1. W ORK AND E NERGY Scalars are back

2. R EVIEW Equations for Motion Along One Dimension

3. R EVIEW Motion Equations for Constant Acceleration 1. 2. 3. 4.

4. R EVIEW 3 Laws of Motion If in Equilibrium If not in equilibrium Change in Motion is Due to Force Force causes a change in acceleration

5. S PRINGS AND OTHER PROBLEMS Force exerted by a spring is dependent on amount of deformity of the spring Amount of force applied changes continuously over time What is the velocity of an object launched from the spring?

6. W ORK Work done on an object by all forces is equal to the change in kinetic energy of the object. This definition is valid even if the force is not constant

7. W ORK – C ONSTANT F ORCE When a force, F, is doing work on an object, the object will move and be displaced. The work done, by the force, F, is defined as Where d is the objects displacement

8. W ORK – C ONSTANT F ORCE We are only interested in the component of the force that is parallel to the direction of motion

9. W ORK – C ONSTANT F ORCE We are only interested in the component of the force that is parallel to the direction of motion or

10. J OULE Work done by 1N of force to move an object 1 meter in the same direction

11. J AMES P RESCOTT J OULE December 24, 1818- October 11, 1889 The mechanical equivalent of heat 838 ft.lbf of work to raise temperature of 1 lb of water by 1 degree farenheit Led to the theory of conservation of energy Helped Lord Kelvin develop the absolute scale of temperature

12. W ORK – Z ERO, N EGATIVE, P OSITIVE When defining work done, its always important to specify which force is acting on what object Work done by man Work done by gravity Work done by barbell

13. T OTAL W ORK Compute work done by forces individually Then just add to get total work done on the object Note: work is scalar

14. E XAMPLE Farmer hitches a tractor with firewood and pulls it a distance 20m on level ground. Total weight of the sled and wood is 14700N and the tractor pulls with a constant force of 5000N at an angle 36.9 o above the horizontal. There is a 3500N friction force opposing the motion. Find the work done by each of the forces and the total work done by all forces.

15. E XAMPLE

16. W ORK DONE BY NON - CONSTANT FORCE Requires the use of integrals

17. E NERGY Energy is a hard to define concept Simplified definition The ability of a physical system to do work on another physical system Many types of energy- these are much easier to define

18. K INETIC E NERGY Energy of motion When work is done to an object the object moves It also affects an objects speed W>0 – object speeds up W<0 – object slows down W=0 – no effect

19. K INETIC E NERGY Newton’s 2 nd Law

20. K INETIC E NERGY

21. Work done is the change in kinetic energy of an object This is translational kinetic energy

22. W ORK – E NERGY T HEOREM Assuming mass is constant Unit of work is Joules Unit of energy is also Joules Note: Energy is also scalar

23. E XAMPLE Farmer hitches a tractor with firewood and pulls it a distance 20m on level ground. Total weight of the sled and wood is 14700N and the tractor pulls with a constant force of 5000N at an angle 36.9 o above the horizontal. There is a 3500N friction force opposing the motion. Suppose it’s initial speed is 2.0 m/s, what is its final speed after travelling 20m.

24. E XAMPLE

25. A 15kg block is placed on a 40 o incline and allowed to slide for 5m. What is it’s final speed?

26. P OTENTIAL E NERGY Energy due to a body’s configuration or surroundings. Many different types Springs Electrical Gravitational

27. G RAVITATIONAL P OTENTIAL An object held in the air has the “potential” to do work once released. Assume object at some height After travelling some distance y

28. G RAVITATIONAL P OTENTIAL An object held in the air has the “potential” to do work once released. KE after travelling some distance y

29. G RAVITATIONAL P OTENTIAL An object held in the air has the “potential” to do work once released. Amount of potential work

30. G RAVITATIONAL P OTENTIAL An object held in the air has the “potential” to do work once released. Note: choose your origin and be consistent

31. E XAMPLE - G IANCOLI 6-28 By how much does the gravitational potential energy of a 64-kg pole vaulter change if his center of mass rises 4.0m?

32. E XAMPLE - G IANCOLI 6-28 By how much does the gravitational potential energy of a 64-kg pole vaulter change if his center of mass rises 4.0m?

33. W ORK D ONE E XAMPLE What is work done to lift a block by 5 m? If a 40 o was used?

34. C ONSERVATIVE AND N ON - CONSERVATIVE FORCE Conservative Force Work Done is independent of the path taken Gravity Elastic Electric You can “store” energy in these types of systems by doing work on the system Non Conservative Force Work done depends on the path taken Friction Air resistance Tension Push-Pull from a person Cannot define potential energy for these types of forces

35. C ONSERVATION OF M ECHANICAL E NERGY If only gravity is acting on the object Valid for all conservative forces If only conservative forces are acting, the total mechanical energy of a system neither increase nor decrease in any process. It stays constant- it is conserved.

36. C ONSERVATION OF M ECHANICAL E NERGY If a non-conservative force is acting on the object Most common non- conservative energy is friction

37. E XAMPLE – F ROM OUR 2 ND LECTURE A motorcycle stuntman rides over a cliff. Just at the cliff edge his velocity is completely horizontal with magnitude 9.0 m/s. Find the motorcycles speed after 0.50s.

38. L IST THE GIVEN Origin is cliff edge a=-g=-9.80m/s 2 At time t=0s At time t=0.50s

39. S PLIT INTO COMPONENTS

40. C ALCULATE COMPONENTS INDEPENDENTLY

41. C ALCULATE VELOCITY

42. N OT NEEDED 29 o below the horizontal

43. A LTERNATE S OLUTION

46. P ROBLEM – Y OUNG AND F REEDMAN 7.14 A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swung so that it makes a maximum angle of 45 o with the vertical. (a) What is the speed of the rock when it passes the vertical position? (b) What is the tension in the string when it makes an angle 45 o with the vertical? (c) What is the tension in the string when it passes through the vertical?

47. P ROBLEM – S ERWAY 7.33 A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100N parallel to the incline, which makes an angle of 20 o with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.00m. (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate-incline system due to friction. (c) How much work is done by the 100N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5m?

48. O THER TYPES OF POTENTIAL ENERGY Elastic Potential For Ideal Springs If a spring is to be stretched a certain distance x Where k is the spring constant (the spring’s stiffness) It’s me again

49. P OTENTIAL E NERGY OF S PRINGS Restoring Force Hooke’s Law – valid for small x

50. P OTENTIAL E NERGY OF S PRINGS Work done ON the spring (from equilibrium) NO Force is not constant We can still use average force Luckily F varies linearly with x

51. P OTENTIAL E NERGY OF S PRINGS Work done ON the spring (from equilibrium) Where U is the elastic potential

52. C ONSERVATION OF M ECHANICAL E NERGY E XPANDED Conservative With Non conservative

53. Y OUNG AND F REEDMAN 7.20 A 1.20kg piece of cheese was placed on a vertical spring of negligible mass and force constant k=1800 N/m that is compressed 15.0 cm. When the spring is released how high does the cheese rise from its original position?

54. P OWER Rate at which work is done SI unit is called the Watt = 1J/s Horsepower = 550ftlb/s = 746W

55. P OWER Rate at which work is done Efficiency

56. E XAMPLE G IANCOLI 6-58 How long will it take a 1750W motor to lift a 315 kg piano to a sixth story window 16.0m above?

57. E XAMPLE G IANCOLI 6-58 How long will it take a 1750W motor to lift a 315 kg piano to a sixth story window 16.0m above?

58. P ROBLEM S ERWAY 7.40 A 650 kg elevator starts from rest. It moves upward for 3s with constant acceleration until it reaches its cruising speed of 1.75m/s. (a) What is the average power of the elevator motor during this period? (b) How does this compare when the elevator moves at cruising speed?

59. Y OUNG AND F REEDMAN – 7.42 A 2.00 kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 37.0 o. (a) what is the speed of the block on the horizontal surface after leaving the spring? (b) How far up the slope does the block travel before starting to slide back down?

60. G IANCOLI 6-56 A 280 g wood block is firmly attached to the end of a horizontal spring. The block can slide along the table with a coefficient of friction of 0.30. A force of 22 N compresses the string 18 cm. if the spring is released, how far from the equilibrium position will it stretch at its first maximum extension.

61. G ROUP W ORK A 1500 kg rocket is to be launched with an initial upward speed of 50.0 m/s. In order to assist the engines, the engineers will start it from rest on a ramp that rises 53 o above the horizontal. The engines provide a constant forward thrust of 2000N and the coefficient of kinetic friction with the ramp is 0.05. At what height should the rocket start?