PHYSICS 149: Lecture 4

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1 PHYSICS 149: Lecture 4 Chapter Inertia and Equilibrium: Newton s First Law of Motion 2.4 Vector Addition Using Components 2.5 Newton s Third Law 1

2 Net Force The net force is the vector sum of all the forces acting on an object. = 10 N East = 10 N West = 10 N East = 12 N West If the book is at rest, it will continue to stay at rest because F net =0 (translational equilibrium). If the book is at rest, it will start moving toward the west since F 2 > F 1 (F net 0). 2

3 Equilibrium When an object is in equilibrium (either at rest or moving with constant velocity), the net force acting on it zero. A vector can only have zero magnitude if all of its components are zero. Nonzero Net Force If the net force on an object is not zero, it is not in equilibrium (that is, a change in velocity will occur), and thus Newton s Second Law must be used to determine its motion. 3

4 Vectors Two vectors A and B are equal if they have the same magnitude and direction, whether or not they have the same initial points. A B A = B A vector having the same magnitude as A but in the opposite direction to A is denoted by A. A -A Note that A - A = A + (-A) = 0 4

5 Vector Components Note that A x and A y are scalars. 5

6 Adding Vectors in 2-D (a) Draw an arrow to represent one of the vectors. (b) Draw the second vector with placing its tail at the tip of the first vector. (c) Draw an arrow starting from the tail of the first and ending at the tip of the second. The new arrow is the vector sum. Note: it does not matter in what order vectors are added F 1 + F 2 = F 2 + F 1 6

7 Vector Addition Using Components D = A + B + C if and only if D x = A x + B x + C x D y = A y + B y + C y Adding x-components of vectors gives the x- component of the vector sum. Adding y-components of vectors gives the y- component of the vector sum. 7

8 Example Two forces A and B of magnitudes A = 3 N and B = 5 N are applied to an object at the origin. We want to find the total force. First, we have to calculate the components of A: B A A) (3cos45, 3sin60 ) N B) (5cos45, 5sin45 ) N C) (3cos45, 3sin45 ) N D) (3cos45, 3sin45 ) N E) ( 3cos45, 3sin45 ) N 8

9 Example Two forces A and B of magnitudes A = 3 N and B = 5 N are applied to an object at the origin. We want to find the total force. The components of B are: B A) ( 5cos60, 5sin60 ) N B) ( 5cos60, 3sin60 ) N A C) (5cos60, 5sin60 ) N D) (5cos60, 5sin60 ) N E) ( 3cos60, 5sin60 ) N 9

10 Example We now found A = (2.12 N, 2.12 N) and B = ( 2.5 N, 4.33 N). The components of the total force A+B are: B A A) ( 0.38, 6.45) N B) ( 4.62, 6.45) N C) ( 0.38, 2.21) N D) ( 4.62, 2.21) N E) ( 0.38, -2.21) N 10

11 Example We now found A + B = ( 0.38 N, 2.21 N) The magnitude is A+B The angle θ is given by θ = tan /0.38 θ 11

12 Vector Subtraction A B = A + ( B) Thus, A B is equivalent to adding A and B. (Note that B is a vector having the same magnitude as B but in the opposite direction to B.) 12

13 Example Vector A in the figure is equal to: (A) B - D (B) B + C (C) C + D + E (D) (D - C)/2 (E) D + C 13

14 Example Vector D in the figure is equal to: (A) A + B (B) C + A (C) C A 14

15 Example Vector E in the figure is equal to: (A) 2(B+C) (B) (C+D) (C) 2A (D) (A+B+C) (E) All of these choices C C+D 15

16 Newton s Laws of Motion 1. An object at rest remains at rest and an object in motion remains in motion unless acted upon by an unbalanced force (law of Inertia) 2. An unbalanced force is equal to the rate of change of momentum ( F = ma ) 3. For every action, there is an equal and opposite reaction. Isaac Newton ( ) Humans could explain/understand the most complex phenomena with only 3 assumptions. 16

17 Newton s First Law of Motion An object s velocity (a vector) does not change if and only if the net force acting on the object is zero. In other words, if there is no net force on an object, its speed and direction of motion do not change (including if it is at rest). Also called the law of inertia. Inertia means resistance to changes in velocity. Example: the start or stop of a car s motion, dusts on clothes, a quarter on top of an index card on a cup. Note that circular motion is NOT a constant motion, that is, net force is not zero. Why? 17

18 Galileo s Experiment Galileo postulated that, if he could eliminate all resistive forces, a ball rolling on a horizontal surface would never stop. h 1 = h 2 h 1 = h 2 Newton was influenced by some of his predecessors including Galileo. 18

19 ILQ 1 The net force on a moving object suddenly becomes zero. The object then: A) Stops abruptly B) Stops during a short time interval C) Changes direction D) Continues at constant velocity E) Slows down gradually 19

20 ILQ 2 Is it possible for an object to be in motion and yet have zero net force acting on it? A) YES B) NO 20

21 Second Law This is a vector relation. The direction of the net force is the same as the direction of the acceleration. Example in one dimension: Sum of forces: 2 N 21

22 Third Law All forces come in pairs Third law forces involve TWO OBJECTS. The two forces are: the force object one exerts on object two the force object two exerts on object one Three ways to state the 3rd law: Forces on each other are equal and opposite For every action there is an equal and opposite reaction You can t push on something without it pushing back on you 22

23 Newton s Third Law of Motion In an interaction between two objects, each object exerts a force on the other. These two forces are equal in magnitude and opposite in direction. To every action, there is always opposed an equal reaction. Forces always come in equal but opposite actionreaction pair. Note that these two forces act on different objects; they do not cancel in any way. Don t forget that forces always exist in pairs. 23

24 Free-Body Diagram (FBD) A simplified sketch of a single object with force vectors drawn to represent every force acting on that object. (It must not include any forces that act on other objects.) FBD is useful to find the net force acting on an object. 24

25 ILQ A book is sitting on a desk top. Identify the 3rd law partner of the weight of the book. A) The force of the desk on the book. B) The force of the book on the desk. C) The force of the earth on the book. D) The force of the book on the earth. 25

26 Why Doesn t the Book Move? Free-Body Diagram Pair Forces acting on book -N -W Pair FBD includes all forces acting on the book only. The book does not move because N + W = 0. 26

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