPE
Fd = mgh
•The KE of a moving object is equal
to the work the object is capable
of doing while being brought to
rest
•Therefore:
W = DKE
2
Fd = ½mv
A forward force of 11.0 N is applied to a
loaded cart over a distance of 15.0 m. If the
cart, which is initially at rest, has a final
speed of 1.98 m/s, what is the combined
mass of the cart and its contents?
•Putting these two ideas together
gives us the general Work-Energy
Theorem:
If no change in energy occurs,
then no work is done. Therefore,
whenever work is done, there is
a change in energy.
Closing Task
• Show your knowledge
of how kinetic and
potential energy are
converted from one
form to the other by
labeling the amount
of KE and PE on the
illustration at various
points. Sketch it into
your notebook