1 / 38

# Chapter 7 - PowerPoint PPT Presentation

Chapter 7. Work and Energy Transfer. Section 7.1- Systems and Environments. System- small portion of the universe being studied Can be a single object Can be a collection of objects Environment- everything outside the boundaries (physical or not) of the system

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Chapter 7' - lilka

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Chapter 7

Work and Energy Transfer

• System- small portion of the universe being studied

• Can be a single object

• Can be a collection of objects

• Environment- everything outside the boundaries (physical or not) of the system

• We will generally discuss the conservation of energy of systems rather than individual particles.

• Energy- the ability to do work

• Work is a scalar quantity

• The product of Force and Displacment

• Work is only done by forces parallel to the displacement

• If F |Δr, no work is done

• At any other angle, only the parallel component of the force does work

• Work/Energy have Dimensions of ML2T-2, units = N.m = Joules

• Work is a form of Energy Transfer

• Work done on a system (+)

• Work done by a system (-)

• Another way of putting it

• Energy transferred to the system (+)

• Energy transferred from the system (-)

• Quick Quizzes p. 185

• See Example 7.1 p. 186

• Work is a scalar that results from the multiplication of 2 vectors.

• This is known as…

• Scalar Product

• Dot Product

• Dot Product

• θ is the angle between A and B

• Bcosθ is the projection of B onto A

• Work is the dot (scalar) product of the Force vector and displacement vector.

• Dot Product Properties-

• Dot products are commutative

A . B = B . A

• Dot products obey distributive laws of mulitplication

A . ( B + C ) = A . B + A . C

• If A is | B then A.B = 0 (cos 90)

• If A || B then A.B = AB

• If A anti-|| B then A.B = -AB

• In Unit vector Notation

• Dealing with Unit Vector Coefficients

Prove this in HW #6

Quick Quiz p. 187

Example 7.2, 7.3

• is only

valid when F is constant.

• For a varying F we

need to look at very

small intervals of Δx

(The smaller the interval, the closer

Fx becomes to a constant value)

• When Δx is infinitely small, the limit of the sum becomes…

• Work is Area under an F vs. x curve.

• Work Done by multiple forces

• The Net work done on an object is equal to the work done by the net force.

• It can also be found by the sum of the work done by all of the individual forces.

• Common Application- Work done by a spring

• (Hooke’s Law)

• x is the position of the attached mass relative to equilibrium

• k is the spring constant (stiffness)

• F is always in the opposite direction of x

• Work Done by the Spring

• Calculate the work done on the blockby the spring in moving from xi = xmax to xf = 0

• Area under the curve

½ bh

½ xmaxFmax

½ xmaxkxmax

½ kxmax2

Work done on block is positive, the spring force is forward while the block moves forward.

Quick Quiz p 192

Example 7.6

• Work is a way of transferring Energy to a system.

• Most commonly this energy now “possessed” by the system is energy of motion

• Kinetic Energy- energy associated with the motion of an object

Work-Kinetic Energy Theorem

• The Net Work done on an object will equal its change in Kinetic Energy

• Derivation (see board)

Quick Quiz p 195

Examples 7.7, 7.8

• Non-Isolated System- external forces from the environment

• Isolated System- no external force (Ch 8)

• Work-KE Theorem only valid for Non-Isolated

• Internal Energy

• There are times where we know work is done on an object yet there is no perceivable ΔKE

• Book Sliding across a table

• Work is done on the table

• The table has no change in Kinetic Energy

• Where did that energy go?

• The tables temperature increases (due to the work done on it) we call that Eint

• Methods of Energy Transfer

• Work

• Mechanical Waves (ex: sound)

• Heat (increase in average particle KE)

• Matter Transfer (fuel/convection)

• Electrical Transmission (charge passing through conductor)

• Energy cannot be created nor destroyed, it is conserved

• It can cross the boundary of our system, but it still exists in the surrounding environment

• Quick Quizzes p 199

• In the case of the book sliding to a stop on the table.

• The work done ON the book BY friction is responsible for the change of kinetic energy to internal energy.

• Or with other forces acting on the object

• Or when looking at the book/table system, because there are no outside interactions

• Therefore the result of a friction force is to transform kinetic energy into an equivalent amount of internal energy

• Quick Quiz p. 201

• Ex 7.9, 7.11

• While similar tasks often require the same amount of work, they may not take the same time.

• Power- the rate of energy transfer

• The rate at which work is done

• Refrigerator Example

And so…

Power is the time rate of change of energy/work

(derivative)

• Power has dimensions of ML2T-3

• Units are J/s or Watt

• Horsepower 1 hp = 746 W

• Energy described in kWh the energy used for 1 hour at a transfer rate of 1000 W (1 kW, 1000 J/s)

1 kWh = 1000 J/s x 3600 s = 3.6x106 J

• Quick Quiz p. 204

• Example 7.12

• Modern Internal Combustion engines are very inefficient using less that 15% of the chemical energy stored in gasoline to power the car.

~ 67% Lost to heat/sound/emr in the engine

~ 10% Lost in friction of the drivetrain

~ 4 -10% lost to power Fuel Pumps/Alternator/AC

Leaves around 13-19% for Kinetic Energy.

• When traveling at constant speeds, the total work done is zero (no change in kinetic energy)

• The work done by the engine is dissipated by resistive forces

• Rolling friction

• Air Resistance ~ v2 (Drag)

• Since drag ~ v2 it is the dominant resistance at high speeds

• Rolling Friction is dominant at low speeds.

• Examples p. 207