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### 1 work

1. 1. WORK AND CONSERVATIONWORK AND CONSERVATION OF ENERGYOF ENERGY STYMVERLY GAWAT JENERUS JUAN AND ALWEN AGYAM
2. 2. Work is the transfer of energy through motion. In order for work to take place, a force must be exerted through a distance. The amount of work done depends on two things: the amount of force exerted and the distance over which the force is applied. There are two factors to keep in mind when deciding when work is being done: something has to move and the motion must be in the direction of the applied force. Work can be calculated by using the following formula: Work=force x distance WorkWork
3. 3. Work is done on the books when they are being lifted, but no work is done on them when they are being held or carried horizontally. WorkWork
4. 4. Work can be positive orWork can be positive or negativenegative • 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
5. 5. Work done by a constant ForceWork done by a constant Force θ ∆Ekin = Wnet • W = F s = |F| |s| cos θ = Fs s |F| : magnitude of force |s| = s : magnitude of displacement Fs = magnitude of force in direction of displacement : Fs = |F| cos θ θ: angle between displacement and force vectors • Kinetic energy : Ekin= 1/2 m v2 • Work-Kinetic Energy Theorem: F s
6. 6. Conservation of Mechanical EnergyConservation of Mechanical Energy Total mechanical energy of an object remains constant provided the net work done by non-conservative forces is zero: Etot = Ekin + Epot = constant or Ekin,f+Epot,f = Ekin,0+Epot,0 Otherwise, in the presence of net work done by non-conservative forces (e.g. friction): Wnc = Ekin,f – Ekin,0 + Epot,f-Epot,i
7. 7. Example ProblemExample Problem Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces? 1. 0J 2. 50J 3. -50J 4. 225J 5. -225J correct Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies. W = (300-75) + ((-25) - 250) = 225 - 275 = -50J. Samar HathoutSamar Hathout
8. 8. ExampleExample Samar Hathout
9. 9. Conservation of EnergyConservation 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 PEf + KEf = PEi + KEi ∆KE = −∆PE Samar Hathout
10. 10. ExampleExample 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
11. 11. ExampleExample 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
12. 12. ExampleExample Three identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward. Neglecting air resistance, which ball has the fastest speed when it hits the ground? A) Ball 1 B) Ball 2 C) Ball 3 D) All have the same speed.
13. 13. Springs (Hooke’s Law)Springs (Hooke’s Law) Proportional to displacement from equilibrium F = −kx
14. 14. Potential Energy of SpringPotential Energy of Spring ∆PE=-F∆x ∆x F ∆PE∑ = 1 2 (kx)x PE = 1 2 kx2
15. 15. x ExampleExample b) To what height h does the block rise when moving up the incline? 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. 3.2 cm
16. 16. PowerPower Average power is the average rate at which a net force does work: Pav = Wnet / t SI unit: [P] = J/s = watt (W) Or Pav = Fnet s /t = Fnet vav
17. 17. ExampleExample 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) 120 mph b) 0.91g
18. 18. ExampleExample 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)