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

7.2 Work/Energy have Dimensions of ML 2 T -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 – θ is the angle between A and B

7.3 Bcos θ 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

7.3 – 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

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 F x 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 block by the spring in moving from x i = x max to x f = 0

7.4 Area under the curve ½ bh ½ x max F max ½ x max kx max ½ kx max 2 Work done on block is positive, the spring force is forward while the block moves forward.

7.4 Quick Quiz p 192 Example 7.6

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

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 E int

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 And so… Power is the time rate of change of energy/work (derivative)

7.8 Power has dimensions of ML 2 T -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 = 3.6x10 6 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 ~ v 2 (Drag)

7.9 Since drag ~ v 2 it is the dominant resistance at high speeds Rolling Friction is dominant at low speeds.

7.9 Examples p. 207