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