These are our class notes from Chapter 4 of Cutnell and Johnson's Physics

1. Newtons’s Laws Chapters 4&5

2. Learning Objectives

3. Table Of Contents

4. Chapter 4: Forces and Newton’s Laws of Motion Section 1: Concepts of Force and Mass

10. Chapter 4: Forces and Newton’s Laws of Motion Section 2: Newton’s First Law of Motion

14. Net Forces Individual Forces Net Force 3 N 4 N 5 N

21. Chapter 4: Forces and Newton’s Laws of Motion Section 3: Newton’s Second Law of Motion

23. SI Unit of Force SI Unit for Force This combination of units is called a newton (N).

27. Comparison of units

28. So, what’s all this mean? A man stands on a scale inside a stationary elevator. Forces acting on the man Reading on scale N mg

29. And then… When Moving Upward With Constant Velocity Forces acting on the man Reading on scale N mg v

30. And then… When Moving Upward With Constant Acceleration Forces acting on the man Reading on scale N mg a

31. And then… a When Moving Downward With Constant Acceleration Forces acting on the man Reading on scale N mg

32. Chapter 4: Forces and Newton’s Laws of Motion Section 4: The Vector Nature of Newton's Second Law of Motion

36. Chapter 4: Forces and Newton’s Laws of Motion Section 5: Newton’s 3 rd Law of Motion

43. Chapter 4: Forces and Newton’s Laws of Motion Section 6: Types of Forces: An Overview

45. Natural Forces Types Range Gravitational Unlimited Electromagnetic Unlimited Weak Nuclear  10  12 m Strong Nuclear  10  15 m Size 10 0 10 6 10 20 10 35

46. Chapter 4: Forces and Newton’s Laws of Motion Section 7: The Gravitational Force

49. Relation Between Mass and Weight

50. On the earth’s surface

54. Chapter 4: Forces and Newton’s Laws of Motion Section 8: The Normal Force

59. Apparent Weight apparent weight true weight

61. Question #17 4.8.3. Consider the three cases shown in the drawing in which the same force is applied to a box of mass M . In which case(s) will the magnitude of the normal force on the box equal ( F sin  + Mg) ? a) Case One only b) Case Two only c) Case Three only d) Cases One and Two only e) Cases Two and Three only

62. Question #18 Consider the situation shown in the drawing. Block A has a mass 1.0 kg and block B has a mass 3.0 kg. The two blocks are connected by a very light rope of negligible mass that passes over a pulley as shown. The coefficient of kinetic friction for the blocks on the ramp is 0.33. The ramp is angled at  = 45  . At time t = 0 s, block A is released with an initial speed of 6.0 m/s. What is the tension in the rope? a) 11.8 N b) 7.88 N c) 15.8 N d) 13.6 N e) 9.80 N

63. Chapter 4: Forces and Newton’s Laws of Motion Section 9: Static and Kinetic Friction Forces

71. Question #20 Three pine blocks, each with identical mass, are sitting on a rough surface as shown. If the same horizontal force is applied to each block, which one of the following statements is false? a) The coefficient of kinetic friction is the same for all three blocks. b) The magnitude of the force of kinetic friction is greater for block 3. c) The normal force exerted by the surface is the same for all three blocks. d) Block 3 has the greatest apparent area in contact with the surface. e) If the horizontal force is the minimum to start block 1 moving, then that same force could be used to start block 2 or block 3 moving.

73. Chapter 4: Forces and Newton’s Laws of Motion Section 10: The Tension Force

78. Chapter 4: Forces and Newton’s Laws of Motion Section 11: Equilibrium Applications of Newton’s Laws of Motion

82. Solution:

84. Question #26 A block of mass M is hung by ropes as shown. The system is in equilibrium. The point O represents the knot, the junction of the three ropes. Which of the following statements is true concerning the magnitudes of the three forces in equilibrium? a) F 1 + F 2 = F 3 b) F 1 = F 2 = 0.5× F 3 c) F 1 = F 2 = F 3 d) F 1 > F 3 e) F 2 < F 3

85. Question #27 A team of dogs pulls a sled of mass 2 m with a force . A second sled of mass m is attached by a rope and pulled behind the first sled. The tension in the rope is . Assuming frictional forces are too small to consider, determine the ratio of the magnitudes of the forces and , that is, P/T . a) 3 b) 2 c) 1 d) 0.5 e) 0.33

86. Chapter 4: Forces and Newton’s Laws of Motion Section 12: Non-equilibrium Applications of Newton’s Laws of Motion

89. The acceleration is along the x axis so

90. y component x component Force

93. Question #28 F v o = 0 m  t = 5 s v = ? F = 20 N m = 5 kg A constant force F acts on a block of mass m . which is initially at rest. Find the velocity of the block after time  t .