1. Chapter 6 Work and Energy © 2014 Pearson Education, Inc. No need to write information in red

2. Work Done by a Constant Force Work is done when a force causes the displacement of an object Units of work are joules: 1 J = 1 N   m © 2014 Pearson Education, Inc.

3. Solving work problems: 1.Draw a free-body diagram. 2.Choose a coordinate system. 3.Apply Newton’s laws to determine any unknown forces. 4.Find the work done by a specific force. 5.To find the net work, either find the net force and then find the work it does, or find the work done by each force and add. © 2014 Pearson Education, Inc.

4. Work done by forces that oppose the direction of motion, such as friction, will be negative. Centripetal forces do no work, as they are always perpendicular to the direction of motion. An object moving at constant speed has no work done on it © 2014 Pearson Education, Inc.

5. Work-Energy Principle Energy is traditionally defined as the ability to do work. But, not all forces are able to do work; But for mechanical energy, this definition applies Mechanical energy - kinetic energy or potential energy Kinetic energy - energy of objects in motion Potential energy – energy of a system due to position of the components © 2014 Pearson Education, Inc.

6. Work-Energy Principle: the net work done on an object is equal to the change in the object’s kinetic energy. + net work means kinetic energy increases. - net work means kinetic energy decreases.

7. W = Fd = mad Write the acceleration in terms of the velocity and the distance, we find that the work done here is Slightly different on equation sheet © 2014 Pearson Education, Inc.

8. Potential Energy – abbreviated as U on equation sheet An object can have PE by virtue of its surroundings. PE is a property of a system as a whole, not just of the object (because it depends on external forces). Examples of PE: springs elastic bands An object at some height above the ground © 2014 Pearson Education, Inc.

9. Gravitational Potential Energy GPE = mgy On equation sheet ΔU = mg Δy Only changes in potential energy can be measured, so y = Δy. PE becomes KE if the object is dropped. © 2014 Pearson Education, Inc.

10. PE of Springs PE is stored in a compressed spring and can then yield kinetic energy. © 2014 Pearson Education, Inc. Hooke’s Law (slightly different on equation sheet): k is the spring constant, needs to be measured for each spring.

11. The force increases as the spring is stretched or compressed further. where x is the distance it was stretched or compressed On equation sheet U s = 1/2kx 2

12. Practice problems 6-1. A person pulls a 50kg crate 40m along a horizontal floor by a force Fp=100N which acts at a 37° angle. The floor is rough and exerts a friction force of 50N. Determine a)the work done by each force on the crate, and b) the net work done on the crate. © 2014 Pearson Education, Inc.

13. Practice problems 6-2. a)Determine the work a hiker must do on a 15.0kg backpack to carry it up a hill of height h=10.0m. b) the work done by gravity on the backpack, and c)the net work done on the backpack. Assume constant velocity. © 2014 Pearson Education, Inc.

14. Practice problems 6-3. The moon revolves around the earth in a nearly circular orbit. Does gravity do positive work, negative work or no work. Explain. © 2014 Pearson Education, Inc.

15. Practice problems 6-4. How much net work is required to accelerate a 1000kg car from 20m/s to 30m/s? © 2014 Pearson Education, Inc.

16. Practice problems 6-5. A car traveling 60km/h can brake to a stop in a distance of 20m. If the car is going twice as fast, what is the stopping distance? Assume the maximum braking force is independent of speed. © 2014 Pearson Education, Inc.

17. Practice problems 6-6. A 1000kg roller coaster car moves from point 1 to point 2 and then to point 3. a)what is the gravitational potential energy at points 2 and 3 relative to point 1? b)What is the change in potential energy when the car goes from point 2 to point 3? © 2014 Pearson Education, Inc.

18. Chapter 6 Conservation of Energy and Power © 2014 Pearson Education, Inc. No need to write information in red

19. Conservative and Nonconservative Forces Conservative forces: the work done in moving a particle between two points is independent of the taken path (i.e. gravity) Nonconservative forces: the work done is dependent on the path (i.e. friction) © 2014 Pearson Education, Inc.

20. Potential energy can only be defined for conservative forces. However, we can find the net work done by nonconservative forces after analyzing ALL forces and applying

21. Principle of Conservation of Mechanical Energy If there are no nonconservative forces, ΔKE + ΔPE = 0 Total mechanical energy: E = KE + PE = ½ mv 2 + mgy © 2014 Pearson Education, Inc.

22. For an elastic force, conservation of energy tells us: © 2014 Pearson Education, Inc. (6-14)

23. Energy Transformations Other forms of energy: electric, nuclear, thermal, chemical, light, sound Work is done when energy is transferred from one object to another. © 2014 Pearson Education, Inc.

24. Law of Conservation of Energy Accounting for all forms of energy, the total energy neither increases nor decreases. Energy as a whole is conserved. KE and PE are often lost as thermal energy because of nonconservative forces © 2014 Pearson Education, Inc.

25. Power Power is the rate at which work is done— Units of power are watts: 1W = 1 J/s 1 horsepower = 746W © 2014 Pearson Education, Inc. On equation sheet P = ΔE/ Δ t

26. Power is also needed for acceleration and for moving against the force of gravity. The average power can be written in terms of the force and the average velocity: © 2014 Pearson Education, Inc. (6-18)

27. Practice problems 6-7. If a rock is held 3.0m above the ground, what is the rock’s velocity when it has fallen to 1.0m above the ground? © 2014 Pearson Education, Inc.

28. Practice problems 6-8. Assuming the height of the hill of a roller coaster is 40m, and the coaster starts from rest at the top, calculate a)the speed of the roller coaster at the bottom of the hill and b)at what height does it have half this speed. Take y=0 to be the bottom of the hill. © 2014 Pearson Education, Inc.

29. Practice problems 6-9. Two water slides at a pool are shaped differently, but start at the same height. Two riders start from rest at the same time on the slides. a)Which rider, Paul or Kathleen, is traveling faster at the bottom? b)Which rider makes it to the bottom first? Ignore friction and assume both slides have the same path length. © 2014 Pearson Education, Inc.

30. Practice problems 6-10. A dart of mass 0.100kg is pressed against the spring of a toy gun. The spring constant is 250N/m, and the spring is compressed 6.0cm and released. If the dart detaches from the spring when the spring reaches its natural length (x=0), what speed does the dart acquire? © 2014 Pearson Education, Inc.

31. Practice problems 6-12. A 1000kg roller coaster reaches a vertical height of 25m on the second hill of the track where it slows to a momentary stop. It traveled a total distance of 400m. Determine the thermal energy produced and estimate the average friction force on the car. © 2014 Pearson Education, Inc.

32. Practice problems 6-13. A 60kg jogger runs up a flight of stairs in 4.0s. The vertical height of the stairs is 4.5m. a)Estimate the jogger’s power in watts and horsepower. b)How much energy did this require? © 2014 Pearson Education, Inc.

33. Practice problems 6-14. Calculate the power required of a 1400kg car under the following circumstances: a)the car climbs a 10 degree hill at a steady 80km/h and b)the car accelerates along a level road from 90 to 110km/h in 6.0s to pass a car. Assume average retarding force on the car is 700N. © 2014 Pearson Education, Inc.