Ballistic Cart Demo Discuss law of cosines for planeinwindb problem Other HW problems?

1. Ballistic Cart Demo Discuss law of cosines for planeinwindb problem Other HW problems?

2. Chapter 4 Forces and Mass

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

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

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

6. Contact and Field Forces

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

8. QCD (Quantum chromodynamics) confines quarksby exchaning gluons Nuclear force: binds protons and neutronsby exchanging pions Strong Nuclear Force

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

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

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

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

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

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

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

16. Weight is magnitude of gravitational force mass weight Weight

17. Mass is an inherent property Weight depends on location Weight vs. Mass

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

19. Newton’s Third Law cont. • F12 is action force F21 is reaction force • You can switch action <-> reaction • Action & reaction forces act on different objects

20. Action-Reaction Pairs

21. Define the OBJECT (free body) • Newton’s Law uses the forces acting ON object • n and Fg act on object • n’ and Fg’ act on other objects

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

23. Identify object (free body) Label all forces acting on object Resolve forces into x- and y-components, using convenient coordinate system Apply equations, keep track of signs! Problem Solving Strategy

24. Strings, ropes and Pulleys Gravity Normal forces Friction Springs (later in the book) Mechanical Forces

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

26. Equilibrium

27. Cable Pull Demo

28. Example 4.1 Given that Mlight = 25 kg, find all three tensions T3 = 245.3 N, T1 = 147.4 N, T2 = 195.7 N

29. Example 4.2 2) Which statements are correct?Assume the objects are static. A) T1 must = T2 B) T2 must = T3 C) T1 must be < Mg D) T1+T2 must be > Mg A) T B) T C) T D) T cos(10o)=0.985 sin(10o)=0.173

30. Example 4.3 a) Find acceleration b) Find T, the tension above the bowling ball c) Find T3, the tension in the rope between the pails d) Find force ceiling must exert on pulley a) a = g/6 = 1.635 m/s2b) T= 57.2 Nc) T3=24.5 Nd) Fpulley=2T = 114.5 N

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

32. Example 4.4 Find the acceleration and the tension a = 4.43 m/s2, T= 53.7 N

33. M Example 4.5 Find M such that the box slides at constant v M=15.6 kg

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

35. Direction parallel to surface, opposite toother forces Nearly independent of the area of contact The coefficient of friction (µ) depends on the surfaces in contact Sliding Friction

36. Coefficients of Friction

37. Static Friction, ƒs • ms is coefficient of static friction • n is the normal force f F

38. Kinetic Friction, ƒk • mk is coefficient of kinetic friction • Friction force opposes F • n is the normal force f F

39. Friction Demo

40. Example 4.6 The man pushes/pulls with a force of 200 N. Thechild 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/s2 / f=29.1 N, a=4.8 m/s2

41. Example 4.7 Given m1 = 10 kg and m2 = 5 kg: a) What value of ms would stop the block from sliding? b) If the box is sliding and mk = 0.2, what is the acceleration? c) What is the tension of the rope? a) ms = 0.5 b) a=1.96 m/s2 c) 39.25 N

42. Example 4.8 What is the minimum ms required to prevent a sled from slipping down a hill of slope 30 degrees? ms = 0.577

43. Other kinds of friction • Air resistance, F ~ Area  v2 • Rolling resistance, F ~ v Terminal velocity:

44. Coffee Filter Demo

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

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

47. Example 4.9 An elevator falls with acceleration a = 8.0 m/s2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read? 36.9 lbs

48. Example 4.10 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/s2:a) At what angle does the ball swing backwards? b) What is the tension in the string? q =17 degT= 25.6 N q