physics chapter 5

© 2010 Pearson Education, Inc.

Lecture Outline

Chapter 5

College Physics, 7th Edition

Wilson / Buffa / Lou

Chapter 5Work and Energy


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


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.




No Motion = No Work


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.



• 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.


• For example: – What 50 Joules of work are produced in a 10 m

distance, how much force was applied to the system?

Is it possible to do work on an

object that remains at rest?

a) yes

b) no

Question 5.1 To Work or Not to Work


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.


Question 5.2a Friction and Work I

a) friction does no work at all

b) friction does negative work

c) friction does positive work

A box is being pulled

across a rough floor at a

constant speed. What

can you say about the

work done by friction?


• 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 ForceIf 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.



• 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?


• 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?

5.2 Work Done by a Variable Force

The force exerted by a spring varies linearly with the displacement:



• 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

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

Question 5.14 Elastic Potential Energy


• 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 _________


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.


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

Question 5.5a Kinetic Energy I



W = K - K0

We can use this relation to calculate the work done:


This relationship is called the work–energy theorem.



• 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?


• 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.



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.



Gravitational potential energy:


Most well known type Formula?

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?

a

d) same speed

for all balls

b c

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 EnergyOnly changes in potential energy are physically significant; therefore, the point where U = 0 may be chosen for convenience.


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]



• 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 EnergySo, 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.



We define the total mechanical energy:


Sum of kinetic and potential energies

The sum of these are _________


For a conservative force:

Total Mechanical Energy is constant

E = E0

For nonconservative forces, mechanical energy is usually lost.



• 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)


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.


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.



• 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?

5.6 Power

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

Question 5.21a Time for Work I

a) Mike

b) Joe

c) both did the same work

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?

Mike performed 5 J of work in

10 secs. Joe did 3 J of work

in 5 secs. Who produced the

greater power?

a) Mike produced more power

b) Joe produced more power

c) both produced the same

amount of power

Question 5.21b Time for Work II

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%.


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


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.


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.


physics chapter 5

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