EQ: How is mechanical energy conserved in regards to potential and kinetic energy? LO: We will...

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