Chap. 4: Newton s Law of Motion And Chap.5 Applying Newton s Laws (more examples) Force; Newton s 3 Laws; Mass and Weight Free-body Diagram (1D) Free-body Diagram (1D, 2 Bodies) Free-body Diagram (2D) Equilibrium Frictional Force Circular Motion / Rotation 1
Who Wanted Force? F 2
What is Force? y g g an interaction between two objects a push or a pull on an object; either a contact force or a long-range force Push up on an apple by hand; contact force Pull down on an apple by earth; long-range force a vector it has both a magnitude and a direction causes an acceleration on an object 2 g (0)ˆ i ( 9.8 m/s ) ˆj ; 2 g g 9.8 m/s F g (0)ˆ i v v ( mg ) ˆj 4
Newton s 3 Laws Newton s 1 st Law Law of inertia Mass (kg) is a measure of the inertia of a body. Newton s 2 nd Law F a m Dynamical analysis using Free-Body Diagram (FBD) Newton s 3 rd Law Action-reaction pair 5
Structure of Newtonian Mechanics Inertial Reference Frame (Newton s 1 st Law) F = m a (Newton s 2 nd Law) Action-Reaction (Newton s 3 rd Law) Mass (m) Kinematics (r, v, a) The Nature of Force The Nature of Object The Nature of Motion 6
WHAT HAPPEN? 9
Force: Acceleration/Equilibrium Acceleration Kinetic Equations (see Chap. 2 &3) F a 0 0 The force on a hokey puck causes the acceleration If the net force on a hokey puck is zero (equilibrium), the acceleration is zero. 11
Diagram to Understand Forces The force of the starting block on the runner has a vertical component that counteracts her weight and a large horizontal component that accelerate her. Vector Nature (see Chap. 1) 12
Force: Vector The two cases are identical as far as the acceleration of the box is concerned. This demonstrates the VECTOR NATURE of the force. F F F F F R 1 2 3 13
Find the magnitude of F 2 and its direction relative to F 1. F R F F 1 2 F 1300 N 90 o 1300 N Similar to Fig. P4.37 Vector direction x-y coordinates 14
Find the magnitude of F 2 and its direction relative to F 1. x F R F F 1 2 1300 N 90 o 1300 N F Similar to Fig. P4.37 y R R x y F F 1x 1y F F 2x 2 y 0 1300 1300 0?? 15
Find the tensions in each of three chains when the weight of a car engine is W. Fig. 5.3 F R(at Point O) T 1 T 2 T 3 0 Also see Fig. E4.2 17
What is 2 nd Law? a F m a a a x y z F m F m F m x y z 18
F = m a Change in velocity for non-zero F (1) A hockey puck is initially at rest on a flat ice surface. y Top View (2) Then, it receives a horizontal kick in a direction of the red arrow. Impulsive Force F (for a short time interval) v k [Quick Quiz] The motion of the puck right after the kick is: (a) Motion with constant velocity (b) Motion with constant acceleration (c) Motion with constant deceleration (d) None of above x 19
Which of the path 1-5 below would the puck most closely follow after receiving the force? y Top View Impulsive Force F (for a short time interval) 5 4 3 2 1 x v 0 A hockey puck is sliding at constant velocity on a flat ice surface 21
Was: What is the acceleration? v 0x = 28 m/s x x 0 = 55 m v x 2 = v 0x 2 + 2 a x (x x 0 ) 25
m = 1500 kg Was: What is the acceleration? Now: What is the net force? v 0x = 28 m/s F x net? x x 0 = 55 m v x 2 = v 0x 2 + 2 a x (x x 0 ) F x net = m a x 26
m = 1500 kg Was: What is the acceleration? Now: What is the net force? v 0x = 28 m/s F x net? x x 0 = 55 m v 2 v 2 = v 2 x = v 2 0x + 2 a x (x 0x x 0 ) + 2 a x = (x 7.1 x 0 ) m/s 2 SF F net x = m a x x = m a x (1500 kg) x (7.1 m/s 2 ) 27
If you exert a force on a body, the body always exerts a force (the reaction ) back upon you. Figure 4.25 shows an action-reaction pair. A force and its reaction force have the same magnitude but opposite directions. These forces act on different bodies. [Follow Conceptual Example 4.8] What is 3 rd Law?
Which force is greater? From Giancoli 3 rd ed. 29
What is 3 rd Law? (II) Push backward on gas by a rocket Push forward on a rocket by gas Action and reaction forces have the same magnitude but are opposite in direction. 30
[Quick Quiz] A massive truck collides head-on with a small sports car. 1) Which vehicle experiences the greater force of impact? 2) Which vehicle experiences the greater acceleration? 31
A stonemason drags a marble block across a floor by pulling on a rope attached to the block. Why does the block move while the stonemason remains stationary? 34
At rest Force on Box exerted By Rope F B-R =10 N Force on Rope exerted By Person x F R-P =10 N Quick Quiz What is the tension here? 0? 10? 20? Or else? F P-G Assume the rope is massless. 38
Free-Body Diagram Draw only force(s) on the apple y g g v v F g (0)ˆ i ( mg ) ˆj 41
Quick Quiz A hockey puck is sliding at a constant velocity across a flat horizontal ice surface. Which is the correct free-body diagram? [A] 44
Free-Body Diagram (1D) 46
Motion Free-Body Diagram (1D) Find a y y m = 10.0 kg 47
Weight in Elevator Example 5.9 y m = 60 kg F g = mg = 588 N SF y = m a y F N =? a y = 0 a y = 4.9 m/s 2 49
Weight on Planet 53
Motion FBD (1B/1D 2B/1D) y Find a y Find a x Motion 54
Free-Body Diagram (x-axis) e.g., 2 boxes sliding on desk (no friction) Find acceleration and tension. Motion P4.43, P4.54 55
Exercise Find F P and F T P4.43 a x = 2.50 m/s 2 F T F P 1) 1B 2B 2) Now a is given. Then you are asked to find forces. 59
Free-Body Diagram (x-axis) The rope has a mass e.g., 2 boxes sliding on desk (no friction) Find acceleration and tension. F P = 40.0 N 1) Draw F.B.D. identify all forces exerted on box1, rope and box2 separately. 2) Apply Newton s 2 nd law: 60
Free-Body Diagram (y-axis) 65
Example 1: One paint bucket (mass m 1 ) is hanging by a massless cord from another paint bucket (mass m 2 ), also hanging by a massless cord. The two buckets are pulled upward with an acceleration by the upper cord. Draw the free-body diagram for each bucket. Determine the tension on each code if a = 3.00 m/s 2. P4.57 y a a 66
Example 1: One paint bucket (mass m 1 ) is hanging by a massless cord from another paint bucket (mass m 2 ), also hanging by a massless cord. The two buckets are pulled upward with an acceleration by the upper cord. Draw the free-body diagram for each bucket. Determine the tension on each code if a = 3.00 m/s 2. F g2 m 2 F T2 F T1 y a F T1 m 1 a F g1 67
Acceleration? Tension at the midpoint of the rope? P4.54 71
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Free-Body Diagram (2D) e.g., Box sliding on desk (no friction) y Motion x m = 10.0 kg 1) 2) 73
Free-Body Diagram (2D) e.g., Box sliding on desk (no friction) y Motion F P F N x F G 1) Draw F.B.D -identify all forces exerted on the box. 2) Apply Newton s 2 nd law: m a x = F P cos(30.0 o ) m a y (=0) = F P sin(30.0 o ) + F N m g 74
Free-Body Diagram (2D) e.g., Box sliding on desk (no friction) y Motion F P F N x F G 1) Draw F.B.D -identify all forces exerted on the box. 2) Apply Newton s 2 nd law: 10.0 a x = 40.0 cos(30.0 o ) 10.0 (0) = 40.0 sin(30.0 o ) + F N (10.0)(9.80) 75
Free-Body Diagram (2D) e.g., Box sliding on desk (no friction) y Motion F P F N x F G Try E4.4 76
Free-Body Diagrams? Circular Motion