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Work

Work. In physics, work is the amount of energy transformed (changed) when a force moves (in the direction of the force). Calculating work. The amount of work done (measured in Joules) is equal to the force used (Newtons) multiplied by the distance the force has moved (metres).

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Work

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  1. Work In physics, work is the amount of energy transformed (changed) when a force moves (in the direction of the force)

  2. Calculating work The amount of work done (measured in Joules) is equal to the force used (Newtons) multiplied by the distance the force has moved (metres). Force (N) Distance travelled (m)

  3. Three Key Ingredients to Work • Force: • Displacement • Cause • In order for work to be done on an object there must be displacement and the force must cause that displacement.

  4. Work (J)= Force(N) x distance(m) W = F*d*cosθ

  5. Important The force has to be in the direction of movement. Carrying the shopping home is not work in physics!

  6. What if the force is at an angle to the distance moved? Work = F*d*cosθ F θ s

  7. Lifting objects When we lift objects, we are doing work because a force is moving. Force Distance moved

  8. Lifting objects Our lifting force is equal to the weight of the object. Lifting force weight

  9. Work done (J) = Force (N) x distance (m) A woman pushes a car with a force of 400 N at an angle of 10° to the horizontal for a distance of 15m. How much work has she done?

  10. Work done (J) = Force (N) x distance (m) A woman pushes a car with a force of 400 N at an angle of 10° to the horizontal for a distance of 15m. How much work has she done? W = F*d*cosθ = 400x15x0.985 W = 5900 J

  11. Work done (J) = Force (N) x distance (m) A man lifts a mass of 120 kg to a height of 2.5m. How much work did he do?

  12. Work done (J) = Force (N) x distance (m) A man lifts a mass of 120 kg to a height of 2.5m. How much work did he do? Force = weight = 1200N Work = F x d = 1200 x 2.5 Work = 3000 J

  13. Power! Power is the amount of energy transformed (changed) per second. It is measured in Watts (1 Watt = 1 J/s) Power = Energy transformed time

  14. Gravitational Potential Energy • An object can store energy as the result of its position. • Stored energy of position possessed by an object is called Potential Energy. • Gravitational Potential Energy (GPE) has a direct relation between height and mass.

  15. Gravitational Potential Energy (GPE) • PE(grav) = mass * gravity * height • PE=m*g*h

  16. GPE Question

  17. Elastic Potential Energy • Energy store in elastic materials as the result of their stretching or compressing. • REMEMBER HOOKE’S LAW? • F(spring)= k*x • PE(spring) = 0.5*k*x² • K=spring constant • X=amount of compression

  18. Work done in stretching a spring Work done in strectching spring = area under graph F/N x/m

  19. Example: • . A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

  20. Answer: • PE: m*g*h • (3kg)*(9.8)*(0.45m) • PE= 13.2 J

  21. Example Woof! (help!) A dog of mass 12 kg falls from an aeroplane at a height of 3.4 km. How much gravitational energy does the dog lose as it falls to the ground

  22. Example On earth g = 9.8 m/s2 Mass of dog = 12 kg Height = 3.4 km = 3400 m

  23. Example On earth g = 10 m/s2 Mass of dog = 12 kg GPE lost by dog = mgh = 12 x 10 x 3400 = 408 000 J Height = 3.4 km = 3400 m

  24. Example GPE lost by dog = mgh = 12 x 9.8 x 3400 = 399840 J Just before the dog hits the ground, what has this GPE turned into?

  25. Kinetic energy

  26. Kinetic energy Kinetic energy of an object can be found using the following formula Ek = mv2 2 where m = mass (in kg) and v = speed (in m/s)

  27. Example A bullet of mass 150 g is traveling at 400 m/s. How much kinetic energy does it have?

  28. Example A bullet of mass 150 g is traveling at 400 m/s. How much kinetic energy does it have? Ek = mv2/2 = (0.15 x (400)2)/2 = 12 000 J

  29. Energy changes

  30. Measuring your work

  31. Mechanical Energy • Can either be KE or PE. • Objects have ME if they are in motion and/or if they are at some position relative to a zero potential energy position. • Example: a brick held at a vertical position above the ground or zero height position.

  32. Mechanical Energy as the Ability to Do Work • An object that possesses mechanical energy is able to do work. • ME is often defined as the ability to do work.

  33. Total Mechanical Energy (TME) • TME=PE+KE • TME=PE(grav)+PE(spring)+KE

  34. Power • Work has nothing to do with time, only displacement and force. • Power is the rate at which work is done. • Power=Work/time • P=W/t • Standard unit of Power is Watt (joule/second)

  35. POWer Continued:

  36. Example: • During a physics lab, Jack and Jill ran up a hill. Jack is twice as massive as Jill; yet Jill ascends the same distance in half the time. Who did the most work? ______________ Who delivered the most power? ______________ Explain your answers.

  37. Answer: Jack does more work than Jill. Jack must apply twice the force to lift his twice-as-massive body up the same flight of stairs. Yet, Jill is just as "power-full" as Jack. Jill does one-half the work yet does it one-half the time. The reduction in work done is compensated for by the reduction in time.

  38. Internal vs. External Forces

  39. What does Work do? • When net work is done upon an object by an external force the TME of that object is changed. • If the work is positive, the object will gain energy. • If the work is negative, the object will lose energy. • The gain or lost can be in the form of PE or KE or both • THE WORK DONE WILL BE EQUAL TO THE CHANGE IN THE ME OF THE OBJECT.

  40. What is an example of Negative Work? • Breaks slowing down a car • The force acts in the opposite direction of the object(s) in motion. • Force doesn’t cause the displacement but hinders it. • This is negative work.

  41. External Forces • Because external forces (those referenced in the previous slide) are capable of changing the TME of an object, they are sometimes referred to as nonconservative forces.

  42. Internal Forces • When the only type of force doing net work upon an object is internal (gravitational), the TME remains constant • Sometimes they are referred to as conservative forces

  43. Relating Work to Energy • TME(i)+W(ext)=TME(final) • Initial amount of TME plus Work done by external force equals final TME. • KE(i)+PR(i)+W(ext) + KE(f) + PE(f) • This just breaks down TME into its components

  44. Example: A 1000-kg car traveling with a speed of 25 m/s skids to a stop. The car experiences an 8000 N force of friction. Determine the stopping distance of the car.

  45. Example Answer: Initially: PE = 0 J (the car's height is zero) KE = 0.5*1000*(25)^2 = 312 500 J Finally: PE = 0 J (the car's height is zero) KE = 0 J (the car's speed is zero) The work done is (8000 N) • (d) • cos 180 = - 8000*d Using the equation, TMEi + Wext = TMEf 312 500 J + (-8000 • d) = 0 J Using some algebra it can be shown that d=39.1 m

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