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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.
• The instant the apple comes loose from the tree, it accelerates due to gravity.
• An apple on a tree has gravitational potential energy due to the Earth pulling down on it.
Energy transformation on a falling object
• Potential energy is transformed into kinetic energy as the velocity increases.
• As objects fall, they lose height and gravitational potential energy
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 on a falling object
• Energy transformations also occur during projectile motion when an object moves in a curved path.
Energy transformation in projectile motion
• However, the mechanical energy of the ball remains constant as it rises and falls.
• 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 transformation in a swing
• 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 motionb. the amount of potential energy remains the same throughout its motionc. the amount of both the kinetic and the potential energy remains the same throughout its motiond. the sum of the kinetic energy and the potential energy remains the same throughout its motion
Check Point
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
Mechanical Energy (J)
PE (J) KE (J) Height (m)
Velocity (m/s)
15,000
0
11250
7500
3750
0
If the mass of the dude is 75 kg, complete the table.
Potential energy + Kinetic energy = Mechanical energy
Example of energy changes in a swing or pendulum.
Energy in a Roller Coaster
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
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?
Energy of a Pendulum Class Activity
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 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.
Conservation of Energy
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?
Step 1: Analyze and Sketch the Problem
Conservation of Mechanical Energy (cont.)
• Sketch the initial and final conditions.• Choose a reference level.
Conservation of Energy
• Draw a bar graph.
Conservation of Mechanical Energy (cont.)
Conservation of Energy
Identify the known and unknown variables.
Unknown:
GPEi = ? KEf = ?
GPEf = ? vf = ?
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
Conservation of Mechanical Energy (cont.)
Conservation of Energy
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
Step 2: Solve for the Unknown
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 limb-Earth 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
The tree limb is initially at rest.
Identify the initial kinetic energy of the limb.
KEi = 0.0 J
Conservation of Energy
Identify the final potential energy of the system.
h = 0.0 m at the roof.
GPEf = 0.0 J
SECTION
11.2 Conservation of Energy
Substitute KEi = 0.0 J, GPEi = 1.6 x 103 J and GPEi = 0.0 J.
Use the principle of conservation of mechanical energy to find the KEf.
KEf + GPEf = KEi + GPEi
KEf = (0.0 J) + (1.6×103 J) – (0.0 J)
= 1.6 x 103 J
SECTION
11.2 Conservation of Energy
B. Solve for the speed of the limb.
Conservation of Mechanical Energy (cont.)
SECTION
11.2 Conservation of Energy
Substitute KEf = 1.6×103 J, m = 22.0 kg
Conservation of Energy
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.
SECTION
11.2 Conservation of Energy
Step 3: Evaluate the Answer
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.
SECTION
11.2 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
SECTION
11.2 Conservation of Energy
Let’s Practice
