College Physics, 7th Edition Lecture Outline Chapter 5 College Physics, 7th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

Chapter 5 Work and Energy © 2010 Pearson Education, Inc.

Units of Chapter 5 Work Done by a Constant Force Work Done by a Variable Force The Work–Energy Theorem: Kinetic Energy Potential Energy Conservation of Energy Power © 2010 Pearson Education, Inc.

5.1 Work Done by a Constant Force Definition of work: The work done by a constant force acting on an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to that displacement. © 2010 Pearson Education, Inc.

5.1 Work Done by a Constant Force No Motion = No Work © 2010 Pearson Education, Inc.

5.1 Work Done by a Constant Force If the force is at an angle to the displacement, as in (c), a more general form for the work must be used: Unit of work: newton • meter (N • m) 1 N • m is called 1 joule. © 2010 Pearson Education, Inc.

5.1 Work Done by a Constant Force For example: The work done by a force of 25 N on an object as the object moves parallel displacement of 2.0 m. Calculate work.

5.1 Work Done by a Constant Force For example: What 50 Joules of work are produced in a 10 m distance, how much force was applied to the system?

Question 5.1 To Work or Not to Work Is it possible to do work on an object that remains at rest? a) yes b) no Answer:

5.1 Work Done by a Constant Force If the force (or a component) is in the direction of motion, the work done is positive. If the force (or a component) is opposite to the direction of motion, the work done is negative. © 2010 Pearson Education, Inc.

Question 5.2a Friction and Work I A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? a) friction does no work at all b) friction does negative work c) friction does positive work Answer:

5.1 Work Done by a Constant Force A student holds her 1.5 kg textbook out a second story window until her arm is tired; then she releases it. A.) How much work is done on the book by the student in simply holding it out the window? B.) How much work is done by the force of gravity during the time in which the book falls 3.0 m?

5.1 Work Done by a Constant Force If there is more than one force acting on an object, it is useful to define the net work: The total, or net, work is defined as the work done by all the forces acting on the object, or the scalar sum of all those quantities of work. © 2010 Pearson Education, Inc.

5.1 Work Done by a Constant Force A worker pulls a 40 kg crate with a rope. The coefficient of kinetic friction between crate and floor is 0.550. If he moves the crate with a constant velocity for a distance of 7.00 m, how much work is done?

5.1 Work Done by a Constant Force A passenger at an airport pulls a rolling suitcase by its handle. If the force used is 10N and the handle makes an angle of 25 degrees to the horizontal, what is the work done by the pulling force while the passenger walks 200 m?

Question 5.3 Force and Work a) one force b) two forces c) three forces d) four forces e) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? Answer:

5.2 Work Done by a Variable Force The force exerted by a spring varies linearly with the displacement: © 2010 Pearson Education, Inc.

5.2 Work Done by a Variable Force An applied force stretches a spring and as the spring is stretched, the restoring force becomes greater. For most springs, the spring force is directly proportional to change in length of the spring. Force on the spring varies with x (so force is a function of position). Called Hooke’s Law W = ½ kx2

Question 5.14 Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? a) same amount of work b) twice the work c) four times the work d) eight times the work Answer:

5.2 Work Done by a Variable Force A 0.15 kg mass is attached to a vertical spring and hangs at rest at a distance of 4.6 cm below its original position. An additional 0.50 kg mass is then suspended from the first mass and the system is allowed to descend to a new equilibrium. What is the total extension of the spring?

5.3 The Work–Energy Theorem: Work is something done on objects, whereas energy is something objects possess. When something possesses energy it has the ability to do _______. No _________ = No _________ © 2010 Pearson Education, Inc.

5.3 The Work–Energy Theorem Consider an object at rest on a frictionless surface. A horizontal force acts on the object and sets it in motion. Work is being done on the object, but where does that work go?

5.3 The Work–Energy Theorem: Kinetic Energy Kinetic energy is therefore defined: The net work on an object changes its kinetic energy. © 2010 Pearson Education, Inc.

Question 5.5a Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled? a) no change at all b) factor of 3 c) factor of 6 d) factor of 9 e) factor of 12 Answer:

5.3 The Work–Energy Theorem: Kinetic Energy We can use this relation to calculate the work done: W = K - K0 © 2010 Pearson Education, Inc.

5.3 The Work–Energy Theorem: Kinetic Energy This relationship is called the work–energy theorem. © 2010 Pearson Education, Inc.

5.3 The Work–Energy Theorem: Kinetic Energy A shuffleboard player pushes a 0.25 kg puck that is initially at rest such that a constant horizontal force of 6.0 N acts on it through a distance of 0.50m. (Neglect friction) A.) What are the kinetic energy and the speed of the puck after the force is removed? B.) How much work would be required to bring the puck to rest?

5.3 The Work–Energy Theorem: Kinetic Energy In a football game, a 140 kg guard runs at a speed of 4 m/s, and a 70 kg free safety moves at 8 m/s. Which of the following is a correct statement? A.) Players have the same kinetic energy. B.) Safety has 2x as much kinetic energy. C.) Guard has 2x as much kinetic energy. D.) Safety has 4x as much kinetic energy.

5.4 Potential Energy Potential energy may be thought of as stored work, such as in a compressed spring or an object at some height above the ground. Work done also changes the potential energy (U) of an object. © 2010 Pearson Education, Inc.

5.4 Potential Energy We can, therefore, define the potential energy of a spring; note that, as the displacement is squared, this expression is applicable for both compressed and stretched springs. © 2010 Pearson Education, Inc.

5.4 Potential Energy Gravitational potential energy: Most well known type Formula? © 2010 Pearson Education, Inc.

Question 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? d) same speed for all balls a b c Answer:

5.4 Potential Energy To walk 1000m on level ground, a 60 kg person requires an expenditure of about 100,000 J of energy. What is the total amount of energy required if the walk is extended another 1000m along a 5 degree incline. (Neglect friction)

5.4 Potential Energy A 0.50 kg ball is thrown vertically upward with an initial velocity of 10 m/s. A.) What is the change in the ball’s kinetic energy between the starting point and the ball’s maximum height? B.) What is the change in the ball’s potential energy?

5.4 Potential Energy Only changes in potential energy are physically significant; therefore, the point where U = 0 may be chosen for convenience. © 2010 Pearson Education, Inc.

5.5 Conservation of Energy Some physical quantities are conserved, meaning constant. We observe that, once all forms of energy are accounted for, the total energy of an isolated system does not change. This is the law of conservation of energy: The total energy of an isolated system is always conserved. [Energy can never be created nor destroyed…only converted to different forms] © 2010 Pearson Education, Inc.

5.5 Conservation of Energy We define a conservative force: A force is said to be conservative if the work done by it in moving an object is independent of the object’s path. Force depends only on the initial and final positions of an object. What does it mean to be independent of path?

5.5 Conservation of Energy So, what types of forces are conservative? Gravity is one; the work done by gravity depends only on the difference between the initial and final height, and not on the path between them. Similarly, a nonconservative force: A force is said to be nonconservative if the work done by it in moving an object does depend on the object’s path. The quintessential nonconservative force is friction. © 2010 Pearson Education, Inc.

5.5 Conservation of Energy We define the total mechanical energy: Sum of kinetic and potential energies The sum of these are _________ © 2010 Pearson Education, Inc.

5.5 Conservation of Energy For a conservative force: Total Mechanical Energy is constant E = E0 For nonconservative forces, mechanical energy is usually lost. © 2010 Pearson Education, Inc.

5.5 Conservation of Energy A painter on a scaffold drops a 1.5 kg can of paint from a height of 6.00m. A.) What is the kinetic energy of the can when the can is at a height of 4.00m? B.) With what speed will the can hit the ground? (Neglect air resistance)

5.5 Conservation of Energy Three balls of equal mass are projected with the same speed in different locations. If air resistance is neglected, which ball would you expect to strike the ground with the greatest speed: a.) ball 1 b.) ball 2 c.) ball 3 d.) all balls same © 2010 Pearson Education, Inc.

5.5 Conservation of Energy If a nonconservative force or forces are present, the work done by the net nonconservative force is equal to the change in the total mechanical energy. © 2010 Pearson Education, Inc.

5.5 Conservation of Energy A skier with a mass of 80 kg starts from rest at the top of a slope and skis down from an elevation of 110 m. The speed of the skier at the bottom of the slope is 20 m/s. A.) Show that the system is nonconservative. B.) How much work is done?

1 horsepower (hp) = 746 Watts The average power is the total amount of work done divided by the time taken to do the work. S.I. Unit: J/s = Watt (W) 1 horsepower (hp) = 746 Watts © 2010 Pearson Education, Inc.

Question 5.21a Time for Work I Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? a) Mike b) Joe c) both did the same work Answer:

Question 5.21b Time for Work II a) Mike produced more power b) Joe produced more power c) both produced the same amount of power Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? Answer: b

5.6 Power A crane hoist lifts a load of 1.0 metric ton a vertical distance of 25 m in 9.0 s at a constant velocity. How much useful work is done by the hoist each second?

5.6 Power The motors of two vacuum cleaners have net power outputs of 1.00 hp and 0.500 hp, respectively. A.) How much work in Joules can each motor do in 3.00 min? B.) How long does each motor take to do 97.0 kJ of work?

5.6 Power Mechanical efficiency: The measure of what you get out for what you put in. The efficiency of any real system is always less than 100%. © 2010 Pearson Education, Inc.

5.6 Power The motor of an electric drill with an efficiency of 80% has a power input of 600 Watts. How much useful work is done by the drill in 30 seconds?

5.6 Power © 2010 Pearson Education, Inc.

Review of Chapter 5 Work done by a constant force is the displacement times the component of force in the direction of the displacement. Kinetic energy is the energy of motion. Work–energy theorem: the net work done on an object is equal to the change in its kinetic energy. Potential energy is the energy of position or configuration. © 2010 Pearson Education, Inc.

Review of Chapter 5 The total energy of the universe, or of an isolated system, is conserved. Total mechanical energy is the sum of kinetic and potential energy. It is conserved in a conservative system. The net work done by nonconservative forces is equal to the change in the total mechanical energy. Power is the rate at which work is done. © 2010 Pearson Education, Inc.