Work, Energy, and Power

1. Work, Energy, and Power Measures of Effort & Motion; Conservation Laws

2. 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

3. 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

4. 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

5. How Much Work Does He Do On Wall? Physics 1100 – Spring 2012

6. 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

7. Gravitational Potential Energy • Gravitational Potential Energy near the surface of the Earth: m Work = Dh m • W = mg Dh Physics 1100 – Spring 2012

8. 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

9. 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

10. 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

11. Conversion of Energy Physics 1100 – Spring 2012

12. Energy Conversion/Conservation Example P.E. = 98 J K.E. = 0 J 10 m • Drop 1 kg ball from 10 m • starts out with mgh = (1 kg)(10m/s2)(10 m) = 100 J of gravitational potential energy • halfway down (5 m from floor), has given up half its 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 energy • ½mv2 = 100 J  v2 = 200m2/s2  v = 14 m/s 8 m P.E. = 73.5 J K.E. = 24.5 J 6 m P.E. = 49 J K.E. = 49 J 4 m P.E. = 24.5 J K.E. = 73.5 J 2 m P.E. = 0 J K.E. = 98 J 0 m Physics 1100 – Spring 2012

13. 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

14. Class Problem • In which car will you be moving fastest at the very bottom of the incline? • a) front carb) middle carc) rear card) Other Physics 1100 – Spring 2012

15. 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

16. 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

17. 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Distance = ForceDistance Physics 1100 – Spring 2012

18. Larger Force Small Force Short Distance Long Distance M Ramps Exert a smaller force over a larger distance to achieve the same change in gravitational potential energy (height raised) Physics 1100 – Spring 2012

19. 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 • Extend over 10 m, and only 98 N (22 lb) is needed • Something we can actually provide • Excludes frictional forces/losses 1 m Physics 1100 – Spring 2012

20. Simple Machines Work input = work output! Physics 1100 – Spring 2012

21. Simple Machines Physics 1100 – Spring 2012

22. Efficiency Efficiency = (Useful energy output)/(total energy input) Physics 1100 – Spring 2012

23. 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

24. Energy In Our Daily Lives Our Energy Sources, Budgets, Expenditures

25. 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

26. Class Problems • 1. If you push an object twice as far while applying the same force, you do • half as much work. • twice as much work. • four times as much work. • 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

27. 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 • four times as much. • twice as much. • the same. • half as much. • 4. After rolling halfway down an incline a marble's kinetic energy is • greater than its potential energy. • less than its potential energy. • the same as its potential energy. • impossible to determine. Physics 1100 – Spring 2012

28. 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

29. 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? • 60 m • 90 m • 180 m • 120 m • 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 • 250,000 N. • 2,500,000 N. • 25,000 N. • 2,500 N. Physics 1100 – Spring 2012

30. 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 • but opposite amounts of momentum. • amounts of kinetic energy. • both of these • neither of these Physics 1100 – Spring 2012

31. 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 • energy. • momentum. • both momentum and energy. • 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