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2. Course of lectures «Contemporary Physics: Part1»Lecture №4Energy and Energy Transfer.Potential Energy.
3. Work Done by a Constant ForceFigure 6.1 An eraser being pushed along a chalkboard tray.
4. Figure 6.2 If an object undergoes a
5. Figure 6.3 When an object is displaced
6. An important consideration for a system approach
7. Work Done by a Varying ForceFigure 6.4 The work done by the force
8. Figure 6.5 The work done by the
9. Work Done by a Spring
10. Kinetic Energy and the Work–Kinetic Energy TheoremFigure
11. (6.5)where vi is the speed of the
12. Kinetic energy is a scalar quantity and
13. (a)(b)(c)Figure 6.7 Energy transfer mechanisms. (a) Energy
14. Figure 6.7 Energy transfer mechanisms. (d) energy
15. One of the central features of the
16. PowerThe time rate of energy transfer is
17. In a manner similar to the way
18. In general, power is defined for any
19. Potential Energy of a SystemFigure 6.8 The
20. The Isolated System–Conservationof Mechanical EnergyFigure 6.9 The
21. Therefore, equating these two expressions for the
22. We define the sum of kinetic and
23. Equation 6.18 is a statement of conservation
24. Conservative and Nonconservative ForcesConservative ForcesNonconservative Forces
25. Conservative forces have these two equivalent properties:1.
26. Nonconservative ForcesA force is nonconservative if it
27. Changes in Mechanical Energyfor Nonconservative Forces(6.19)(6.20)
28. Relationship Between Conservative Forcesand Potential Energy(6.21)(6.22)(6.22)
29. That is, the x component of a
30. Скачать презентацию
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Course of lectures «Contemporary Physics: Part1»Lecture №4Energy and Energy Transfer.Potential Energy.

Quick Quiz 3 Which of the following is impossible for a car

Work Done by a Constant ForceFigure 6.1 An eraser being pushed along a chalkboard tray.

Figure 6.2 If an object undergoes a displacement ∆r under the action

Figure 6.3 When an object is displaced on a frictionless, horizontal surface,

An important consideration for a system approach to problems is to note

Work Done by a Varying ForceFigure 6.4 The work done by the force

Figure 6.5 The work done by the component Fx of the varying

Kinetic Energy and the Work–Kinetic Energy TheoremFigure 6.6 An object undergoing a

(6.5)where vi is the speed of the block when it is at

Kinetic energy is a scalar quantity and has the same units as

(a)(b)(c)Figure 6.7 Energy transfer mechanisms. (a) Energy is transferred to the block

Figure 6.7 Energy transfer mechanisms. (d) energy enters the automobile gas tank

One of the central features of the energy approach is the notion

PowerThe time rate of energy transfer is called power. If an external

In a manner similar to the way we approached the definition of

In general, power is defined for any type of energy transfer. Therefore,

Potential Energy of a SystemFigure 6.8 The work done by an external

The Isolated System–Conservationof Mechanical EnergyFigure 6.9 The work done by the gravitational

Therefore, equating these two expressions for the work done on the book,Now,

We define the sum of kinetic and potential energies as mechanical energy:We

Equation 6.18 is a statement of conservation of mechanical energy for an

Conservative and Nonconservative ForcesConservative ForcesNonconservative Forces

Conservative forces have these two equivalent properties:1. The work done by a

Nonconservative ForcesA force is nonconservative if it does not satisfy properties 1

Changes in Mechanical Energyfor Nonconservative Forces(6.19)(6.20)

Relationship Between Conservative Forcesand Potential Energy(6.21)(6.22)(6.22)

That is, the x component of a conservative force acting on an

Quick Quiz 1 A block of mass m is projected across a

Слайды презентации

Слайд 2 Course of lectures «Contemporary Physics: Part1»
Lecture №4

Energy and

Energy Transfer.
Potential Energy.

Слайд 3 Work Done by a Constant Force
Figure 6.1 An

eraser being pushed along a chalkboard tray.

Слайд 4 Figure 6.2 If an object undergoes a displacement

Figure 6.2 If an object undergoes a displacement ∆r under the

∆r under the action of a constant force F,

the work done by the force is F∆rcosθ.

The work W done on a system by an agent exerting a constant force on the system is the product of the magnitude F of the force, the magnitude ∆ r of the displacement of the point of application of the force, and cos θ, where θ is the angle between the force and displacement vectors:

(6.1)

Слайд 5 Figure 6.3 When an object is displaced on

Figure 6.3 When an object is displaced on a frictionless, horizontal

a frictionless, horizontal surface, the normal force n and

the gravitational force mg do no work on the object. In the situation shown here, F is the only force doing work on the object.

Work is a scalar quantity, and its units are force multiplied by length. Therefore, the SI unit of work is the newton· meter (N·m). This combination of units is used so frequently that it has been given a name of its own: the joule ( J).

Слайд 6 An important consideration for a system approach to

An important consideration for a system approach to problems is to

problems is to note that work is an energy

transfer. If W is the work done on a system and W is positive, energy is transferred to the system; if W is negative, energy is transferred from the system. Thus, if a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundary. This will result in a change in the energy stored in the system.

Слайд 7 Work Done by a Varying Force
Figure 6.4 The

work done by the force

Слайд 8 Figure 6.5 The work done by the component

Figure 6.5 The work done by the component Fx of the

Fx of the varying force as the particle moves

from xi to xf is exactly equal to the area under this curve.

(6.2)

(6.3)

Слайд 9 Work Done by a Spring

Слайд 10 Kinetic Energy and the Work–Kinetic Energy Theorem
Figure 6.6

Kinetic Energy and the Work–Kinetic Energy TheoremFigure 6.6 An object undergoing

An object undergoing a displacement ∆r=∆xˆi and a change

in velocity under the action of a constant net force ƩF.

(6.4)

Слайд 11 (6.5)
where vi is the speed of the block

(6.5)where vi is the speed of the block when it is

when it is at x = xi and vf

is its speed at xf.

Слайд 12 Kinetic energy is a scalar quantity and has

Kinetic energy is a scalar quantity and has the same units

the same units as work.
(6.6)
(6.7)
Equation 6.7 is an important

result known as the work–kinetic energy theorem:

In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system.

Слайд 13 (a)
(b)
(c)
Figure 6.7 Energy transfer mechanisms. (a) Energy is

(a)(b)(c)Figure 6.7 Energy transfer mechanisms. (a) Energy is transferred to the

transferred to the block by work; (b) energy leaves

the radio from the speaker by mechanical waves; (c) energy transfers up the handle of the spoon by heat.

Слайд 14 Figure 6.7 Energy transfer mechanisms. (d) energy enters

Figure 6.7 Energy transfer mechanisms. (d) energy enters the automobile gas

the automobile gas tank by matter transfer; (e) energy

enters the hair dryer by electrical transmission; and (f) energy leaves the light bulb by electromagnetic radiation.

(d)

(e)

(f)

Слайд 15 One of the central features of the energy

One of the central features of the energy approach is the

approach is the notion that we can neither create

nor destroy energy—energy is always conserved. Thus, if the total amount of energy in a system changes, it can only be due to the fact that energy has crossed the boundary of the system by a transfer mechanism such as one of the methods listed above. This is a general statement of the principle of conservation of energy. We can describe this idea mathematically as follows:

(6.8)

Слайд 16 Power
The time rate of energy transfer is called

PowerThe time rate of energy transfer is called power. If an

power. If an external force is applied to an

object (which we assume acts as a particle), and if the work done by this force in the time interval ∆t is W, then the average power during this interval is defined as

Слайд 17 In a manner similar to the way we

In a manner similar to the way we approached the definition

approached the definition of velocity and acceleration, we define

the instantaneous power as the limiting value of the average
power as ∆t approaches zero:

(6.9)

Слайд 18 In general, power is defined for any type

of energy transfer. Therefore, the most general expression for

power is

The SI unit of power is joules per second ( J/s), also called the watt (W) (after James Watt):

A unit of power in the U.S. customary system is the horsepower (hp):

(6.10)

Слайд 19 Potential Energy of a System
Figure 6.8 The work

Potential Energy of a SystemFigure 6.8 The work done by an

done by an external agent on the system of

the book and the Earth as the book is lifted from a height ya to a height yb is equal to mgyb - mgya.

(6.11)

Слайд 20 The Isolated System–Conservation
of Mechanical Energy
Figure 6.9 The work

The Isolated System–Conservationof Mechanical EnergyFigure 6.9 The work done by the

done by the gravitational force on the book as

the book falls from yb to a height ya is equal to mgyb - mgya.

Слайд 21 Therefore, equating these two expressions for the work

Therefore, equating these two expressions for the work done on the

done on the book,
Now, let us relate each side

of this equation to the system of the book and the Earth. For the right-hand side,

(6.12)

(6.13)

(6.14)

Слайд 22 We define the sum of kinetic and potential

We define the sum of kinetic and potential energies as mechanical

energies as mechanical energy:
We will encounter other types of

potential energy besides gravitational later in the text, so we can write the general form of the definition for mechanical energy without a subscript on U:

(6.15)

(6.16)

(6.17)

Слайд 23 Equation 6.18 is a statement of conservation of

Equation 6.18 is a statement of conservation of mechanical energy for

mechanical energy for an isolated system. An isolated system

is one for which there are no energy transfers across the boundary. The energy in such a system is conserved—the sum of the kinetic and potential energies remains constant.

(6.18)

Слайд 24 Conservative and Nonconservative Forces
Conservative Forces
Nonconservative Forces

Слайд 25 Conservative forces have these two equivalent properties:

1. The

Conservative forces have these two equivalent properties:1. The work done by

work done by a conservative force on a particle

moving between any two points is independent of the path taken by the particle.
2. The work done by a conservative force on a particle moving through any closed path is zero. (A closed path is one in which the beginning and end points are identical.)

Слайд 26 Nonconservative Forces
A force is nonconservative if it does

Nonconservative ForcesA force is nonconservative if it does not satisfy properties

not satisfy properties 1 and 2 for conservative forces.

Nonconservative forces acting within a system cause a change in the mechanical energy Emech of the system. We have defined mechanical energy as the sum of the kinetic and all potential energies.