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Work and Machines Formulas

Work and Machines Formulas. Using machines. Machines like a car jack, a crow bar, and a claw hammer make work easier by making the output force greater than in input force. The ratio of the input force to the output force is the mechanical advantage of a machine.

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Work and Machines Formulas

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  1. Work and Machines Formulas

  2. Using machines • Machines like a car jack, a crow bar, and a claw hammer make work easier by making the output force greater than in input force. • The ratio of the input force to the output force is the mechanical advantage of a machine. Mechanical Advantage = Output Force ÷ Input Force MA = Fout/Fin • There are NO units for mechanical advantage since you are dividing the output force in newtons by the input force in newtons.

  3. Using machines Example: • Calculate the mechanical advantage of a hammer if the input force is 125-N and the output force is 2000-N. MA = Fout/Fin MA = 2000-N/125-N MA = 16 • This means that the hammer has increased your force by a factor of 16.

  4. Using machines • Example: • What is the mechanical advantage of a crowbar when you apply 100-N of force to lift a 250-N rock. MA = Fout/Fin MA = 250-N/100-N MA = 2.5

  5. Using machines • Efficiency is a measure of how much of the work put into a machine is changed into useful output work by the machine. • A machine with high efficiency produces less heat from friction so more of the input work is changed into useful output work. Efficiency = (Output Work ÷ Input Work) × 100 E = (Wout/Win) × 100 • Efficieny is expressed as a percent.

  6. Using machines Example: • Find the efficiency of a machine that does 800-J of work if the input work is 2400-J. E = (Wout/Win) × 100 E = (800/2400) × 100 E = 33.3% • This means that the machine only converts 33.3% of the energy put into the machine into energy put out by the machine. The other 66.7% of the energy is lost due to friction.

  7. Work What is work? • Work is the transfer of energy that occurs when a force makes an object move. Work = Force × Distance W = Fd • Units for work: Newton•meter (N•m) or Joule (J)

  8. Work Example: • You push a refrigerator with a force of 100-N. If you move the refrigerator a distance of 5-m, how much work do you do? Work = Force × Distance Work = (100-N) × (5-m) Work = 500-J

  9. Work Example: • A force of 75-N is exerted on a 45-kg couch and the couch is moved 5-m. How much work is done in moving the couch? Work = Force × Distance Work = (75-N) × (5-m) Work = 375-J

  10. Work Example: • A lawn mower is pushed with a force of 80-N. If 12 000-J of work are done in mowing a lawn, what is the total distance the lawn mower was pushed? Work = Force × Distance 12000-J = 80-N × Distance Distance = (12000-J) ÷ (80-N) Distance = 150-m

  11. Work Example: • The brakes on a car do 240 000-J of work in stopping the car. If the car travels a distance of 50-m while the brakes are being applied, what is the total force the brakes exert on the car? Work = Force × Distance 240000-J = Force × 50-m Force = (240000-J) ÷ (50-m) Force = 4800-N

  12. Work • Power is the rate at which work is done, or the amount of work done per unit time. Power = Work ÷ Time P = W/t P = Fd/t • Units for power: N•m/sec or J/sec or Watt (W) or kilowatts (kW) for large quantities. • 1 horsepower (hp) = 745.56 watts

  13. Work Example: • You do 900-J of work pushing a sofa. If it took 5-seconds to move the sofa, what was your power? Power = Work ÷ Time Power = (900-J) ÷ (5-sec) Power = 180-W

  14. Work Example: • To lift a baby from a crib 50-J of work are done. How much power is needed if the baby is lifted in 0.5-seconds? Power = Work ÷ Time Power = (50-J) ÷ (0.5-sec) Power = 100-W

  15. Work Example: • If a runner’s power is 130-W, how much work is done by the runner in 10-minutes? Power = Work ÷ Time 130-W = Work ÷ 600-sec Work = (130-W) × (600-sec) Work = 78000-J

  16. Work Example: • The power produced by an electric motor is 500-W. How long will it take the motor to do 10 000-J of work? Power = Work ÷ Time 500-W = 10000-J ÷ Time 500-W × Time = 10000-J Time = (10000-J) ÷ (500-W) Time = 20-sec

  17. Formulas Mechanical Advantage = Output Force ÷ Input Force MA = Fout/Fin Efficiency = (Output Work ÷ Input Work) × 100 E = (Wout/Win) × 100 Work = Force × Distance W = Fd Power = Work ÷ Time P = W/t P = Fd/t

  18. 1. Calculate the mechanical advantage of a hammer if the input force is 105-N and the output force is 1500-N • A lawn mower is pushed with a force of 85-N. If 13000-J of work are done in mowing a lawn, what is the total distance the lawn mower was pushed? • Find the efficiency of a machine that does 1800-J of work if the input work is 2600-J. • You push a refrigerator with a force of 200-N. If you move the refrigerator a distance of 15-m, how much work do you do?

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