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Work, Energy, and Power Measures of Effort & Motion; Conservation Laws Chapter 7 - Energy • Work • Power • Mechanical Energy – Potential Energy – Kinetic Energy – Work-Energy Theorem • • • • • Conservation of Energy Machines Efficiency Source of Energy Energy for Life Physics 1100 – Spring 2012 Work is Exchange of Energy • Energy is the capacity to do work • Two main categories of energy – Kinetic Energy: Energy of motion • A moving baseball can do work • A falling anvil can do work – Potential Energy: Stored (latent) capacity to do work • Gravitational potential energy (perched on cliff) • Mechanical potential energy (like in compressed spring) • Chemical potential energy (stored in bonds) • Nuclear potential energy (in nuclear bonds) • Energy can be converted between types Physics 1100 – Spring 2012 Work, defined • Work carries a specific meaning in physics – Simple form: work = force distance W=F·d • Work can be done by you, as well as on you – Are you the pusher or the pushee • Work is a measure of expended energy – Work makes you tired • Machines make work easy (ramps, levers, etc.) – Apply less force over larger distance for same work Physics 1100 – Spring 2012 How Much Work Does He Do On Wall? Physics 1100 – Spring 2012 Mechanical Energy • Potential Energy – object can store energy just because of its position – work is required to elevate an object in earths gravity, that work is stored as gravitational potential energy: PE = mgh – only changes in PE are significant • Kinetic Energy – if we do work on an object, we change energy of motion of that object KE = ½ mv2 • Work – Energy Theorem Work = DKE Physics 1100 – Spring 2012 Gravitational Potential Energy • Gravitational Potential Energy near the surface of the Earth: m Work = Dh m W = mg Dh Physics 1100 – Spring 2012 Kinetic Energy • Kinetic energy is proportional to v2… • Watch out for fast things! – Damage to car in collision is proportional to v2 – Trauma to head from falling anvil is proportional to v2, or to mgh (how high it started from) – Hurricane with 120 m.p.h. packs four times the punch of gale with 60 m.p.h. winds Physics 1100 – Spring 2012 Conservation of Energy • Energy can neither be created or destroyed; it may be transformed from one form to another, but the total amount of energy never changes. Physics 1100 – Spring 2012 Conversion of Energy • Falling object converts gravitational potential energy into kinetic energy • Friction converts kinetic energy into vibrational (thermal) energy – makes things hot (rub your hands together) – irretrievable energy • Doing work on something changes that object’s energy by amount of work done, transferring energy from the agent doing the work • If there are no “dissipative” forces KE + PE = CONSTANT Physics 1100 – Spring 2012 Conversion of Energy Physics 1100 – Spring 2012 Energy Conversion/Conservation Example 4m P.E. = 98 J K.E. = •0 J Drop 1 kg ball from 10 m – starts out with mgh = (1 kg)(10m/s2)(10 m) = 100 J of gravitational potential energy P.E. = 73.5 J– halfway down (5 m from floor), has given up half its K.E. = 24.5 J potential energy (50 J) to kinetic energy • ½mv2 = 50J v2 = 100 m2/s2 v = 10 m/s – at floor (0 m), all potential energy is given up to kinetic P.E. = 49 J energy K.E. = 49 J • ½mv2 = 100 J v2 = 200m2/s2 v = 14 m/s 2m P.E. = 24.5 J K.E. = 73.5 J 10 m 8m 6m 0m P.E. = 0 J K.E. = 98 J Physics 1100 – Spring 2012 Energy Conservation Demonstrated • • • • Roller coaster car lifted to initial height (energy in) Converts gravitational potential energy to motion Fastest at bottom of track Re-converts kinetic energy back into potential as it climbs the next hill Physics 1100 – Spring 2012 Class Problem • • In which car will you be moving fastest at the very bottom of the incline? a) front car b) middle car c) rear car d) Other Physics 1100 – Spring 2012 Work and Power • Work is defined as: W = F x d [unit is Joules] – where the force is the direction of the displacement • Power is the work done per unit time Power = W/(time interval) [unit is Watts] Physics 1100 – Spring 2012 Power • • • • • • P=W/t Power is simply energy exchanged per unit time, or how fast you get work done (Watts = Joules/sec) One horsepower = 745 W Perform 100 J of work in 1 s, and call it 100 W Run upstairs, raising your 70 kg (700 N) mass 3 m (2,100 J) in 3 seconds 700 W output! Shuttle puts out a few GW (giga-watts, or 109 W) of power! Physics 1100 – Spring 2012 Working at an advantage • Often we’re limited by the amount of force we can apply. – Putting “full weight” into wrench is limited by your mg • Ramps, levers, pulleys, etc. all allow you to do the same amount of work, but by applying a smaller force over a larger distance Work = Force = Force Distance Distance Physics 1100 – Spring 2012 Ramps Exert a smaller force over a larger distance to achieve the same change in gravitational potential energy (height raised) Larger Force Short Distance Small Force Long Distance M Physics 1100 – Spring 2012 Ramp Example • Ramp 10 m long and 1 m high • Push 100 kg all the way up ramp • Would require mg = 980 N (220 lb) of force to lift directly (brute strength) • Work done is (980 N)(1 m) = 980 N·m in direct lift 1m • Extend over 10 m, and only 98 N (22 lb) is needed – Something we can actually provide – Excludes frictional forces/losses Physics 1100 – Spring 2012 Simple Machines Work input = work output! Physics 1100 – Spring 2012 Simple Machines Physics 1100 – Spring 2012 Efficiency Efficiency = (Useful energy output)/(total energy input) Physics 1100 – Spring 2012 Work Examples “Worked” Out • How much work does it take to lift a 30 kg suitcase onto the table, 1 meter high? W = (30 kg) (10 m/s2) (1 m) = 300 J • Unit of work (energy) is the N·m, or Joule (J) – One Joule is 0.239 calories, or 0.000239 Calories (food) • Pushing a crate 10 m across a floor with a force of 250 N requires 2,500 J (2.5 kJ) of work • Gravity does 20 J of work on a 1 kg (10 N) book that it has pulled off a 2 meter shelf Physics 1100 – Spring 2012 Energy In Our Daily Lives Our Energy Sources, Budgets, Expenditures Where Does Energy Come From • Ultimately, from the Big Bang – Energy is, after all, conserved • In our daily lives: 93% Sun, 7% nuclear – – – – – – Food energy: sunlight, photosynthesis Hydroelectric energy: sunlight-driven water cycle (7%) Fossil Fuels: Stored deposits of plant energy (85%) Wind Energy: solar-driven weather (< 1%) Solar Energy: well…from the sun, of course (< 1%) Our nuclear energy, in essence, derives from products of former stars (supernovae) Physics 1100 – Spring 2012 Class Problems 1. If you push an object twice as far while applying the same force, you do A) half as much work. B) twice as much work. C) four times as much work. D) the same amount of work. 2. If you do work on an object in one-third the usual time, your power output is A) three times the usual power output. B) the usual power output. C) one third the usual power output. D) impossible to predict without additional information. Physics 1100 – Spring 2012 Class Problems 3. A clerk can lift containers a vertical distance of 1 meter or can roll them up a 2 meter-long ramp to the same elevation. With the ramp, the applied force required is about A) four times as much. B) twice as much. C) the same. D) half as much. 4. After rolling halfway down an incline a marble's kinetic energy is A) greater than its potential energy. B) less than its potential energy. C) the same as its potential energy. D) impossible to determine. Physics 1100 – Spring 2012 Class Problems 5. It takes 40 J to push a large box 4 m across a floor. Assuming the push is in the same direction as the move, what is the magnitude of the force on the box? A) 10 N B) 4 N C) 160 N D) 40 N E) none of these 6. A machine puts out 100 Watts of power for every 1000 Watts put into it. The efficiency of the machine is A) 110%. B) 90%. C) 10%. D) 50%. E) none of these Physics 1100 – Spring 2012 Class Problems 7. A car moving at 50 km/hr skids 20 m with locked brakes. How far will the car skid with locked brakes if it were traveling at 150 km/hr? A) 60 m B) 90 m C) 180 m D) 120 m E) 20 m 8. A 2500-N pile-driver ram falls 10 m and drives a post 0.1 m into the ground. The average impact force on the ram is A) 250,000 N. B) 2,500,000 N. C) 25,000 N. D) 2,500 N. Physics 1100 – Spring 2012 Class Problems 9. A flower pot of mass m falls from rest to the ground below, a distance h. Which statement is correct? A) The speed of the pot when it hits the ground depends on m. B) The KE of the pot when it hits the ground is proportional to h. C) The KE of the pot when it hits the ground does not depend on m. D) The speed of the pot when it hits the ground is proportional to h. E) None of these are correct. 10. When a rifle is fired it recoils as the bullet is set in motion. The rifle and bullet ideally acquire equal A) but opposite amounts of momentum. B) amounts of kinetic energy. C) both of these D) neither of these Physics 1100 – Spring 2012 Class Problems 11. Two pool balls, each moving at 2 m/s, roll toward each other and collide. Suppose after bouncing apart, each moves at 4 m/s. This collision violates conservation of A) energy. B) momentum. C) both momentum and energy. D) none of the above choices 12. If several balls are thrown straight up with varying initial velocities, the quantity that will have the same value for each trial is the ball's A) initial momentum. B) time of travel. C) maximum height. D) acceleration. E) None of the above choices are correct. Physics 1100 – Spring 2012