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Chapter 5 Work and Energy

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Forms of Energy Mechanical oKinetic, gravitational Thermal oMicroscopic mechanical Electromagnetic Nuclear Energy is conserved!

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Work Relates force to change in energy Scalar quantity Independent of time

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Units of Work and Energy SI unit = Joule 1 J = 1 N m = 1 kg m 2 /s 2

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Work can be positive or negative Man does positive work lifting box Man does negative work lowering box Gravity does positive work when box lowers Gravity does negative work when box is raised

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Kinetic Energy Same units as work Remember the Eq. of motion Multiply both sides by m/2,

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Example 5.1 A skater of mass 60 kg has an initial velocity of 12 m/s. He slides on ice where the frictional force is 36 N. How far will the skater slide before he stops? 120 m

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Potential Energy If force depends on distance, For gravity (near Earth’s surface)

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Mysterious Rolling Demo

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Conservation of Energy Conservative forces: Gravity, electrical, QCD… Non-conservative forces: Friction, air resistance… Non-conservative forces still conserve energy! Energy just transfers to thermal energy

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Example 5.2 A diver of mass m drops from a board 10.0 m above the water surface, as in the Figure. Find his speed 5.00 m above the water surface. Neglect air resistance. 9.9 m/s

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Example 5.3 A skier slides down the frictionless slope as shown. What is the skier’s speed at the bottom? H=40 m L=250 m start finish 28.0 m/s

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Two blocks, A and B (m A =50 kg and m B =100 kg), are connected by a string as shown. If the blocks begin at rest, what will their speeds be after A has slid a distance s = 0.25 m? Assume the pulley and incline are frictionless. s Example 5.4 1.51 m/s

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Example 5.5 Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal as in the figure below. Neglecting air resistance, rank the speeds of the balls as they reach the ground. All 3 have same speed!

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Springs (Hooke’s Law) Proportional to displacement from equilibrium

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Potential Energy of Spring PE=-F x xx F

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x Example 5.6 b) Find the maximum distance d the block travels up the frictionless incline if the incline angle θ is 25°. A 0.50-kg block rests on a horizontal, frictionless surface as in the figure; it is pressed against a light spring having a spring constant of k = 800 N/m, with an initial compression of 2.0 cm. a) After the block is released, find the speed of the block at the bottom of the incline, position (B). a) 0.8 m/s b) 7.7 cm

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Example 5.7 A spring-loaded toy gun shoots a 20-g cork 40 m into the air after the spring is compressed by a distance of 1.5 cm. a) What is the spring constant? b) What is the maximum acceleration experienced by the cork? a) 69,760 N/m b) 52,320 m/s 2

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Graphical connection between F and PE F x x1x1 x2x2 xx

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PE x F = -slope, points down hill

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Graphs of F and PE for spring PE=(1/2)kx 2 x x F=-kx Force pushes you to bottom of potential well

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Example 5.8 PE (J) x (m) 10 20 30 40 50 60 1.02.03.04.00 0 A particle of mass m = 0.5 kg is at a position x = 1.0 m and has a velocity of -10.0 m/s. What is the furthest points to the left and right it will reach as it oscillates back and forth? 0.125 and 3.75 m E tot

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Power Power is rate of energy transfer SI units are Watts (W) US Customary units are hp (horse power)

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Example 5.9 An elevator of mass 550 kg and a counterweight of 700 kg lifts 23 drunken 80-kg students to the 7th floor of a dormitory 30 meters off the ground in 12 seconds. What is the power required? (in both W and hp) 41 kW =55.6 hp

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Example 5.10 A 1967 Corvette has a weight of 3020 lbs. The 427 cu-in engine was rated at 435 hp at 5400 rpm. a) If the engine used all 435 hp at 100% efficiency during acceleration, what speed would the car attain after 6 seconds? b) What is the average acceleration? (in “g”s) a) 119 mph b) 0.91g

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Power: Force and velocity For the same force, power is higher for higher v

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Example 5.11 Consider the Corvette (w=3020 lbs) having constant acceleration of a=0.91g a) What is the power when v=10 mph? b) What is the power output when v=100 mph? a) 73.1 hp b) 732 hp (in real world a is larger at low v)

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Example 5.12 A physics professor bicycles through air at a speed of v=30 km/hr. The density of air is 1.29 kg/m 3. The professor has cross section of 0.35 m 2. Assume all of the air the professor comes in contact with is accelerated to v. a) What is the mass of the air swept out by the professor in one second? b) What is the power required to accelerate this air? a) 10.75 kg b) 373 W = 0.5 hp

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Example 5.13 Find the dimensions of the drag coefficient in the equation is dimensionless If =0.4, and the professor’s conversion of food to work is 20% efficient, how many kilocalories must the professor burn to cycle for 3 hours? ( =1.29 kg/m 3, A= 0.35 m 2, v=30 km/hr, 1 kcal=4186 J) 673 kcal When we discuss diets cal.s actually refer to kcal!

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Example 5.14 If a professor burns 75 W bicycling at 30 km/hr, how much power would burn bicycling at Lance Armstrong’s speed of 45 km/hr? 253 W

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Ergometer Demo

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Example 5.15 A dam wishes to produce 50 MW of power. If the height of the dam is 75 m, what flow of water is required? (in m 3 /s) 68.9 m 3 /s = 1.80x10 4 gallons/s

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Example 5.16 2001 cost of electricity How much money does it cost to run a 100-W light bulb for one year if the cost of electricity is 8.0 cents/kW hr? $ 70.08

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Some energy facts http://css.snre.umich.edu US consumes 24% of Worlds energy (5% of population) Each day, each of us consumes: o3 gallons of oil o20 lbs of coal o221 cubic feet of natural gas In 2000 the US consumed 9.9x10 16 BTUs 1 BTU is energy required to raise 1 lb of H20 1 degree F 1BTU = 1055 J

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Einstein... c is velocity of light For small velocities, “Rest” energy For any v,

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Example Suppose one had a supply of anti-matter which one could mix with matter to produce energy. What mass of antimatter would be required to satisfy the U.S. energy consumption in 2000? (9.9x10 16 BTUs) 574 kg

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