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Math Skills

Section 1 Work, Power, and Machines. Chapter 12. Math Skills. Work Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N?. Given: force, F = 190 N

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Math Skills

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  1. Section 1 Work, Power, and Machines Chapter 12 Math Skills WorkImagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N? • Given: force, F = 190 N • distance, d = 2.0 m • Unknown: work, W = ? J

  2. Section 1 Work, Power, and Machines Chapter 12 Math Skills, continued 2. Write the equation for work. • work = force  distance • W = f  d 3. Insert the known values into the equation, and solve. • W = 190 N 2.0 m = 380 N•m • W = 380 J

  3. Section 1 Work, Power, and Machines Chapter 12 Math Skills PowerIt takes 100 kJ of work to lift an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process? • Given: work, W = 100 kJ = 1  105 J • time, t = 20 s • The distance of 18 m will not be needed to • calculate power. • Unknown: power, P = ? W

  4. Section 1 Work, Power, and Machines Chapter 12 Math Skills, continued 3. Insert the known values into the equation, and solve. 2. Write the equation for power.

  5. Section 1 Work, Power, and Machines Chapter 12 Math Skills Mechanical Advantage Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high. . • Given:length= 5.0 m • height= 1.5 m • Unknown: mechanical advantage = ?

  6. Section 1 Work, Power, and Machines Chapter 12 Math Skills, continued 2. Write the equation for mechanical advantage. 3. Insert the known values into the equation, and solve.

  7. Section 3 What is Energy? Chapter 12 Math Skills Gravitational Potential EnergyA 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff? 1. List the given and unknown values. Given: mass, m = 65 kg height, h = 35 m free-fall acceleration, g = 9.8 m/s2 Unknown: gravitational potential energy, PE = ? J

  8. Section 3 What is Energy? Chapter 12 Math Skills, continued 2.Write the equation for gravitational potential energy. • PE = mgh • 3. Insert the known values into the equation, and solve. • PE = (65 kg)(9.8 m/s2)(35 m) • PE = 2.2  104 kg•m2/s2 • PE = 2.2  104 J

  9. Section 3 What is Energy? Chapter 12 Math Skills Kinetic EnergyWhat is the kinetic energy of a 44 kg cheetah running at 31 m/s? 1. List the given and unknown values. Given: mass, m = 44 kg speed, v = 31 m/s Unknown: kinetic energy, KE = ? J

  10. Section 3 What is Energy? Chapter 12 Math Skills, continued 2.Write the equation for kinetic energy. 3. Insert the known values into the equation, and solve.

  11. Section 4 Conservation of Energy Chapter 12 Math Skills EfficiencyA sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percentage. 1. List the given and unknown values. Given: work input = 180 J useful work output = 140 J Unknown: efficiency = ? %

  12. Section 4 Conservation of Energy Chapter 12 Math Skills, continued 2. Write the equation for efficiency. 3. Insert the known values into the equation, and solve.

  13. Section 4 Conservation of Energy Chapter 12 Concept Map

  14. Standardized Test Prep Chapter 12 Understanding Concepts, continued 3. Which of these statements describes the law of conservation of energy? A. No machine is 100% efficient. B. Energy is neither created nor destroyed. C. The energy resources of Earth are limited. D. The energy of a system is always decreasing.

  15. Standardized Test Prep Chapter 12 Understanding Concepts, continued 3. Which of these statements describes the law of conservation of energy? A. No machine is 100% efficient. B. Energy is neither created nor destroyed. C. The energy resources of Earth are limited. D. The energy of a system is always decreasing.

  16. Standardized Test Prep Chapter 12 4. A coal-burning power plant produces electrical energy with an efficiency of 30%. If the chemical energy produced by burning one gram of coal is 25,000 joules (J), how many joules of electrical energy are produced by the combustion of one gram of coal?

  17. Standardized Test Prep Chapter 12 Understanding Concepts, continued 4. A coal-burning power plant produces electrical energy with an efficiency of 30%. If the chemical energy produced by burning one gram of coal is 25,000 joules (J), how many joules of electrical energy are produced by the combustion of one gram of coal? Answer: 7500 J

  18. Standardized Test Prep Chapter 12 Interpreting Graphics 6. If the input force on this pulley system is 100 N, what is the output force? F. 100 N G. 200 N H. 300 N I. 400 N

  19. Standardized Test Prep Chapter 12 Interpreting Graphics, continued 6. If the input force on this pulley system is 100 N, what is the output force? F. 100 N G. 200 N H. 300 N I. 400 N

  20. Standardized Test Prep Chapter 12 Interpreting Graphics, continued 7. How could the amount of force required to raise the bucket be decreased even more? A. Add additional pulleys. B. Increase the length of the rope. C. Thread the rope through the pulleys in opposite order. D. Increase the amount of force on the free end of the rope.

  21. Standardized Test Prep Chapter 12 Interpreting Graphics, continued 7. How could the amount of force required to raise the bucket be decreased even more? A. Add additional pulleys. B. Increase the length of the rope. C. Thread the rope through the pulleys in opposite order. D. Increase the amount of force on the free end of the rope.

  22. Practice Problems #8. A crane lifts an 8,000 N beam 75 m to the top of a building in 30 seconds. How much power does the crane use? Power = Work Time Work = Force X Distance Work = 8,000 N X 75 m Power = 600,000 J 30 s Work = 600,000 J Power = 20,000 W W F D W P T Work Triangle Power Triangle

  23. Practice Problems #9. A motor exerts a force of 10,000 N to lift an elevator 6 m in 5 seconds. What is the power produced by the motor? Power = Work Time Work = Force X Distance Work = 10,000 N X 6 m Power = 60,000 J 5 s Work = 60,000 J Power = 12,000 W W F D W P T Work Triangle Power Triangle

  24. Practice Problems #10. A tow truck exerts a force of 9,000 N to pull a car out of a ditch. It moves the car a distance of 6 m in 25 s. What is the power of the tow truck? Power = Work Time Work = Force X Distance Work = 9,000 N X 6 m Power = 54,000 J 25 s Work = 54,000 J Power = 2,160 W W F D W P T Work Triangle Power Triangle

  25. Identify one form of potential energy and one form of kinetic energy.

  26. Practice Problems 12. An 80 kg man is jogging at a velocity of 4 m/s. What is his kinetic energy? K.E. = mv2 2 K.E. = 80 kg X (4 m/s)2 2 K.E. = 80 kg X 16 m/s 2 K.E. = 640 J

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