Fundamental of Physics

PETROVIETNAM UNIVERSITYFUNDAMENTAL SCIENCE DEPARTMENT

Hanoi, August 2012

Pham Hong QuangE-mail: quangph@pvu.edu.vn

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Chapter 3 Work and Energy

Pham Hong Quang Fundamental Science Department

3.1 Work      3.2 Kinetic Energy      3.3 Work and Kinetic Energy      3.4 Power3.5 Potential Energy3.6 Conservation of Mechanical Energy3.7 Conservation of Energy in General

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3.1 Work  

Pham Hong Quang Fundamental Science Department

•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.

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3.1 Work

Pham Hong Quang Fundamental Science Department

•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 is a scalar quantity. Unit for work is Joule (J) also.

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3.1 Work

Pham Hong Quang Fundamental Science Department

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1

( )x

xxW F x dxWork Done by

Variable Forces

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3.1 Work

Pham Hong Quang Fundamental Science Department

Work Done by a Spring Force

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3.2 Kinetic Energy

Pham Hong Quang Fundamental Science Department

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3.3 Work and Kinetic Energy

Pham Hong Quang Fundamental Science Department

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1

22

1

2

1

2

1

2

1 2... vmdvdvmvd

dtxdmxd

dtvdmxdFx

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22 2

121 mvmvA

Net Work–Kinetic Energy TheoremWhen a external force does work A on an object, the change of kinetic energy of the object equals to the work:

12 KKA

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3.4 Power

Pham Hong Quang Fundamental Science Department

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3.5 Potential Energy

Pham Hong Quang Fundamental Science Department

The Path Independence Test for a Gravitational Force

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3.5 Potential Energy

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Path Dependence of Work Done by a Friction Force

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3.5 Potential Energy

Pham Hong Quang Fundamental Science Department

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,

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3.5 Potential Energy

Pham Hong Quang Fundamental Science Department

Determining Potential Energy Values

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3.5 Potential Energy

Pham Hong Quang Fundamental Science Department

The gravitational potential energy The product of the magnitude of the gravitational force mg acting on an object and the height y of the object is so important in physics that we give it a name: the gravitational potential energy. The symbol for gravitational potential energy is Ug , and so the defining equation for gravitational potential energy is

Gravitational potential energy is the potential energy of the object–Earth system.This potential energy is transformed into kinetic energy of the system by the gravitational force.

mgydymgUy

g )(0

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3.5 Potential Energy

Pham Hong Quang Fundamental Science Department

Elastic Potential Energy

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3.6 Conservation of Mechanical Energy

Pham Hong Quang Fundamental Science Department

What is mechanical energy of a system?

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3.6 Conservation of Mechanical Energy

Pham Hong Quang Fundamental Science Department

In a system where no work is done on it by external forces and only conservative internal forces act on the system elements, then the internal forces in the system can cause energy to be transferred between kinetic energy and potential energy, but their sum, the mechanical energy Emec of the system, cannot change.

0mecsys sys sysE K U

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3.6 Conservation of Mechanical Energy

Pham Hong Quang Fundamental Science Department

Example

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3.6 Conservation of Mechanical Energy

Pham Hong Quang Fundamental Science Department

ExampleA 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. 2

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mvhmg

)(2 02 yygv t

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3.7 Conservation of Energy in General

Pham Hong Quang Fundamental Science Department

•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 energy is called internal energy.

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3.7 Conservation of Energy in General

Pham Hong Quang Fundamental Science Department

•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.

22Nguyen Van A 22 PetroVietnam University

Thank you!