Chapter 7: Work and Energy - Laulima · Goals for Chapter 7 • Overview energy. • Study work as defined in physics. • Relate work to kinetic energy. • Consider work done by

Chapter 7 Lecture

Chapter 7: Work and Energy

© 2016 Pearson Education, Inc.

Goals for Chapter 7

•  Overview energy. •  Study work as defined in physics. •  Relate work to kinetic energy. •  Consider work done by a variable force. •  Study potential energy. •  Understand energy conservation. •  Include time and the relationship of work to

power.


Introduction

•  In previous chapters, we studied motion. •  We used Newton's three laws to understand the

motion of an object and the forces acting on it. •  Sometimes this can be hard. •  We introduce energy as the next step.


An Overview of Energy

•  Energy is conserved. •  Kinetic energy describes motion and relates to the mass

of the object and its speed squared.

•  Energy on earth originates from the sun. •  Energy on earth is stored thermally and

chemically. •  Chemical energy is released by

metabolism. •  Energy is stored as potential energy in

object height and mass and also through elastic deformation.


A Study of Energy Transformation – Figure 7.4 •  This transformation begins as

elastic potential energy in the elastomer. It then becomes kinetic energy as the projectile flies upward. During the upward flight, kinetic energy becomes potential until at the top of the flight, all the energy is potential. Finally, the stored potential energy changes back to kinetic energy as the projectile falls.


Internal Energy Can be "Lost" as Heat

•  Atoms and molecules of a solid can be thought of as particles vibration randomly on spring like bonds. This vibration is an an example of internal energy.

•  Energy can be dissipated by heat (motion transferred at the molecular level). This is referred to as dissipation.


What is "Work" as Defined in Physics?

•  Formally, work is the product of a constant force F through a parallel displacement s.

•  Work is the product of the component of the force in the direction of displacement and the magnitude s of the displacement.


Consider Only Parallel F and S – Figure 7.9

•  Forces applied at angles must be resolved into components.

•  W is a scalar quantity that can be positive, zero, or negative.

•  If W > 0 (W < 0), energy is added to (taken from) the system.


Applications of Force and Resultant Work – Figure 7.10


Sliding on a Ramp – Example 7.2

•  Please refer to the worked example at the bottom of page 186.


Work Done By Several Forces – Example 7.3


Work and Kinetic Energy

•  Unbalanced work causes kinematics. •  Work-energy theorem:

•  The kinetic energy K of a particle with mass m moving with speed is During any displacement of the particle, the work done by the net external force on it is equal to its change in kinetic energy.

•  Although Ks are always positive, Wtotal may be positive, negative, or zero (energy added to, taken away, or left the same).

•  If Wtotal = 0, then the kinetic energy does not change and the speed of the particle remains constant.


Work and Energy Related – Example 7.4

•  Using work and energy to calculate speed. •  Returning to the tractor pulling a sled problem of

Example 7.3: •  If you know the initial speed,

and the total work done, you can determine the final speed after displacement s.


A Pile Driver Application – Example 7.5

•  Refer to the worked example on pages 191–192.


Work Done By a Varying Force

•  In Section 7.2, we defined work done by a constant force.

•  Work by a changing force is sometimes considered.

•  On a graph of force as a function of position, the total work done by the force is represented by the area under the curve between the initial and final positions.


Work Done By a Varying Force

•  In Section 5.4, we learned that force due to elongation/compression of a spring followed Hooke's law:

•  As seen, this is a prime example of a varying force. The work done by a stretching/compressing a spring is equal to the area of the shaded triangle, or


Work Done on a Spring Scale – Example 7.6

•  Energy may be stored in compressed springs on a bathroom scale.

•  Refer to the worked example on page 194.


Potential Energy

In cases of conservative forces (gravity or elastic forces), there can be "stored" energy due to the spatial arrangement of a system, or

potential energy. • Gravitational potential energy

(Ugrav), near the surface of the


Potential Energy

•  The change in the potential energy due to The change in the potential energy due to conservative forces is related to the work done conservative forces is related to the work done by the net force: by the net force:

• •  If only conservative forces act, then by the work-energy theorem we can define the total mechanical energy:


A Solved Baseball Problem – Example 7.7

• •  When the ball, with initial When the ball, with initial

speed i is thrown straight upward, it slows down on the way up as the kinetic energy is converted to potential

energy (mgy>0). • At the top, the kinetic energy

is zero and potential energy is maximum. • 

On the way back down, the potential energy is converted back to kinetic energy, and

Conservation of total Conservation of total mechanical energy


Energy Stored in Spring Displacement – Figure 7.25 Energy Stored in Spring Displacement –

•  Elastic stored energy stored in a spring can be related to position.

• 

• 

Elastic stored energy stored (Hooke's law), the elastic in a spring can be related to position. • 


Potential Energy on an Air Track with Mass and Spring and Spring

energy, we use this to find the final state at any position. • Using conservation of Using conservation of total mechanical energy:


Conversion and Conservation – Figures 7.27 and 7.28 •  As kinetic and potential energy are interconverted,

dynamics of the system may be solved.

Refer to the worked examples on page 202–203. © 2016 Pearson Education, Inc.

Conservative and Nonconservative Forces

• •  In the previous section, we discussed that if we In the previous section, we discussed that if we had only conservative forces acting, then we

had only conservative forces acting, then we energy.

•  If we have nonconservative forces which do work, we have to add this to the total energy:

•  Wother is the work done by nonconservative forces (e.g. friction).


could used conservation of total mechanical

Problems With Nonconservative Forces – Example 7.12 Problems With Nonconservative Forces – • 

now we also include the work done an external, a This is the same problem as Example 7.8, but

now we also include the work done an external, a nonconservative force F.

• In addition to the

spring force, there is a constant force F

Wf = Kf +Uf( )− K i +Ui( )Wf =

12 mυf

2 + 12 kxf

2( )− 12 mυi

2 + 12 kxi

2( )where Wf = Fx > 0


Conservative Forces II – Figure 7.35

The work done by a conservative force is independent of the path taken.

•  When the starting and ending points are the same, the total work is zero. same, the total work is zero.


•  When a quantity of work ΔW is done during a time interval •  When a quantity of work ΔW is done during a time interval

•  Pav or work per unit time is: Units of watt [W], or 1 watt = 1 joule per second [J/s] •  The rate at which work is done is not always constant.

•  Units of watt [W], or 1 watt = 1 joule per second [J/s]


Power – Considers Work and Time to do It

•  Example 7.16: A marathon stair climb • 

Example 7.16: A marathon stair climb

• If the runner is initially at

rest and ends at rest, the work done by the runner is

equal to the work done by gravity on the runner.

• 


Documents

Chapter 7: Work and Energy - Laulima · Goals for Chapter 7 • Overview energy. • Study work as defined in physics. • Relate work to kinetic energy. • Consider work done by