GENERAL PHYSICS (101 PHYS)

Transcription

1 INAYA MEDICAL COLLEGE (IMC) PHYS 101- LECTURE 1 GENERAL PHYSICS (101 PHYS) DR. MOHAMMED MOSTAFA EMAM

2 LECTURES & CLASS ACTIVITIES Password: drmohammedemam DR. MOHAMMED MOSTAFA EMAM 2

3 GENERAL PHYSICS (101 PHYS) PART I

4 PART I Force, Vectors and Newton s law of motion

5 Vocabularies add to notes Force: Push or Pull (strength or energy). DR. MOHAMMED MOSTAFA EMAM 5

6 Newton s Laws of Motion

7 Background Sir Isaac Newton ( ) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. DR. MOHAMMED MOSTAFA EMAM 7

8 A force is simply a push or a pull. All forces have both size and direction. Mass is a measure of the amount of stuff contained in an object; MASS ONLY HAS SIZE AND IT DOES NOT HAS DIRECTION. (add to notes) DR. MOHAMMED MOSTAFA EMAM 8

9 Remember FORCE DR. MOHAMMED MOSTAFA EMAM 9

10 NET FORCES When two or more forces are combined! DR. MOHAMMED MOSTAFA EMAM 10

11 Some tips: 1. Forces in the same direction- add the two forces together. + = 1. Forces in different directions- subtract the two and figure out which direction was the stronger of the two. - = DR. MOHAMMED MOSTAFA EMAM 11

12 Balanced vs. unbalanced forces Unbalanced: when the net force on an object is not zero. These produce a change in motion. Balanced: when the net force on an object equals zero. These do NOT produce change in motion. DR. MOHAMMED MOSTAFA EMAM 12

13 Vectors An Introduction

14 There are two kinds of quantities Scalars are quantities that have magnitude only, such as position speed time mass Vectors are quantities that have both magnitude and direction, such as displacement velocity acceleration DR. MOHAMMED MOSTAFA EMAM 14

15 Notating vectors This is how you notate a vector R R This is how you draw a vector R head tail DR. MOHAMMED MOSTAFA EMAM 15

16 Direction of Vectors Vector direction is the direction of the arrow, given by an angle. This vector has an angle that is between 0 o and 90 o. A x DR. MOHAMMED MOSTAFA EMAM 16

17 Vector angle ranges Quadrant 2 90 o < < 180 o Quadrant o < < 270 o y Quadrant 1 0 < < 90 o x Quadrant o < < 360 o DR. MOHAMMED MOSTAFA EMAM 17

18 Direction of Vectors What angle range would vector B have? What would be the exact angle, and how would you determine it? Between 180 o and 270 o x or Between -90 o and -180 o BDR. MOHAMMED MOSTAFA EMAM 18

19 Magnitude of Vectors The best way to determine the magnitude (or size) of a vector is to measure its length. The length of the vector is proportional to the magnitude (or size) of the quantity it represents. DR. MOHAMMED MOSTAFA EMAM 19

20 Sample Problem If vector A represents a displacement of three miles to the north, then what does vector B represent? Vector C? B A C DR. MOHAMMED MOSTAFA EMAM 20

21 Equal Vectors Equal vectors have the same length and direction, and represent the same quantity (such as force or velocity). Draw several equal vectors. DR. MOHAMMED MOSTAFA EMAM 21

22 Inverse Vectors Inverse vectors have the same length, but opposite direction. Draw a set of inverse vectors. A -A DR. MOHAMMED MOSTAFA EMAM 22

23 Graphical Addition and Subtraction of Vectors II

24 Graphical Addition of Vectors 1) Add vectors A and B graphically by drawing them together in a head to tail arrangement. 2) Draw vector A first, and then draw vector B such that its tail is on the head of vector A. 3) Then draw the sum, or resultant vector, by drawing a vector from the tail of A to the head of B. 4) Measure the magnitude and direction of the resultant vector. DR. MOHAMMED MOSTAFA EMAM 24

25 Practice Graphical Addition B B A R A + B = R R is called the resultant vector! DR. MOHAMMED MOSTAFA EMAM 25

26 The Resultant and the Equilibrant The sum of two or more vectors is called the resultant vector. The resultant vector can replace the vectors from which it is derived. The resultant is completely canceled out by adding it to its inverse, which is called the equilibrant. DR. MOHAMMED MOSTAFA EMAM 26

27 The Equilibrant Vector B A -R R A + B = The vector -R is called the equilibrant. If you add R and -R you get a null (or zero) vector. R DR. MOHAMMED MOSTAFA EMAM 27

28 Addition of Vectors Graphical Methods The parallelogram method may also be used; here again the vectors must be tail-to-tip. DR. MOHAMMED MOSTAFA EMAM 28

29 Graphical Subtraction of Vectors 1) Subtract vectors A and B graphically by adding vector A with the inverse of vector B (-B). 2) First draw vector A, then draw -B such that its tail is on the head of vector A. 3) The difference is the vector drawn from the tail of vector A to the head of -B. DR. MOHAMMED MOSTAFA EMAM 29

30 Practice Graphical Subtraction -B B C A A - B = C DR. MOHAMMED MOSTAFA EMAM 30

31 3-2 Addition of Vectors Graphical Methods For vectors in one dimension, simple addition and subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates. DR. MOHAMMED MOSTAFA EMAM 31

32 H.W. A man walks at40 meters East and 30 meters North. Find the magnitude of resultant displacement and its vector angle. Use Graphical Method. DR. MOHAMMED MOSTAFA EMAM 32

33 Practice Problem You are driving up a long inclined road. After 1.5 miles you notice that signs along the roadside indicate that your elevation has increased by 520 feet. a) What is the angle of the road above the horizontal? b) How far do you have to drive to gain an additional 150 feet of elevation? DR. MOHAMMED MOSTAFA EMAM 33

34 Practice Problem Find the x- and y-components of the following vectors a) R = 175 meters, = 95 o b) v = 25 m/s, = -78 o c) a = 2.23 m/s 2, = 150 o DR. MOHAMMED MOSTAFA EMAM 34

35 Practice Problem Vector A points in the +x direction and has a magnitude of 75 m. Vector B has a magnitude of 30 m and has a direction of 30 o relative to the x axis. Vector C has a magnitude of 50 m and points in a direction of -60 o relative to the x axis. a) Find magnitude and direction of A + B b) Find magnitude and direction of A + B + C c) Find magnitude and direction of A B. DR. MOHAMMED MOSTAFA EMAM 35

36 Component Addition of Vectors 1) Resolve each vector into its x- and y- components. A x = Acos B x = Bcos A y = Asin B y = Bsin C x = Ccos C y = Csin etc. 2) Add the x-components (A x, B x, etc.) together to get R x and the y-components (A y, B y, etc.) to get R y. DR. MOHAMMED MOSTAFA EMAM 36

37 Component Addition of Vectors 3) Calculate the magnitude of the resultant with the Pythagorean Theorem (R = R x 2 + R y2 ). 4) Determine the angle with the equation = tan -1 R y /R x. DR. MOHAMMED MOSTAFA EMAM 37

38 Practice Problems In a daily prowl through the neighborhood, a cat makes a displacement of 120 m due north, followed by a displacement of 72 m due west. Find the magnitude and displacement required if the cat is to return home. If the cat in the previous problem takes 45 minutes to complete the first displacement and 17 minutes to complete the second displacement, what is the magnitude and direction of its average velocity during this 62-minute period of time? DR. MOHAMMED MOSTAFA EMAM 38

39 Sample problems A surveyor stands on a riverbank directly across the river from a tree on the opposite bank. She then walks 100 m downstream, and determines that the angle from her new position to the tree on the opposite bank is 50 o. How wide is the river, and how far is she from the tree in her new location? You are standing at the very top of a tower and notice that in order to see a manhole cover on the ground 50 meters from the base of the tower, you must look down at an angle 75 o below the horizontal. If you are 1.80 m tall, how high is the tower? DR. MOHAMMED MOSTAFA EMAM 39

40 WRITE DOWN THESE STATMENTS A quantity with magnitude and direction is a vector. A quantity with magnitude but no direction is a scalar. Vector addition can be done either graphically or using components. The sum is called the resultant vector. Projectile motion is the motion of an object near the Earth s surface under the influence of gravity. DR. MOHAMMED MOSTAFA EMAM 40