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 Energy3.7 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 workUnits: Joules (J)

Types of energy include:

Mechanical: Energy of movement and positionChemical: Energy stored in chemical bonds of molecules

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

Nuclear: Energy produced from the splitting of atomsRadiant 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.

W.

3.2 Work

( )

WFx d x

Work Done by Variable Forces

3.2 Work

Work Done by a Spring Force

3.3 Work and Kinetic Energy

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

v0 35.0/,0,1.00103 , k 8.00103

210 mvx

fk  

( N x  kgms

3.3 Work and Kinetic Energy

(b) We know

Find the speed at impact.

Write down the work-energy theorem:

netWfxmvmvW 

vf  2 2 k

smvf 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 conservative Forces; Potential Energy; Elastic Potential

Non-Energy; Mechanical Non-Energy; Equipotentials; Conservation of Energy

Summaries•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:

FW 

Summaries•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

Summaries•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 1If 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 2A 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 5An 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!