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Work, Power, and Energy

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  1. Work, Power, and Energy

  2. Energy, Work, and Power • Energy • Work • Power • Conservation of Energy

  3. Energy • The capacity to do work • Easy forms of mechanical energy • Kinetic Energy • Potential Energy • Examples of other types • Radiant • Thermal • Internal • Unit: Joules (J) – one newton x 1 meter

  4. Kinetic Energy • Definition: Energy due to Motion • KE = (1/2)mv2 m = mass of the object in motion v = velocity of the object Example #1: 10 m/s KE = (1/2)1000*(10)2 = 50,000 J 1000 kg Example #2: 20 m/s KE = (1/2)1000*(20)2 = 200,000 J 1000 kg

  5. Potential Energy • Definition: Stored Energy due to Position • Gravitational potential energy ~energy due to position PE = mgh • m = mass of object • g = accel.due to gravity (10 m/s2) • h = height of the object (above some arbitrary point) h

  6. Example: What is the potential energy? m g h = (1kg)(10m/s2)(2m)= 20 Joules Example of Potential Energy 1kg 2 m Don’t worry– it will always be clear what the calculation should be relative to!

  7. Where does the skier have more PE? When he’s higher! Potential Energy Greater height, Greater mgh, Greater PE Lower height, Smaller mgh, Smaller PE

  8. Springs • Springs can be compressed or stretched • They have an equilibrium position: the rest position when no forces are applied • x is the distance from equilibrium

  9. Spring Constant K = Spring constant • Spring constant (k): An indication of how hard it is to stretch (or compress) the spring • Unit: N/m (correct the unit sheet!) • Fs= kx (Hooke’s Law) • Note: Fs is the force required to stretch the spring x meters-- but also the force the spring exerts when it’s stretched that far x Fs

  10. Spring Constant K = Spring constant • Fs= kx • Example: 15N = k * 0.5m • K = 30 N/m 0.5m 15N

  11. Finding the Spring Constant • If you’re given force required to compress a spring a distance x, just solve Fs= kx • If you’re given a graph of force vs. distance, just take the slope (or take any point on the graph)

  12. Spring PE K = Spring constant • The elastic PE or spring PE is given by the equation PEs= ½ kx2 • Example: PEs= ½ 30 * 0.52 = 3.75 J 0.5m 15N

  13. Energy, Work, and Power • Energy • Work • Power • Conservation of Energy

  14. Work So we can “pump energy into a system” by doing work on it That increases the total energy When no work is being done, energy is conserved Work and Energy • Work is a means of putting energy into a system (or taking it out) Energy in the system

  15. Work • Work is a means of putting energy into a system (or taking it out) • Work is done only if a force F causes an object to move a distance D in the direction of the force. W = F  d • The units for work are Newton-meters (Nm) or Joules (J). 1 Nm = 1 J

  16. Work • Remember that d = vt, so if they give you force, velocity and time, you can still find the work • Example: As I push a ball with a force of 10 N, it moves at 3 m/s for 2 s. What is the work done? • Answer: d = vt = 3m/s * 2s = 6 m. W = F d = 10N * 6m = 60 J

  17. Work is done No work is done Negative work is done– energy is taken out of the system (think of friction or stopping forces) Work • Work is only done by the component of force in the direction of movement. d F F d d F

  18. No work is done by perpendicular component Work is done by the force in the same direction as the displacement Work • Work is only done by the component of force in the direction of movement. F Fy Fx d W = Fx d

  19. Examples • I roll my garbage can 20 meters out to the curb with a horizontal force of 100N. • Answer: Force and distance are in same direction. Work = F d = 100N * 20m = 2000 J. • I hold a 10,000N car over my head while rollerskating • Answer: No work is done! My force is up– by displacement is horizontal.

  20. How much work is done lifting a 3-kg box 2m? How much potential energy was gained? PE vs. Work d = 2m h = 2m F = mg = 30N Work = Fxd = 60 J PE = mgh = 60 J The energy of the box increased by the amount of work done on the box!

  21. How to think about work & energy • Work = change in energy • When no work is being done, total energy is conserved

  22. Work, Power, and Energy • Energy • Work • Power • Conservation of Energy

  23. Power • James Watt, an Englishman in the 1700’s, needed a term to distinguish a “good” steam engine from a “bad” engine. • The difference he determined was the time to do work. • POWER is the rate of doing work. P = W/t Power = Work /t • The units for power are J/s or watts (W) 1 J/s = 1 W

  24. Example Problems • You exert a 100 N force to move a box 3 m in 4 seconds. How much work did you do on the box? What was your Power Output? 100 N Box 3 meters in 4 seconds W=300 J P=75 W

  25. Another way of looking at power • Power = W/t = (Fd)/t = F (d/t) = F v • Power = force * velocity • You exert a 100 N force to move a box 3 m in 4 seconds. What was your Power Output? 100 N Box 3 meters in 4 seconds, so v = 0.75 P=100 * 0.75 = 75 W

  26. Example • An electric pump lifts 5000 N of water from the bottom of a 6 m deep well in 1 minute. • W=F x d = 5,000N x 6m = 30,000 J P= W/t = 30,000J/60s = 500 W

  27. Work, Power, and Energy • Energy • Work • Power • Conservation of Energy

  28. Conservation of Energy • Total mechanical energy doesn’t change • …unless we have friction, air resistance, or put work into the system. MEinitial = MEfinal So KEinitial + PEinitial = KEfinal + PEfinal

  29. Diving Board example PE = 500JKE = 0 • On the trip down, energy is conserved • Total energy is 500J at top • Total energy is 500J all the way down PE = 300JKE = 200J PE = 100JKE = 400J

  30. Diving Board example PE = 500JKE = 0 • On the trip down, energy is conserved • How did that energy get there? • Work was done! (He climbed up, putting energy into the system) PE = 300JKE = 200J PE = 100JKE = 400J

  31. Work So we can “pump energy into a system” by doing work on it That increases the total energy When no work is being done, energy is conserved Work and Energy • Work is a means of putting energy into a system (or taking it out) Energy in the system

  32. Work = change in energy • Equation: W = Fd = ΔET

  33. Diving Board example PE = 500JKE = 0 • He climbed up, putting energy into the system • How much work did he do? • W = Fd = ΔET • Since he started with 0J, ended with 500J, work= ΔET = 500J PE = 300JKE = 200J PE = 100JKE = 400J

  34. Diving Board example • Let’s not waste his energy! • He will now do work on the seesaw • How much energy does the diver lose? • W = ΔET = 500J • Which goes into the energy of the seesaw (and then the clown) PE = 500JKE = 0 PE = 300JKE = 200J PE = 100JKE = 400J

  35. Diving Board example • So 500J of work is done on the clown • W = ΔET = 500J • So the clown’s total energy is now increased (from 0) to around 500J • In real life, some of that 500J would get converted to internal energy (heat, friction, etc.) PE = 500JKE = 0 PE = 300JKE = 200J PE = 0JKE = 0J

  36. We directly model the impact of the force on the object using PE These forces do work on the object, changing the total mechanical energy When is Energy Conserved? • Not Conserved • Applied forces • Normal forces • Friction • Normal forces • Conserved • Gravitational force • Spring force

  37. Unconserved Situations • I throw a snowball toward a wall • It has kinetic energy • The wall exerts a normal force on the snowball, removing its kinetic energy • The snowball’s energy is not conserved • (But it is converted to other forms of energy, like internal energy of the wall)

  38. Unconserved Situations, II • A ball rolls on a surface with friction • It has kinetic energy • The kinetic energy decreases • Friction has done work on the ball to decrease its total energy

  39. Examples… • I throw a 2-kg ball upward with a velocity of 20m/s. How high does it go? • We’re talking about velocity (KE), and height (PE), so it’s a conservation question • At the beginning (call it h=0): KE = 1/2mv2 = 400J • PE = 0J • Total Energy = 400J • At the top: Total Energy = 400J • KE = 0J (it stops) • PE = 400 – 0 = 400 J • So PE = mgh 400J = 2 * 10 * h • h = 20 m

  40. Example II • A 1-kg ball starts rolling with a velocity of 10 m/s. A few seconds later, it is rolling at 4 m/s. How much work was done on the ball by friction? • Starting KE = 1/2mv2 = 50 J • Final KE = 8 J • Work = ΔE = 42 J

  41. How to think about work & energy • Work = change in energy • When no work is being done, total energy is conserved