2. Introduction to Work Monday, September 14, 2015

3. Work Work tells us how much a force or combination of forces changes the energy of a system. Work is the bridge between force and energy W = Fd F: force (N) d: displacement (m)

4. Units of Work SI System: Joule (J) or Newton-Meter (Nm) 1 Joule of work is done when 1 N acts on a body moving it a distance of 1 meter

5. iClicker Question If a man holds a 50 kg box at arms length for 2 hours as he stands still, how much work does he do on the box? A. 0J B. 50J C. 100J D. 360,000J E. There is not enough information to answer

6. Force and Direction of Motion Both Matter There is no work done by a force if it causes no displacement. Forces can do positive, negative, or zero work. When an box is pushed on a flat floor, for example… The normal force and gravity do no work, since they are perpendicular to the direction of motion. The person pushing the box does positive work, since she is pushing in the direction of motion. Friction does negative work, since it points opposite the direction of motion.

7. If a man holds a 50 kg box at arms length for 2 hours as he walks 1 km at constant velocity, how much work does he do on the box?

8. If a man lifts a 50 kg box 2.0 meters, how much work does he do on the box?

9. Work and Energy Work changes mechanical energy! If an applied force does positive work on a system, it tries to increase mechanical energy. If an applied force does negative work, it tries to decrease mechanical energy. The two forms of mechanical energy are called potential and kinetic energy.

10. Jane uses a vine wrapped around a pulley to lift a 70-kg Tarzan to a tree house 9.0 meters above the ground. a. How much work does Jane do when she lifts Tarzan? b. How much work does gravity do when Jane lifts Tarzan?

11. Joe pushes a 10-kg box and slides it across the floor at constant velocity of 3.0 m/s. The coefficient of kinetic friction between the box and floor is 0.50. a) How much work does Joe do if he pushes the box for 15 meters? b) How much work does friction do as Joe pushes the box?

12. iClicker Question How much work does gravity do when a 2.5kg object falls a distance of 3.5m? A. -88 J B. -8.8 J C. 0 J D. 8.8 J E. 88 J

13. Kinetic Energy Monday, September 14, 2015

14. Kinetic Energy Energy due to motion K = ½ mv 2 K: Kinetic Energy m: mass in kg v: speed in m/s Unit: Joules

15. A 10 kg ball has a speed of 1.2 m/s. a) What is the kinetic energy of the bullet? b) What is the bullet’s kinetic energy if the mass is doubled? c) Taking the original mass, what is the bullet’s kinetic energy if the speed is doubled?

16. iClicker Question An object contains 10 J of kinetic energy. The object’s mass is tripled and its velocity is doubled. What is the new kinetic energy of the object? A. 10 J B. 60 J C. 120 J D. 180 J E. 360 J

17. The Work-Energy Theorem The net work due to all forces equals the change in the kinetic energy of a system. W =  K W: Work done on the object (J)  K: change in kinetic energy (K f – K i )

18. iClicker Question An 2kg ball is moving at 3m/s. A force of 6N does 18J of work on it. What is the new energy of the ball? A. 9J B. 15J C. 18J D. 27J E. 33J

19. Work Done by Variable Forces Monday, September 14, 2015

20. An 2 kg pineapple falls from a tree and lands on the ground 10.0 m below with a speed of 11.0 m/s. a) What would the speed of the pineapple have been if there had been no air resistance? b) Did air resistance do positive, negative or zero work on the acorn? Why?

21. Constant force and work The force shown is a constant force. W = Fd can be used to calculate the work done by this force when it moves an object from d a to d b. The area under the curve from d a to d b can also be used to calculate the work done by the force when it moves an object from d a to d b F(x) x dada dbdb

22. Variable force and work The force shown is a variable force. W = Fd CANNOT be used to calculate the work done by this force! The area under the curve from d a to d b can STILL be used to calculate the work done by the force when it moves an object from d a to d b F(x) x xaxa xbxb

23. How much work is done by the force shown when it acts on an object and pushes it from x = 0.25 m to x = 0.75 m?

24. How much work is done by the force shown when it acts on an object and pushes it from x = 2.0 m to x = 4.0 m?

25. Power Monday, September 14, 2015

26. Power Power is the rate of which work is done. P = W/  t W: work in Joules  t: elapsed time in seconds When we run upstairs, t is small so P is big. When we walk upstairs, t is large so P is small.

27. Unit of Power SI unit for Power is the Watt. 1 Watt = 1 Joule/s Named after the Scottish engineer James Watt (1776-1819) who perfected the steam engine.

28. Power Consider the units to develop another method. [W] = [J]/[s] [W] = [N][m]/[s] P = Fv Once again… When we run upstairs, t is small so P is big. When we walk upstairs, t is large so P is small.

29. Calculate the power output of a 0.10 kg bug as it walks straight up a window pane at 2.0 m/s.

30. Potential energy Energy of position or configuration “Stored” energy For gravity: U g = mgh m: mass g: acceleration due to gravity h: height above the “zero” point

31. Sample problem A diver drops to the water from a height of 20.0 m, his gravitational potential energy decreases by 12,500 J. What is the diver’s mass?

32. iClicker Question A student weighing 70kg climbs at constant speed to the top of an 8m vertical rope in 10s. The average power expended by the student to overcome gravity is most nearly (A) 1.1 W (B) 87.5 W (C) 560 W (D) 875 W (E) 5,600 W

33. Conservation of Mechanical Energy Monday, September 14, 2015

34. Law of Conservation of Energy In any isolated system, the total energy remains constant. Energy can neither be created nor destroyed, but can only be transformed from one type of energy to another.

35. Law of Conservation of Mechanical Energy E = K + U = Constant K: Kinetic Energy U: Potential Energy  E = 0

36. Conservation of Energy Springs and pendulums obey conservation of energy. The equilibrium position has high kinetic energy and low potential energy. The positions of maximum displacement have high potential energy and low kinetic energy. Total energy of the oscillating system is constant.

37. Pendulums and Energy Conservation Energy goes back and forth between K and U. At highest point, all energy is U. As it drops, U goes to K. At the bottom, energy is all K.

38. h Pendulum Energy ½mv max 2 = mgh For minimum and maximum points of swing K 1 + U 1 = K 2 + U 2 For any points 1 and 2.

39. Sample problem What is the speed of the pendulum bob at point B if it is released from rest at point A? 1.5 m A B 40 o

40. A 0.21 kg apple falls from a tree to the ground, 4.0 m below. Ignoring air resistance, determine the apple’s gravitational potential energy and kinetic energy when its height above the ground is 2.0 m.