Understanding Fundamental Forces in Classical Mechanics

1. Chapter 4 Forces and Mass

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

3. Newton’s First Law • If the net force SF exerted on an object is zerok 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!

4. Forces • Usually think of a force as a push or pull • Vector quantity • May be contact or field force

5. Contact and Field Forces

6. Fundamental Forces • Types • Strong nuclear force • Electromagnetic force • Weak nuclear force • Gravity • Characteristics • All field forces • Listed in order of decreasing strength • Only gravity and electromagnetic in mechanics

7. Fundamental Forces • Types • Strong nuclear force • Electromagnetic force • Weak nuclear force • Gravity • Characteristics • All field forces • Listed in order of decreasing strength • Only gravity and electromagnetic in mechanics

8. Strong Nuclear Force • QCD (Quantum chromodynamics) confines quarks to interior of protons and neutrons • Force between protons and neutrons responsible for formation of nuclei • QCD: Exchange of gluons • Nuclear Force: Exchange of pions

9. Electromagnetic Force • Opposites attract, like-signs repel • Electric force responsible for binding of electrons to atoms and atoms to each other • Magnetic forces arise from moving charges and currents • Electric motors exploit magnetic forces

10. Electromagnetic Force • Opposites attract, like-signs repel • Electric force responsible for binding of electrons to atoms and atoms to each other • Magnetic forces arise from moving charges and currents • Electric motors exploit magnetic forces

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

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

13. Inertia • Tendency of an object to continue in its original motion

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

15. Newton’s Second Law • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. • F and a are both vectors

16. Units of Force • SI unit of force is a Newton (N) • US Customary unit of force is a pound (lb) • 1 N = 0.225 lb • See table 4.1

17. Weight • The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object

18. Weight and Mass • Mass is an inherent property • Weight is not an inherent property of an object • Weight depends on location

19. Newton’s Third Law • If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1. • Equivalent to saying a single isolated force cannot exist • For every action there is an equal and opposite reaction

20. Newton’s Third Law cont. • F12 may be called the action force and F21 the reaction force • Either force can be the action or the reaction force • The action and reaction forces act on different objects

21. Some Action-Reaction Pairs • n and n’ • n is the normal force, the force the table exerts on the TV • n is always perpendicular to the surface • n’ is the reaction – the TV on the table • n = - n’

22. More Action-Reaction pairs • Fg and Fg’ • Fg is the force the Earth exerts on the object • Fg’ is the force the object exerts on the earth • Fg = -Fg’

23. Forces Acting on an Object • Newton’s Law uses the forces acting on an object • n and Fg are acting on the object • n’ and Fg’ are acting on other objects

24. Applying Newton’s Laws • Assumptions • Objects behave as particles • ignore rotational motion (for now) • Masses of strings or ropes are negligible • Interested only in the forces acting on the object • neglect reaction forces

25. Problem Solving Strategy • Make a free-body diagram • 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!

26. Examples of Mechanical Forces • Strings, ropes and Pulleys • Gravity • Normal forces • Friction • Springs (later in the book)

27. Some Rules for Ropes and Pulleys • When a rope is attached to an object, the force of the rope on that object is away from that object • The magnitude of the force is called the tension • The tension does not change when going over a pulley (if frictionless)

28. Equilibrium • An object either at rest or moving with a constant velocity is said to be in equilibrium • The net force acting on the object is zero

29. Do Cable Pull Demo

30. Example Given that Mlight = 25 kg, find all three tensions T3 = 245.3, T1 = 147.6 kg, T2 = 195.9 kg

31. Example a) Find acceleration b) Find T c) Find T3 d) Find force ceiling must exert on pulley a) a=g/6, b) T= 57.2 Nc) T3=24.5 N, d) Fpulley=2T = 114.5 N

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

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

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

35. Sliding Friction • Proportional to the normal force • Direction is parallel to surface and opposite other forces • Force of friction is nearly independent of the area of contact • The coefficient of friction (µ) depends on the surfaces in contact

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. Example 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=4.7 m/s2 / f=29.1 N, a=5.7 m/s2

40. Example 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? ms = 0.5, a=1.96 m/s2

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

42. 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/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

43. Quiz, All Sections 1) What is your section number?

44. Quiz, Section 1 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 only • A and B only • A, B and C only • All statements • None of the statements cos(10o)=0.985 sin(10o)=0.173

45. Quiz, Section 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 only • A and B only • A, B and C only • All statements • None of the statements cos(10o)=0.985 sin(10o)=0.173

46. Quiz, Section 3 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 only • A and B only • A, B and C only • All statements • None of the statements cos(10o)=0.985 sin(10o)=0.173