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 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

 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, 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.

Where is the velocity going to be the greatest? Where is the object going to have the same speed?

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 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: GPE i = ?KE f = ? GPE f = ?v f = ? Known: m = 22.0 kg g = 9.80 N/kg h limb = 13.3 m v i = 0.0 m/s h roof = 6.0 m KE i = 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 = h limb – h roof Conservation of Energy Step 2: Solve for the Unknown

Substitute h limb = 13.3 m, h roof = 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. GPE i = mgh Substitute m = 22.0 kg, g = 9.80 N/kg, h = 7.3 m PE i = (22.0 kg) (9.80 N/kg) (7.3 m) = 1.6×10 3 J Conservation of Energy

The tree limb is initially at rest. Identify the initial kinetic energy of the limb. KE i = 0.0 J Conservation of Energy

Identify the final potential energy of the system. h = 0.0 m at the roof. GPE f = 0.0 J SECTION Conservation of Energy

Substitute KE i = 0.0 J, GPE i = 1.6 x 10 3 J and GPE i = 0.0 J. Use the principle of conservation of mechanical energy to find the KE f. KE f + GPE f = KE i + GPE i KE f = (0.0 J) + (1.6×10 3 J) – (0.0 J) = 1.6 x 10 3 J SECTION Conservation of Energy

B.Solve for the speed of the limb. Conservation of Mechanical Energy (cont.) SECTION Conservation of Energy

Substitute KE f = 1.6×10 3 J, m = 22.0 kg Conservation of Energy

Are the units correct? Velocity is measured in m/s and energy is measured in kg·m 2 /s 2 = J. Do the signs make sense? KE and the magnitude of velocity are always positive. SECTION 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 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 Conservation of Energy