chapter 3 cong va nang luong revised

Learning outcomeThe students should be able to:•Apply the relationship between a particle’s kinetic energy, mass, and speed.•Apply the relationship between a force magnitude and directio

TẬP ĐOÀN DẦU KHÍ VIỆT NAM

TRƯỜNG ĐẠI HỌC DẦU KHÍ VIỆT NAM

General Physics I

Chapter 3 Work and Energy

3.1 Kinetic Energy 3.2 Work

3.3 Work and Kinetic Energy 3.4 Power

3.5 Potential Energy 3.6 Conservation of Mechanical Energy 3.7 Conservation of Energy in General

Learning outcome

The students should be able to:

•Apply the relationship between a particle’s kinetic energy,

mass, and speed

•Apply the relationship between a force (magnitude and

direction) and the work done on a particle by the force when the particle undergoes a displacement

•Apply the work–kinetic energy theorem to relate the work done

by a force (or the net work done by multiple forces) and the

resulting change in kinetic energy

•Calculate the work done by the gravitational force when an

object is lifted or lowered

•Calculate the work done on an object by a spring force by

integrating the force from the initial position to the final position

Learning outcome

•Given a variable force as a function of position, calculate the work done by it on an object by integrating the function from the initial to the final position of the object, in one or more dimensions

•Apply the relationship between average power, the work done by

a force, and the time interval in which that work is done

•Distinguish a conservative force from a non-conservative force

•For a particle moving between two points, identify that the work

done by a conservative force does not depend on which path the particle takes

•Calculate the gravitational potential energy of a particle (or, more properly, a particle–Earth system)

•Calculate the elastic potential energy of a block–spring system

•After first clearly defining which objects form a system, identify

that the mechanical energy of the system is the sum of the kinetic

Learning outcome

•For an isolated system in which only conservative forces act,

apply the conservation of mechanical energy to relate the initial potential and kinetic energies to the potential and kinetic

energies at a later instant

•Given a particle’s potential energy as a function of its position

x, determine the force on the particle.

•Given a graph of potential energy versus x, determine the force

on a particle

•When work is done on a system by an external force,

determine the changes in kinetic energy and potential energy

•For an isolated system (no net external force), apply the

conservation of energy to relate the initial total energy (energies

of all kinds) to the total energy at a later instant

Energy: The ability of an object to do work

Units: Joules (J) Types of energy include:

Mechanical: Energy of movement and position Chemical: Energy stored in chemical bonds of molecules

Thermal: “Heat energy” stored in materials at a certain temperature

Nuclear: Energy produced from the splitting of atoms Radiant Energy: Energy traveling the form of

electromagnetic waves Electric Energy: Energy traveling as the flow of charged particles (i.e electrons)

3.1 Kinetic Energy

3.1 Kinetic Energy

3.2 Work

•Work W is energy transferred to or from an object

by means of a force acting on the object

•Energy transferred to the object is positive work,

•Energy transferred from the object is negative work.

3.2 Work

•Only the force component along the object’s displacement will contribute to work

•A force does positive work when it has a vector component

in the same direction displacement,

• A force does negative work when it has a vector

component in the opposite direction

Work done by a constant force

s F

W   

3.2 Work

2 1

( )

x

x x

W   F x d x

Work Done by Variable

Forces

3.2 Work

Work Done by a

Spring Force

3.3 Work and Kinetic Energy

d dt

v

d m x

2 2

2

1 2

1

mv mv

Net Work–Kinetic

Energy Theorem

When a external force

does work A on an object,

the change of kinetic

energy of the object equals

to the work :

The driver of a 1.00103 kg car traveling on the interstate at

35.0 m/s slam on his brakes to avoid hitting a second

vehicle in front of him, which had come to rest because of

congestion ahead After the breaks are applied, a constant

friction force of 8.00103 N acts on the car Ignore air

resistance (a) At what minimum distance should the brakes

be applied to avoid a collision with the other vehicle? (b) If

the distance between the vehicles is initially only 30.0 m, at

what speed would the collisions occur?

3.3 Work and Kinetic Energy

 (a) We know

 Find the minimum necessary stopping distance

N f

kg m

v s m

v0  35 0 / ,  0 ,  1 00  103 , k  8 00  103

2 2

2

12

1

i f

fric N

g fric

2 0

2

1

0 mv x

f k  



2 3

3 ( 1 00 10 )( 35 0 / )

2

1 )

10 00

8 (  N x    kg m s

 (b) We know

 Find the speed at impact.

 Write down the work-energy theorem:

N f

kg m

s m v

m

0 35 0 / , 1 00 10 , 8 00 10 ,

0





2 2

2

1 2

1

i f

k fric

net W f x mv mv

W      

x

f m

v

v f  2  2 k

0 2

2 2 3

3

2

2 )( 8 00 10 )( 30 ) 745 /

10 00

1

2 (

) / 35

kg

s m

vf  27 3 /

3.3 Work and Kinetic Energy

3.4 Power

3.5 Potential Energy

The Path Independence Test for a Gravitational Force

3.5 Potential Energy

Path Dependence of Work Done by a Friction

Force

3.5 Potential Energy

Conservative and Non-conservative

Forces

•conservative forces are the forces

that do path independent work;

•The work done by a conservative

force along any closed path is zero

•non-conservative force is the force

that do path dependent work

•The work done by a conservative

internal force can be stored in the

system as potential energy,

3.5 Potential Energy

3.5 Potential Energy

3.5 Potential Energy

Elastic Potential Energy

3.5 Potential Energy

Potential Energy Curves and Equipotentials

The curve of a hill or a roller coaster is itself essentially a

plot of the gravitational potential energy:

3.5 Potential Energy

Potential Energy Curves and Equipotentials

The potential energy curve for a spring:

3.5 Potential Energy

Potential Energy Curves and Equipotentials

Contour maps are also a form of potential energy curve:

3.6 Conservation of Mechanical Energy

3.6 Conservation of Mechanical Energy

Example 1:

A motorcyclist is trying to leap across the canyon shown in

Figure by driving horizontally off the cliff at a speed of 38.0

m/s Ignoring air resistance, find the speed with which the

cycle strikes the ground on the other side

Example 2: Toy dart gun.

A dart of mass 0.100 kg is pressed

against the spring of a toy dart gun

The spring (with spring stiffness

Constant k= 250 N/m and ignorable

mass) is compressed 6.0 cm and

released If the dart detaches from

the spring when the spring reaches

its natural length (x= 0), what speed

does the dart acquire?

3.6 Conservation of Mechanical Energy

3.6 Conservation of Mechanical Energy

Example 3:

A ball of mass m= 2.60 kg,

starting from rest, falls a

vertical distance h= 55.0 cm

before striking a vertical coiled

spring, which it compresses

an amount Y= 15.0 cm

Determine the spring stiffness

constant of the spring

Assume the spring has

negligible mass, and ignore

air resistance

3.6 Conservation of Mechanical Energy

3.7 Conservation of Energy in General

•We have seen that the total mechanical energy of a system is constant when only conservative forces

act within the system Mechanical energy is lost

when non-conservative forces such as friction are

present.

•We shall find that mechanical energy can be

transformed into energy stored inside the various

objects that make up the system This form of

3.7 Conservation of Energy in General

•We shall see that on a submicroscopic scale, this internal energy

is associated with the vibration of atoms about their equilibrium

positions Such internal atomic motion involves both kinetic and potential energy

•Therefore, if we include in our energy expression this increase in the internal energy of the objects that make up the system, then energy is conserved

That is, energy can never be created or destroyed Energy

may be transformed from one form to another, but the total energy of an isolated system is always constant.

Example:

The roller-coaster car shown

reaches a vertical height of only

25 m on the second hill before

coming to a momentary stop It

traveled a total distance of 400

m Determine the thermal

energy produced and estimate

the average friction force

(assume it is roughly constant)

on the car, whose mass is 1000

kg

3.7 Conservation of Energy in General

Key words of the chapter

Kinetic energy; Work; Power; Conservative and

Non-conservative Forces; Potential Energy; Elastic Potential

Energy; Mechanical Energy; Equipotentials; Conservation of Energy

•SI unit of work and Kinetic Energy : the joule, J

•If the force is constant and parallel to the displacement, work is

force times distance

•If the force is not parallel to the displacement,

•Total work is equal to the change in kinetic energy:

•Work done by a spring force:

• Power is the rate at which work is done:



cos

.d

F

W 

•Conservative forces conserve mechanical energy

•Non-conservative forces convert mechanical energy into other

forms

•Conservative force does zero work on any closed path

•Work done by a conservative force is independent of path

•Conservative forces: gravity, spring

•Work done by non-conservative force on closed path is not zero, and depends on the path

• Non-conservative forces: friction, air resistance, tension

• Energy in the form of potential energy can be converted to kinetic

or other forms

• Work done by a conservative force is the negative of the change in the potential energy

• Gravity: U = mgy

•Mechanical energy is the sum of the kinetic and potential energies;

it is conserved only in systems with purely conservative forces

• Non-conservative forces change a system’s mechanical energy

• Work done by non-conservative forces equals change in a

system’s mechanical energy

• Potential energy curve: U vs position

Check your understanding 1

If the unit for force is F, the unit for velocity V, and the unit for time

T, then the unit for energy is:

Check your understanding 2

A force of 10 N stretches a spring that has a spring constant of 20 N/m The potential energy stored in the spring is:

(A) 2.5 J (B) 5.0 J (C) 10 J (D) 40 J (E) 200 J

Ans A Two step problem Do F = kΔx, solve for Δx then sub in x, solve for Δx, solve for Δx then sub in x then sub in the Usp = ½ kΔx, solve for Δx then sub in x2

Check your understanding 3

A pendulum bob of mass m on a

cord of length L is pulled sideways

until the

cord makes an angle θ with the

vertical as shown in the figure to

the right The

change in potential energy of the

bob during the displacement is:

(A) mgL (1–cos θ) (B) mgL (1–sin θ)

(C) mgL sin θ

(D) mgL cos θ (E) 2mgL (1–sin θ)mgL (1–sin θ)

Ans A The potential energy at the first position will be the

amount “lost” as the ball falls and this will be the change in

Check your understanding 4

From the top of a high cliff, a ball is thrown

horizontally with initial speed vo Which of the

following graphs best represents the ball's kinetic

energy K as a function of time t ?

Ans E Since the ball is thrown with initial velocity it must start

with some initial K As the mass falls it gains velocity directly

proportional to the time (V=Vi+at) but the K at any time is equal

to 1/2 mv2 which gives a parabolic relationship to how the K

Check your understanding 5

An automobile engine delivers 24000 watts of power to a car’s

driving wheels If the car maintains a constant speed of 30 m/s,

what is the magnitude of the retarding force acting on the car?

(A) 800 N (B) 960 N (C) 1950 N (D) 720,000 N (E) 1,560,000 N

Ans A P = Fv, plug in to get the pushing force F and since its constant speed, Fpush = fk

Thank you!