Transcript Conservation of Mechanical Energy

EQ:
How is mechanical energy conserved in
regards to potential and kinetic energy?
LO:
We will understand that energy can take many forms but the total energy in a system is constant.
CT:
I will investigate and calculate the changes of different forms of energy.
Energy can neither be created nor destroyed. Energy is
always changing from one kind to another. The total energy
of an object never changes.
Energy transformation on a falling object
• An apple on a tree has
gravitational potential energy
due to the Earth pulling down
on it.
• The instant the apple comes
loose from the tree, it
accelerates due to gravity.
Energy transformation on a falling object
• As objects fall, they lose
height and gravitational
potential energy
• Potential energy is
transformed into kinetic
energy as the velocity
increases.
Energy transformation on a falling object
• If the potential energy is being converted into kinetic
energy, then the mechanical energy of the apple doesn’t
change as it falls.
• The potential energy that the apple loses is gained back
as kinetic energy.
• The form of energy changes, but the total amount of
energy remains the same.
Energy transformation in projectile motion
• Energy transformations also occur during projectile
motion when an object moves in a curved path.
• However, the mechanical energy of the ball remains constant
as it rises and falls.
Energy transformation in a swing
• When you ride on a swing part of the fun is the feeling of
almost falling as you drop from the highest
point to the lowest point of
the swing’s path.
• Energy can change from one form to another, but the total
amount of energy never changes.
Check Point
The total mechanical energy of an object is the ______.
a. KE minus the PE of the object
b. PE minus the KE of the object
c. the initial KE plus the initial PE of the object
d. KE plus the PE of the object at any instant during its motion
e. final amount of KE and PE minus the initial amount of KE
and PE
Check Point
If an object moves in such a manner as to conserve its total mechanical energy,
then ______.
a. the amount of kinetic energy remains the same throughout its motion
b. the amount of potential energy remains the same throughout its motion
c. the amount of both the kinetic and the potential energy remains the same
throughout its motion
d. the sum of the kinetic energy and the potential energy remains the same
throughout its motion
If the mass of the dude is 75 kg, complete the table.
(J) knowledge
KE (J)
Height
ShowPE
your
of how kinetic and(m)
15,000energy
0
potential
are
converted from one
form to
the other by
11250
labeling the amount of
KE and
PE on the
7500
illustration at various
points.3750Sketch it into
your notebook
Mechanical

Energy (J)
0
Velocity
(m/s)
Potential energy + Kinetic energy = Mechanical energy
Example of energy
changes in a swing
or pendulum.
Where is the
velocity going
to be the
greatest?
Where is the
object going to
have the same
speed?
MEi =MEf
PEi + KEi= PEf + Kef
1
1
2
2
𝑚𝑔ℎ𝑖 + 𝑚𝑣𝑖 = 𝑚𝑔ℎ𝑓 + 𝑚𝑣𝑓
2
2
Check Point
The largest apple ever grown had a mass of about 1.47 kg. Suppose
you hold such an apple in your hand. You accidentally drop the apple,
then manage to catch it just before it hits the ground. If the speed of
the apple at that moment is 5.42 m/s, what is the kinetic energy of the
apple? From what height did you drop it?
When work is done on a pendulum, energy is stored
first as potential energy, which is converted to
kinetic energy, then back to potential energy and so
on as the pendulum moves back and forth. The
more work you do on the pendulum—that is, the
greater the height to which you raise the bob from
its resting position—the greater the kinetic energy
of the bob at the bottom of the swing.
Conservation of Energy
Conservation of Mechanical Energy
During a hurricane, a large tree limb, with a mass of 22.0 kg
and at a height of 13.3 m above the ground, falls on a roof that
is 6.0 m above the ground.
A. Ignoring air resistance, find the kinetic energy of the
limb when it reaches the roof.
B. What is the speed of the limb when it reaches the
roof?
Conservation of Energy
Conservation of Mechanical Energy (cont.)
Step 1: Analyze and Sketch the Problem
• Sketch the initial and final conditions.
• Choose a reference level.
Conservation of Energy
Conservation of Mechanical Energy (cont.)
• Draw a bar graph.
Conservation of Energy
Conservation of Mechanical Energy (cont.)
Identify the known and unknown variables.
Known:
m = 22.0 kg
g = 9.80 N/kg
hlimb = 13.3 m
vi = 0.0 m/s
hroof = 6.0 m
KEi = 0.0 J
Unknown:
GPEi = ? KEf = ?
GPEf = ? vf = ?
Conservation of Energy
Step 2: Solve for the Unknown
A. Set the reference level as the height of the roof.
Solve for the initial height of the limb relative to
the roof.
h = hlimb – hroof
Conservation of Energy
Substitute hlimb = 13.3 m, hroof = 6.0 m
h = 13.3 m – 6.0 m
= 7.3 m
Conservation of Energy
Solve for the initial potential energy of the limbEarth system.
GPEi = mgh
Substitute m = 22.0 kg, g = 9.80 N/kg, h = 7.3 m
PEi = (22.0 kg) (9.80 N/kg) (7.3 m)
= 1.6×103 J
Conservation of Energy
Identify the initial kinetic energy of the limb.
The tree limb is initially at rest.
KEi = 0.0 J
1
SECTION
1.2
Conservation of Energy
Identify the final potential energy of the system.
h = 0.0 m at the roof.
GPEf = 0.0 J
1
SECTION
1.2
Conservation of Energy
Use the principle of conservation of mechanical
energy to find the KEf.
KEf + GPEf = KEi + GPEi
Substitute KEi = 0.0 J, GPEi = 1.6 x 103 J and GPEi = 0.0
J.
KEf = (0.0 J) + (1.6×103 J) – (0.0 J)
= 1.6 x 103 J
1
SECTION
1.2
Conservation of Energy
Conservation of Mechanical Energy (cont.)
B. Solve for the speed of the limb.
Conservation of Energy
Substitute KEf = 1.6×103 J, m = 22.0 kg
1
SECTION
1.2
Conservation of Energy
Step 3: Evaluate the Answer
Are the units correct?
Velocity is measured in m/s and energy is measured
in kg·m2/s2 = J.
Do the signs make sense?
KE and the magnitude of velocity are always positive.
1
SECTION
1.2
Conservation of Energy
The steps covered were:
Step 1: Analyze and Sketch the Problem
Sketch the initial and final conditions.
Choose a reference level.
Draw a bar graph.
1
SECTION
1.2
Conservation of Energy
The steps covered were:
Step 2: Solve for the Unknown
Set the reference level as the height of the roof. Solve
for the initial height of the limb relative to the roof.
Solve for the speed of the limb.
Step 3: Evaluate the Answer