1. Forces and Mass

2. Classical Mechanics does not apply for very tiny objects (< atomic sizes) objects moving near the speed of light

3. Newton’s First Law If the net force  F exerted on an object is zero the object continues in its original state of motion. That is, if  F = 0, an object at rest remains at rest and an object moving with some velocity continues with the same velocity. Contrast with Aristotle!

4. Forces Usually a push or pull Vector Either contact or field force

5. Contact and Field Forces

6. Fundamental (Field) Forces Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity

7. Strong Nuclear Force QCD (Quantum chromodynamics) confines quarks by exchaning gluons Nuclear force: binds protons and neutrons by exchanging pions

8. Electromagnetic Forces Opposites attract, like-signs repel Electric forces bind electrons in atoms Magnetic forces arise from moving charges

9. Weak Nuclear Force Involves exchange of heavy W or Z particle Responsible for decay of neutrons

10. Gravity Attractive force between any two bodies Proportional to both masses Inversely proportional to square of distance

11. Inertia (Newton’s First Law) Tendency of an object to continue in its original motion

12. Mass A measure of the resistance of an object to changes in its motion due to a force Scalar SI units are kg

13. Newton’s Second Law Acceleration is proportional to net force and inversely proportional to mass.

14. Units of Force SI unit is Newton (N) US Customary unit is pound (lb) 1 N = 0.225 lb

15. Weight Weight is magnitude of gravitational force weight mass

16. Weight vs. Mass Mass is inherent property Weight depends on location

17. Newton’s Third Law Single isolated force cannot exist For every action there is an equal and opposite reaction Force on “1” due to “2”

18. Newton’s Third Law cont. F 12 is action force F 21 is reaction force You can switch action reaction Action & reaction forces act on different objects

19. Action-Reaction Pairs

20. Define the OBJECT (free body) Newton’s Law uses the forces acting ON object n and F g act on object n’ and F g ’ act on other objects

21. Assumptions for F=ma Objects behave as particles ignore rotational motion (for now) Consider only forces acting ON object neglect reaction forces

22. Definition of Equilibrium

23. Example A Ford Pinto is parked in a parking lot There is no net force on the Pinto A) True B) False

24. Example A Ford Pinto is parked in a parking lot The contact force acting on the Pinto from the parking lot surface ______________. A) Points upwards B) Is zero C) Points downward

25. Example A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance) The Pinto’s acceleration is __________ A) Less than zero B) Equal to zero C) Greater than zero

26. Example A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance) The force acting on the Pinto from the contact with the highway is vertical. A) True B) False

27. Mechanical Forces Strings, ropes and Pulleys Gravity Normal forces Friction Springs (later)

28. Some Rules for Ropes and Pulleys Force from rope points AWAY from object Magnitude of the force is tension Tension does not change when going over frictionless pulley

29. Example a) Find acceleration b) Find T, the tension above the bowling ball c) Find T 3, the tension in the rope between the pails d) Find force ceiling must exert on pulley a) a = g/6 = 1.635 m/s 2 b) T = 57.2 N c) T 3 =24.5 N d) F pulley =2T = 114.5 N

30. Example 2) Which statements are correct? Assume the objects are static. T 1 is _____ T 2 cos(10 o )=0.985 sin(10 o )=0.173 A) Less than B) Equal to C) Greater than

31. Example 2) Which statements are correct? Assume the objects are static. T 2 is ______ T 3 cos(10 o )=0.985 sin(10 o )=0.173 A) Less than B) Equal to C) Greater than

32. Example 2) Which statements are correct? Assume the objects are static. cos(10 o )=0.985 sin(10 o )=0.173 A) Less than B) Equal to C) Greater than T 1 is _____ Mg

33. Example 2) Which statements are correct? Assume the objects are static. T 1 +T 2 is ______ Mg cos(10 o )=0.985 sin(10 o )=0.173 A) Less than B) Equal to C) Greater than

34. Example Given that M light = 25 kg, find all three tensions T 3 = 245.3 N, T 1 = 147.4 N, T 2 = 195.7 N

35. Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components

36. Example Find the acceleration and the tension a = 4.43 m/s 2, T= 53.7 N

37. Example Find M such that the box slides at constant v M=15.6 kg M

38. Forces of Friction RESISTIVE force between object and neighbors or the medium Examples: Sliding a box Air resistance Rolling resistance

39. Sliding Friction Parallel to surface, opposite to other forces ~ independent of the area of contact Depends on the surfaces in contact

40. Coefficients of Friction

41. Static Friction, ƒ s  s is coefficient of static friction N is the normal force f F

42. Kinetic Friction, ƒ k  k is coefficient of kinetic friction Friction force opposes F n is the normal force F f

43. Example The man pushes/pulls with a force of 200 N. The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0.15. For each case: What is the frictional force opposing his efforts? What is the acceleration of the child? f=59 N, a=3.80 m/s 2 / f=29.1 N, a=4.8 m/s 2

44. Example Given m 1 = 10 kg and m 2 = 5 kg: a) What value of  s would stop the block from sliding? b) If the box is sliding and  k = 0.2, what is the acceleration? c) What is the tension of the rope? a)  s = 0.5 b) a=1.96 m/s 2 c) 39.25 N

45. Example What is the minimum  s required to prevent a sled from slipping down a hill of slope 30 degrees?  s = 0.577

46. Other kinds of friction Air resistance, F ~ Area  v 2 Rolling resistance, F ~ v Terminal velocity:

47. Example An elevator falls with acceleration a = 8.0 m/s 2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read? 36.9 lbs

48. Accelerating Reference Frames Equivalent to “Fictitious” gravitational force

49. Fictitious Force: Derivation Eq. of motion in fixed frame F-ma f looks like force in new frame, ma f acts like fake gravitational force!

50. Example You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards. If M = 2.5 kg and the acceleration, a = 3.0 m/s 2 : a) At what angle does the ball swing backwards? b) What is the tension in the string?  =  17 deg T= 25.6 N 

51. Example A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. In the instant just after the elevator begins to move upward, the reading on the scale will be ______________ 20 lbs. a)Greater than b)Less than c)Equal to

52. Example A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. On the way back down, while descending at constant velocity, the reading on the scale will be ________________ 20 lbs. a)Greater than b)Less than c)Equal to

53. Example A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale. In the instant just before the elevator comes to a stop on the 78th floor, the mass of the fish will be ______________ 9.072 kg. a)Greater than b)Less than c)Equal to