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

7.2- Work

- 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

- The product of Force and Displacment

- Work is a scalar quantity

7.2

- 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 (-)

7.2

- Quick Quizzes p. 185
- See Example 7.1 p. 186

7.3 The Scalar Product

- Work is a scalar that results from the multiplication of 2 vectors.
- This is known as…
- Scalar Product
- Dot Product

- This is known as…
- Dot Product
- θ is the angle between A and B

7.3

- Bcosθ is the projection of B onto A

7.3

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

7.3

- 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

- Dot products are commutative

7.3 In Unit vector Notation

- 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

7.3

- Dealing with Unit Vector Coefficients
Prove this in HW #6

Quick Quiz p. 187

Example 7.2, 7.3

7.4 Work and Varying Force

- 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)

7.4

- When Δx is infinitely small, the limit of the sum becomes…
- Work is Area under an F vs. x curve.

7.4

- 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.

7.4

- 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

7.4

- Work Done by the Spring
- Calculate the work done on the blockby the spring in moving from xi = xmax to xf = 0

7.4

- 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.

7.5 Kinetic Energy

- 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

7.5

- 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

- Derivation (see board)

7.6 The Non-Isolated System

- Non-Isolated System- external forces from the environment
- Isolated System- no external force (Ch 8)
- Work-KE Theorem only valid for Non-Isolated

7.6

- 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

7.6

- 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)
- Electromagnetic Radiation (Light/UV/IR/radio etc)

7.6

- 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

7.7 Involving Kinetic Friction

- 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

7.7

- 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

7.7

- Quick Quiz p. 201
- Ex 7.9, 7.11

7.8 Power

- 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

7.8

- 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

7.8

- Quick Quiz p. 204
- Example 7.12

7.9 Energy and Automobiles

- 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.

7.9

- 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)

7.9

- Since drag ~ v2 it is the dominant resistance at high speeds
- Rolling Friction is dominant at low speeds.

7.9

- Examples p. 207

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