Chapter 6 Work and Energy

Objectives: The student will be able to: 1.Define and calculate gravitational potential energy. 2.State the work energy theorem and apply the theorem to solve problems. 3.Distinguish between a conservative and a non-conservative force and give examples of each type of force.

6-4 Potential Energy An object can have potential energy by virtue of its surroundings. Familiar examples of potential energy: A wound-up spring A stretched elastic band An object at some height above the ground

How is all energy divided? Potential Energy Kinetic Energy All Energy Gravitation Potential Energy Elastic Potential Energy Chemical Potential Energy

What is Potential Energy? oEnergy that is stored and waiting to be used later

What is Gravitational Potential Energy? oPotential energy due to an object ’ s position oP.E. = mass x height x gravity height x gravity Don’t look down, Rover! Good boy!

What is Elastic Potential Energy? oPotential energy due compression or expansion of an elastic object. Notice the ball compressing and expanding

What is Chemical Potential Energy? oPotential energy stored within the chemical bonds of an object

Which object has more potential energy? A B

ANSWER A This brick has more mass than the feather; therefore more potential energy!

Changing an objects’ height can change its potential energy. If I want to drop an apple from the top of one of these three things, where will be the most potential energy? A B C

ANSWER The higher the object, the more potential energy! A

Roller Coasters When does the train on this roller coaster have the MOST potential energy? AT THE VERY TOP! The HIGHER the train is lifted by the motor, the MORE potential energy is produced. At the top of the hill the train has a huge amount of potential energy, but it has very little kinetic energy.

6-4 Potential Energy In raising a mass m to a height h, the work done by the external force is We therefore define the gravitational potential energy: (6-5a) (6-6)

10/16/2015 Potential Energy Potential energy is associated with the position of the object Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface The gravitational potential energy –m is the mass of an object –g is the acceleration of gravity –y is the vertical position of the mass relative the surface of the Earth –SI unit: joule (J)

10/16/2015 Reference Levels A location where the gravitational potential energy is zero must be chosen for each problem –The choice is arbitrary since the change in the potential energy is the important quantity –Choose a convenient location for the zero reference height often the Earth’s surface may be some other point suggested by the problem –Once the position is chosen, it must remain fixed for the entire problem

10/16/2015 Work and Gravitational Potential Energy PE = mgy Units of Potential Energy are the same as those of Work and Kinetic Energy

6-4 Potential Energy This potential energy can become kinetic energy if the object is dropped. Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces). If, where do we measure y from? It turns out not to matter, as long as we are consistent about where we choose y = 0. Only changes in potential energy can be measured.

6-4 Potential Energy Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.

6-4 Potential Energy The force required to compress or stretch a spring is: where k is called the spring constant, and needs to be measured for each spring. (6-8)

Elastic Potential Energy: Learning Goals The student will describe the elastic potential energy of a spring or similar object in qualitative and quantitative terms and will investigate the transformation of gravitational potential to elastic potential.

Elastic Potential Energy

Hooke’s Law The stretch or compression of an elastic device (e.g. a spring) is directly proportional to the applied force:

Hooke’s Law The stretch or compression of an elastic device (e.g. a spring) is directly proportional to the applied force:

The spring constant The constant k is called the spring constant or force constant. It has units of N/m and is the slope of the line in a force-extension graph.

Example 1 A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.

Example 1 A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.

Example 1 A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.

Example 1 A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.

Example 1 A student stretches a spring 1.5 cm horizontally by applying a force of magnitude 0.18 N. Determine the force constant of the spring.

Elastic Potential Energy The force stretching or compressing a spring is doing work on a spring, increasing its elastic potential energy. Note that this force is not constant but increases linearly from 0 to kx. The average force on the spring is ½ kx.

Elastic Potential Energy The force stretching or compressing a spring is doing work on a spring, increasing its elastic potential energy. Note that this force is not constant but increases linearly from 0 to kx. The average force on the spring is ½ kx.

Example 2 An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?

Example 2 An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?

Example 2 An apple of mass 0.10 kg is suspended from a vertical spring with spring constant 9.6 N/m. How much elastic potential energy is stored in the spring if the apple stretches the spring 20.4 cm?

Example 2 Follow-Up How much gravitational potential energy did the apple lose?

Example 2 Follow-Up How much gravitational potential energy did the apple lose?

Example 2 Follow-Up How much gravitational potential energy did the apple lose?

Example 2 Follow-Up How much gravitational potential energy did the apple lose?

The ideal spring An ideal spring is one that obeys Hooke’s Law – within compression/stretching limits. Beyond those limits the spring may deform.

The ideal spring An ideal spring is one that obeys Hooke’s Law – within compression/stretching limits. Beyond those limits the spring may deform. Be gentle with my springs!

10/16/2015 Potential Energy in a Spring Elastic Potential Energy: –SI unit: Joule (J) –related to the work required to compress a spring from its equilibrium position to some final, arbitrary, position x Work done by the spring

6-4 Potential Energy The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written: (6-9)

6-5 Conservative and Nonconservative Forces If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force.

10/16/2015 Types of Forces Conservative forces –Work and energy associated with the force can be recovered –Examples: Gravity, Spring Force, EM forces Nonconservative forces –The forces are generally dissipative and work done against it cannot easily be recovered –Examples: Kinetic friction, air drag forces, normal forces, tension forces, applied forces …

10/16/2015 Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points –The work depends only upon the initial and final positions of the object –Any conservative force can have a potential energy function associated with it –Work done by gravity –Work done by spring force

10/16/2015 Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. –The work depends upon the movement path –For a non-conservative force, potential energy can NOT be defined –Work done by a nonconservative force –It is generally dissipative. The dispersal of energy takes the form of heat or sound

6-5 Conservative and Nonconservative Forces Potential energy can only be defined for conservative forces.

6-5 Conservative and Nonconservative Forces Therefore, we distinguish between the work done by conservative forces and the work done by nonconservative forces. We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies: (6-10)

Applying Potential Energy to Problems Practice Problem 1 By how much does the gravitational potential energy of a 64-kg pole vaulter change if her center of mass rises about 4.0 m during the jump?

Applying Potential Energy to Problems Practice Problem 2 #30 in text A 1.60-m tall person lifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to (a) the ground, and (b) the top of the person’s head? (c) How is the work done by the person related to the answers in parts (a) and (b)?

Applying Potential Energy to Problems A 1.60-m tall person lifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to (a) the ground, and (b) the top of the person’s head? (c) How is the work done by the person related to the answers in parts (a) and (b)? (a) Relative to the ground, the PE is given by b) Relative to the top of the person’s head, the PE is given by c) The work done by the person in lifting the book from the ground to the final height is the same as the answer to part (a), 45.3 J. In part (a), the PE is calculated relative to the starting location of the application of the force on the book. The work done by the person is not related to the answer to part (b).

Homework Problems in Chapter 6 #26, 27, 28, 29, 31, 32

Closure Kahoot