Significant Figures & Vectors

Size: px
Start display at page:

Download "Significant Figures & Vectors"

Transcription

1 You have to complete this reading Booklet before you attempt the Substantive Assignment. Significant Figures Significant Figures & Vectors There are two kinds of numbers in the world Exact: o Example: There are exactly 12 eggs in a dozen. o example: Most people have exactly 10 fingers and 10 toes. Inexact numbers: o Example: any measurement. If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be mm (4 significant figures). Precision versus Accuracy Accuracy refers to how closely a measured value agrees with the correct value. Precision refers to how closely individual measurements agree with each other. accurate (the average is accurate) not precise precise not accurate accurate and precise In any measurement, the number of significant figures is critical. The number of significant figures is the number of digits believed to be correct by the person doing the measuring. It includes one estimated digit. 1

2 How can we determine how many significant numbers a measurement has? The following rules apply to determining the number of significant figures in a measured quantity: 1. All nonzero digits are significant. 457 cm (three significant figures) 0.25 g (two significant figures). 2. Zeros between nonzero digits (Captive Zeros) are significant kg (four significant figures) 1.03 cm (three significant figures).. 3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point g (one significant figure) cm (two significant figures). 4. When a number ends in zeros that are to the right of the decimal point, they are significant g (three significant figures) 3.0 cm (two significant figures). 5. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant. 130 cm (two or three significant figures) 10,300 g (three, four, or five significant figures) Use of standard exponential notation avoids the potential ambiguity of whether the zeros at the end of a number are significant. For example, a mass of 10,300 g can be written in exponential notation showing three, four, or five significant figures: 1.03 x 10 4 g (three significant figures) x 10 4 g (four significant figures) x 10 4 g (five significant figures) In these numbers all the zeros to the right of the decimal point are significant (rules 2 and 4). 2

3 Rule for Multiplication and Division In multiplication and division, the result must be reported as having no more significant figures than the measurement with the fewest significant figures. Example 1 Multiply 3.22 cm by 2.1 cm. Solution: 3.22 cm 2.1 cm cm 2 The less precise factor, 2.1 cm, contains two significant digits. Therefore the product has only two significant digits. The answer is then best stated as 6.8 cm 2. Example 2 Divide 36.5 m by s. Solution: 36.5 m s m/s The less precise factor, 36.5 m, contains three significant digits. Therefore the division has only three significant digits. The answer is then best stated as 10.7 m/s. 3

4 Rule for Addition and Subtraction In addition and subtraction, the result must be reported to the same number of decimal places as that of the term with the least number of decimal places. Example 1 Add m m m Solution: m m 3.21 m m =30.24 m Note that 3.21 m is the least precise measurement. Therefore round off the result to the nearest hundredth on one meter and the answer is best stated as m. You will follow the same rule for subtraction. Rounding Rules 1. Look at the leftmost digit to be removed. If less than 5: truncate (preceding number is unchanged) If 5 or greater: increase by 1(round up) 2. When a calculation involves two or more steps, retain at least two additional digits beyond the correct number of significant figures for intermediate calculations. Round off to the correct number of significant figures only for the answer you want to report (which is usually the final answer). This helps to avoid accumulated round-off error. 4

5 Scalars and Vectors If you add 5 L of water to another 5 L of water, you end up with 10 L of water. Similarly, if you add 5 kg of salt to 5 kg of salt, you will have 10 kg of salt. Volumes and masses are added by the rules of ordinary arithmetic. Volume and mass are scalar quantities. Scalar quantities have magnitude (size) only. Other scalar quantities with which you may be familiar are: length, energy, density and temperature. If you add a 5 N force to another 5 N force, the two forces together may add up to 10 N, but they may also add up to 0 N or to any value between 0 N and 10 N! This is because forces have direction as well as magnitude. Quantities that have direction as well as magnitude are called vector quantities. Forces and other vector quantities must be added by the special rules of vector addition, which take into account direction as well as magnitude. In addition to forces, other vector quantities you will encounter in this course include: velocity, displacement, acceleration, momentum, electrical field strength a n d magnetic field strength. When you describe any velocity, displacement, acceleration, force, momentum or other vector quantity, you must specify both magnitude and direction! Adding Vectors Figure 1.1 In In figure Figure1.1, 1.1. an an object object is is hanging hanging from from a spring a spring balance. Two forces pull on the object. The The earth exetsrt exerts a 10 a 10N N force force of gravity of gravity downward downward on it, on and it, thhe and spring the spring baalance balance exerts a exert 10 N the force same up on size it. force Both on the the earth object. and the The spring net force bala nce on the exert object the ssame is not size 10N offorce or 20N on as thee one object. might The expect. net force on the objecist not 10 N or 20 N as one might expect. It is, in It is, in fact 0N! fact, 0 N! To understand why the resultant force is zero in this To understand why the netor resultant force is zero situation, you must know (a) what is vector and (b) how in this siutuation, you must know (a) what a vector is and vectors (b) how are vectors added. are added d. To draw a vector you must construct a line segment whose length is proportional to the magnitude of the quantity being represented (in this case, a force). See Figure 1.2. You draw a segment in the direction the quantity is acting, and place an arrow tip on the line segment to show its proper direction. The line segment, drawn to an appropriate scale complete with arrow tip, is a vector. 5

6 Figure 1.2 Figure 1.2 shows how the two forces in Figure 1.1 can be represented with vectors. Figure 1.2 (a) shows vectors representing the upward force F 1 exerted by the spring balance and the downward gravitational force F 2 individually, while Figure 1.2(b) shows the two forces added together by vector addition. Note! There are two ways to indicate that a quantity is a vector quantity. In diagrams, or in hand-written notes, a small arrow may be drawn above the symbol for the quantity. For example, F indicates that a force vector is being discussed. In a textbook like this the symbol for a vector quantity may be typed in bold italics, like this: F. This symbol also indicates that a force vector is being discussed. If only the magnitude of a vector is of importance, the symbol F (italics, but not bold) will be used. To add vector F 1 to vector F 2, draw vector F 1 first, to scale and in the proper direction. Then draw vector F 2 so that its tail begins at the tip of vector F 1 and the line segment of F 2 points in the proper direction. Be sure to draw the tip of an arrow to show which way F 2 points. The net or resultant force is the vector going from the tail of F 1 to the tip of F 2. In Figure 1.2, the resultant is clearly zero. When two or more forces acting on a body have a resultant of zero, the body is said to be in equilibrium. Sometimes a force like F 2, which balances one or more other forces and creates a condition where there is no net force, is called the equilibrant. In Figure 1.3, a 10 N object is suspended by strings connected to two different spring balances. The strings form an angle of 120 where they are attached to the object. Notice that both scales read 10 N. Can the object possibly be in equilibrium if there are two 10 N forces pulling it up, and just one 10 N force pulling it down? To find out what the resultant of the two upward forces is, the rule for adding vectors is used again. In Figure 1.4, vectors F 1, F 2 and F 3 have been drawn acting at a single point (where the three strings meet). The vectors are all drawn to a suitable scale and are aimed in the proper directions relative to one another. 6

7 Vector F 1 (dashed line) has been added to vector F 2. The tail of vector F 1 starts at the tip of vector F 2 and vector F 1 is aimed in the direction it acts, which is 60 left of the vertical. Figure 1.3 Figure 1.4 The resultant of F 1 and F 2 starts at the tail of F 2, and ends at the tip of F 1. The resultant is drawn with a bold line and is labelled F R. Notice that F R is equal in magnitude but opposite in direction to F 3. (You might call F R the equilibrant of F 3.) Adding Three Vectors Figure 1.5 Figure 1.5 shows another way of looking at the vector situation in Figure 1.3. This time, all three forces have been added together by vector addition. The vector sum of the three forces is zero. The fact that the resultant force is zero should not surprise you. The point at which the three forces act was stationary, and you will recall from an earlier 7

8 course that a body that is stationary will remain so if the net force on it is zero. (Newton s First Law of Motion.) Two ways of writing the result of the vector analysis in Figure 1.5 are: (1) F 1 + F 2 + F 3 = 0, and (2) F = 0. The symbol means 'the sum of'. In this situation, it is the vector sum. Subtracting Vectors Figure 1.6(a) On occasion, you will have to find the difference between two vectors. For example, if the velocity of a body changes from v 1 to v 2, you may wish to calculate the change in velocity, v. A vector difference is defined as the vector sum of the second vector and the negative of the first vector. v = v 2 + ( 1)v 1, or, v = v 2 v 1. When subtracting vectors, simply remember that the negative of any vector is a vector of the same magnitude (size) but pointing in the opposite direction. The difference of two vectors is the sum of the first vector and the negative of the second vector. See Figure 1.6(a). 8

9 10 v = v 2 v 1 = v 2 + ( v 1 ) Figure 1.6(b) Note! The difference between two vectors can also be found by drawing the vectors tail to tail as in Figure 1.6(b). The resultant, v is the vector drawn from tip to tip. From Figure 1.6(b), v 1 + v = v 2, v = v 2 v 1. Vector Components Figure 1.9 Figure 1.9 shows three ways one might travel from A to B. The vectors are displacement vectors. In each of the three 'trips', the resultant displacement is the same. D 1 + D 2 = D R 9

10 Any two or more vectors that have a resultant such as D R are called components of the resultant vector. A vector such as D R can be resolved into an endless number of component combinations. Figure 1.9 shows just three possible combinations of components of D R. In many problems, the most useful way of resolving a vector into components is to choose components that are perpendicular to each other. Figure 1.10 shows one situation where it is wise to use perpendicular components. Figure 1.10 In Figure 1.10, a 60.0 N force is exerted down the handle of a snow shovel. The force that actually pushes the snow along the driveway is the horizontal component, F x. The vertical component, F y, is directed perpendicular to the road. (See Figure 1.11.) Figure 1.11 To find out what the horizontal component F x is, a scale diagram like Figure 1.11 can be drawn. First, you draw a horizontal reference line. Then you draw a line forming an angle of with the horizontal reference line, because this is the angle formed by the snowplow handle with the road. Using a scale of 1.0 cm for each 10.0 N, construct a force vector to represent F R, where F R = 60.0 N. Next, drop a line down from the tail of F R meeting the horizontal reference line at an angle of 90. This gives you both the vertical and the horizontal 10

11 component forces. directions. Label these F y and F x, and place arrows on them to show their Since the horizontal component vector has a length of 4.8 cm, and each 1.0 cm represents 10.0 N, then F x = 48.0 N. The vertical component vector is 3.6 cm long, therefore F y = 36. N. Vector Questions Figure 1.12(a) 1. Figure 1.12(a) shows a typical force vector situation, where there are three forces acting, but no motion resulting. (Static equilibrium exists.) Two strings support a 36.0 N object. One string makes an angle of with the vertical, and the other string is horizontal. The question is, "What is the tension in each string?" (The tension in a string is simply the force exerted along the string.) Figure 1.12(b) Solution: Figure 1.12(b) shows one way to look at this problem. The 36.0 N object is not moving, so the three forces acting on it must have a resultant of zero. That means the vector sum of the three forces acting on the object is zero. The vector to draw first is the one about which you have the most complete information. You know that the force of gravity F g has a magnitude of 36.0 N, and is directed down. 11

12 You do not know the magnitude of the tension along string #1 (F 1 ) but you know its direction, which is 30 to the vertical. You do not know the magnitude of the tension in string #2 (F 2 ), but you know that it acts in a direction perpendicular to F g. You also know that vectors F 1, F 2 and F g form a closed triangle (since their resultant is zero). In Figure 1.12(b), dashed lines show the directions of F 1 and F 2. To complete the vector triangle of forces, arrows must be added to show that F 1 ends at the tail of F g and F 2 starts at the tip of F g. If F g has been drawn to scale, then both F 1 and F 2 will have the same scale. Figure 1.12(c) Figure 1.12(c) shows what the completed vector diagram looks like. To solve for tension forces F 1 and F 2, you must know to what scale F g was drawn. In the next set of Exercises, you will be asked to complete the solution to this problem. Figure

13 2. In Figure 1.13(a), a block of wood rests on an inclined plane. Since the block is motionless, the forces acting on it must have a vector sum of zero. The block is in static equilibrium. (a) What are the forces acting on the block? Solution Let us represent the block by an imaginary particle, and draw all the forces that act on this particle. A force diagram like Figure 1.13(b) is sometimes called a free body diagram. There are three forces acting on the block. These forces are all shown on the free body diagram. 1) The force of gravity exerted on the block, F g = mg. 2) The force exerted outward on the block by the inclined board. This force is normal (perpendicular) to the board, so it is called the normal force, F N. 3) The force of static friction, F f, which acts in a direction parallel to and toward the top of the inclined board. (b) If the force of gravity on the block is 56 N, and the board is inclined at an angle of 30 to the horizontal, what is the magnitude of: (i) the normal force and (ii) the force of static friction? Solution Since the three forces produce no acceleration, their resultant is zero. F = mg + F N + F f = 0. The three force vectors form a vector triangle. See Figure To solve this problem using a scale diagram, begin by drawing a vector to represent the force of gravity (mg), which is 56 N downward. 13

14 Figure 1.14 Use a scale of 1.0 cm = 10.0 N. The direction of the friction force, F f, is 30 to the horizontal, so draw a line in that direction, beginning at the tip of the mg vector. The direction of the normal force vector F N will be 30 to the vertical, and the F N vector must end at the tail of the mg vector, because the three vectors form a closed triangle if their resultant is zero. Since mg was drawn to scale, and the three angles in the vector triangle are correct, then the vector triangle just completed has all three forces to the same scale (1.0 cm = 10.0 N). The vector triangle is completed by drawing tips on the vectors representing the normal force and the force of static friction. Since the vector representing F N on the scale diagram is 4.9 cm long, the normal force is 49 N. Similarly, the vector representing the force of static friction is 2.8 cm long so that force is 28 N. (c) What is the coefficient of static friction, µ s, if the block is on the verge of sliding down the inclined board? Solution: µ s = F f F N = 28 N 49 N = The coefficient of static friction is

15 A Velocity Vector Problem A motorboat operator is trying to travel across a fast-moving river. (See Figure 1.18.) Although he aims his boat directly across the stream, the water carries his boat to the right. If the boat's resultant velocity (as seen by an observer on the bank) is 15.0 m/s in the direction shown, how fast is the boat moving (a) in a direction downstream? (b) in a direction across the river? Figure 1.18 Solution: Consider the resultant velocity to have two component velocities: v y, the boat s velocity relative to the water, and v x, the water s velocity relative to the bank. Figure

16 Component v y is directed across the river, perpendicular to the bank, while component v x is directed down the stream. For your vector diagram, only a neat sketch is needed, since you will be using trigonometric ratios rather than a scale diagram. See Figure To solve for v y, use sin 55 = v y m/s v y = (15.0 m/s) (sin 55 ) = (15.0 m/s) (0.8192) = 12.3 m/s. To solve for v x, use cos 55 = v x m/s v x = (15.0 m/s) (cos 55 ) = (15.0 m/s) (0.5736) = 8.60 m/s. 16

17 A Displacement Vector Problem Example 1 Physics 12 Reading Booklet Mr. Smith was training for his race. During his training run he ran 5.0 km [ 20 0 N of E], then he altered his path to run another 7.0 km [ 40 0 N of W], and he ended his run by travelling another 4.0 km [ 25 0 E of S ]. Determine his final location in reference to his starting point. Solution Y B A X C 17

18 Resolve all vectors into their x and y components. A x = +Acos2 0 A x = km cos2 0 A x = +4.7 km B x = +Bcos4 0 B x = km cos4 0 B x = -5.4 km C x = +Csi n25 C x = km sin25 C x = +1.7 km T he x component of the resultant vector is R x = A x + B x + C x R x = 4.7 km km km R x = 1.0 km Repeating the above for y componet gives A y = +Asin km sin 20 = +1.7 km B y = +Bsin4 0 = km sin 40 = +4.5 km C y = -Ccos 25 = km cos 25 = -3.6 km T he y component of the resultant vector is R y = A y + B y + C y R y = 1.7 km km km R y = 2.6 km 18

19 Now the magnitude of the resultant can be found from the Pythagorean Theorem The angle that R makes with the positive x axis is Therefore, Mr. Smith is N of E or 21 0 E of N with respect to his starting point. 19

20 20

21 Practice all the question in Worksheet 1, 2, 3 and 4, and check your answers. Worksheet 1:Adding Colinear Vectors Problem 1 B A C D A box rests on the floor. Four forces (pushes) act on the package. Force A is 50 Newtons (N); Force B is 75 N; Force C is 75 N and Force D is also 75 N, respectively. Find the net (overall) force on the box. Answer = _ N Which direction? Problem 2. There are two velocities acting on the plane. The engine of the plane gives it a velocity of 150 mph north and a head wind acts against it with a velocity of 50 mph south. Draw the velocities vectors on the plane and find the net (overall) velocity vector. Answer = mph (remember to give direction) Problem 3. The engine accelerates the helicopter upward with an acceleration of 20 m/s 2. However, the earth pulls down on the helicopter with the acceleration due to gravity (9.8 m/s 2 ). Find the net (overall) acceleration vector. Draw the vectors on the helicopter, too. Answer = m/s 2 (remember to give direction, too) 1 21

22 Worksheet 2: Adding Perpendicular Vectors. Use the mathematical treatment on these (Pythagorean theorem to find the magnitude of the resultant and arctan(θ) to find the angle.) Problem 1. The softball is given an acceleration to the right (along the x axis) of 15 m/s 2. However the acceleration due to gravity is 9.8 m/s 2 (along the y axis). Draw the two vectors along the coordinate grid and find the resultant acceleration vector (magnitude and direction). Find the direction using quadrants and angles. y (90 degrees) x (0, 360 degrees) Answer = Problem 2. There are two kids trying to push a box. One kid pushes it with a force of 80 N northward; the other pushes it west with a force of 50 N. Draw the two vectors along the coordinate grid and find the resultant force vector (magnitude and direction). Find the direction using quadrants and angles and also using compass headings. y (90 degrees) x (0, 360 degrees) Answer = Problem 3. The helicopter flies at 180 degrees with a velocity of 100 mph along the -x axis. It encounters a downdraft pushing on it with a velocity of 25 y (90 degrees) mph. Draw the two vectors along the coordinate grid and find the resultant velocity vector (magnitude and direction). Find the direction using quadrants and angles. x (0, 360 degrees) Answer = 22

23 Worksheet 3: Vector Resolution Physics 12 Reading Booklet Break the one vector up into its x and y components using trigonometry. A x = Acosθ A y = Asinθ #1 Y, North The wind blows at 100 mph at an angle of 35 degrees North of East. Find Ax and Ay. Ax = mph, East X, East Ay = mph, North #2. You walk 40 km at an angle of (or 20 0 North of West) from your house. Find Ax and Ay. y, North Ax = km, West --x, West x Ay = km, North #3. The box is pushed with a force of 125 N (Newtons) at an angle of 240 degrees (30 0 West of South). Find Ax and Ay. --x, West y x Ax = N, West Ay = N, South --y, South #4. The spaceship accelerates at 10m/s 2 at an angle of 350 degrees (10 0 South of East). Find Ax and Ay. y Ax = m/s 2, East --x X, East Ay = m/s 2, South 23

24 Worksheet 4: Putting it all together. Physics 12 Reading Booklet Add vectors that are not colinear and are not perpendicular. Problem 1. We have two force vectors. One (Vector A) is a 50 N force acting at 30 0 and the other (Vector B) is a 70 N force vector acting at Find the one vector that these two represent (magnitude and direction). y x 24

25 Problem 2. We have two velocity vectors. One (Vector A) is a 225 mph velocity acting at 20 0 and the other (Vector B) is a 100 mph velocity vector acting at (3 rd quadrant). Find the one vector that these two represent (magnitude and direction). y x 25

26 Problem 3. We have two force vectors. One (Vector A) is a 45 N force acting at and the other (Vector B) is a 50 N force vector acting at Find the one vector that these two represent (magnitude and direction). y x 26

27 Problem 4. We can do the same thing with more than two vectors. In this example, let s say you are going camping and will take three hikes (three displacement vectors). Starting from your original campsite, on day one, you hike 15 meters at (vector A). Then you turn directly north (90 0, along the y axis) and hike 20 additional meters on day two (Vector B); finally, on the third day, you hike 25 meters along a line directed 22 degrees (4 th quadrant). Find your resultant displacement vector from the original campsite to your final position. [Resultant: the one vector in which these three combine (magnitude and direction)]. Vector C: 25 meter at -22 degrees Vector B: 20 meter at 90 degrees (directly North) y Vector A: 15 meter at 120 degrees Resultant displacement vector x 27

28 Answer keys for Worksheets 1 to 4 Worksheet 1 1. Answer = 25 N left (or 25 N) 2. Answer = 100 mph North m/s 2 up Worksheet m/s 2 at 33.1 degrees (or 33.1 degrees S of E or degrees) [4 th quadrant angle] N at 122 degrees [2 nd Quadrant] (or 58 degrees N of W or 32 degrees W of N mph at 194 degrees [3 rd Quadrant] (14 degrees S of W) Worksheet 3 1. A x = 81.9 mph (East); A y = 57.4 mph (North) 2. A x = km (West); A y = 13.7 km (North) 3. A x = N (West); A y = N (South) 4. A x = 9.8 m/s 2 (East); A y = -1.7 m/s 2 (South) Worksheet 4 1. Resultant = 113 N at (first quadrant or you can say North of East) 2. Resultant = mph at (fourth quadrant) or South of East or Resultant = 27.4 N at (first quadrant) 4. Resultant = 28.3 meters at (first quadrant) 28

29 29

30 30

31 31

Chapter 2 Mechanical Equilibrium

Chapter 2 Mechanical Equilibrium Chapter 2 Mechanical Equilibrium I. Force (2.1) A. force is a push or pull 1. A force is needed to change an object s state of motion 2. State of motion may be one of two things a. At rest b. Moving uniformly

More information

Chapter 5. Forces in Two Dimensions

Chapter 5. Forces in Two Dimensions Chapter 5 Forces in Two Dimensions Chapter 5 Forces in Two Dimensions In this chapter you will: Represent vector quantities both graphically and algebraically. Use Newton s laws to analyze motion when

More information

Chapter 5: Forces in Two Dimensions. Click the mouse or press the spacebar to continue.

Chapter 5: Forces in Two Dimensions. Click the mouse or press the spacebar to continue. Chapter 5: Forces in Two Dimensions Click the mouse or press the spacebar to continue. Chapter 5 Forces in Two Dimensions In this chapter you will: Represent vector quantities both graphically and algebraically.

More information

DISPLACEMENT AND FORCE IN TWO DIMENSIONS

DISPLACEMENT AND FORCE IN TWO DIMENSIONS DISPLACEMENT AND FORCE IN TWO DIMENSIONS Vocabulary Review Write the term that correctly completes the statement. Use each term once. coefficient of kinetic friction equilibrant static friction coefficient

More information

FORCE TABLE INTRODUCTION

FORCE TABLE INTRODUCTION FORCE TABLE INTRODUCTION All measurable quantities can be classified as either a scalar 1 or a vector 2. A scalar has only magnitude while a vector has both magnitude and direction. Examples of scalar

More information

Vectors A Guideline For Motion

Vectors A Guideline For Motion AP Physics-1 Vectors A Guideline For Motion Introduction: You deal with scalar quantities in many aspects of your everyday activities. For example, you know that 2 liters plus 2 liters is 4 liters. The

More information

Vector Addition and Subtraction: Graphical Methods

Vector Addition and Subtraction: Graphical Methods Vector Addition and Subtraction: Graphical Methods Bởi: OpenStaxCollege Displacement can be determined graphically using a scale map, such as this one of the Hawaiian Islands. A journey from Hawai i to

More information

General Physics I, Spring Vectors

General Physics I, Spring Vectors General Physics I, Spring 2011 Vectors 1 Vectors: Introduction A vector quantity in physics is one that has a magnitude (absolute value) and a direction. We have seen three already: displacement, velocity,

More information

Definitions In physics we have two types of measurable quantities: vectors and scalars.

Definitions In physics we have two types of measurable quantities: vectors and scalars. 1 Definitions In physics we have two types of measurable quantities: vectors and scalars. Scalars: have magnitude (magnitude means size) only Examples of scalar quantities include time, mass, volume, area,

More information

Newton 3 & Vectors. Action/Reaction. You Can OnlyTouch as Hard as You Are Touched 9/7/2009

Newton 3 & Vectors. Action/Reaction. You Can OnlyTouch as Hard as You Are Touched 9/7/2009 Newton 3 & Vectors Action/Reaction When you lean against a wall, you exert a force on the wall. The wall simultaneously exerts an equal and opposite force on you. You Can OnlyTouch as Hard as You Are Touched

More information

Vectors and 2D Kinematics. AIT AP Physics C

Vectors and 2D Kinematics. AIT AP Physics C Vectors and 2D Kinematics Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels

More information

Vectors. An Introduction

Vectors. An Introduction Vectors An Introduction 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,

More information

Kinematics in Two Dimensions; Vectors

Kinematics in Two Dimensions; Vectors Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors

More information

Experiment 3 Forces are Vectors

Experiment 3 Forces are Vectors Name Partner(s): Experiment 3 Forces are Vectors Objectives Preparation Pre-Lab Understand that some quantities in physics are vectors, others are scalars. Be able to perform vector addition graphically

More information

GENERAL PHYSICS (101 PHYS)

GENERAL PHYSICS (101 PHYS) INAYA MEDICAL COLLEGE (IMC) PHYS 101- LECTURE 1 GENERAL PHYSICS (101 PHYS) DR. MOHAMMED MOSTAFA EMAM LECTURES & CLASS ACTIVITIES https://inayacollegedrmohammedemam.wordpress.com/ Password: drmohammedemam

More information

Lab 3. Adding Forces with a Force Table

Lab 3. Adding Forces with a Force Table Lab 3. Adding Forces with a Force Table Goals To describe the effect of three balanced forces acting on a ring or disk using vector addition. To practice adding force vectors graphically and mathematically

More information

Physics 12. Chapter 1: Vector Analysis in Two Dimensions

Physics 12. Chapter 1: Vector Analysis in Two Dimensions Physics 12 Chapter 1: Vector Analysis in Two Dimensions 1. Definitions When studying mechanics in Physics 11, we have realized that there are two major types of quantities that we can measure for the systems

More information

Lab 3. Adding Forces with a Force Table

Lab 3. Adding Forces with a Force Table Lab 3. Adding Forces with a Force Table Goals To describe the effect of three balanced forces acting on a ring or disk using vector addition. To practice adding force vectors graphically and mathematically

More information

Kinematics in Two Dimensions; 2D- Vectors

Kinematics in Two Dimensions; 2D- Vectors Kinematics in Two Dimensions; 2D- Vectors Addition of Vectors Graphical Methods Below are two example vector additions of 1-D displacement vectors. For vectors in one dimension, simple addition and subtraction

More information

Physics 11 Reading Booklet

Physics 11 Reading Booklet In Order complete the Physics 11 Substantive Assignment, you must read and complete the self-marking exercises in this booklet. 1. Read all the information provided. 2. Complete the Practice and Self Check

More information

1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below.

1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. Name Vectors Practice 1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the object, will establish

More information

BELLWORK feet

BELLWORK feet BELLWORK 1 A hot air balloon is being held in place by two people holding ropes and standing 35 feet apart. The angle formed between the ground and the rope held by each person is 40. Determine the length

More information

Vectors. Example: Example: 2 cm. Parts of a vector: 3 cm. Body / Line Segment. Tail / Toe. Tip / Head

Vectors. Example: Example: 2 cm. Parts of a vector: 3 cm. Body / Line Segment. Tail / Toe. Tip / Head Vectors The study of motion involves the introduction of a variety of quantities which are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity,

More information

Chapter 3. Vectors and. Two-Dimensional Motion Vector vs. Scalar Review

Chapter 3. Vectors and. Two-Dimensional Motion Vector vs. Scalar Review Chapter 3 Vectors and Two-Dimensional Motion Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and

More information

Chemistry 11. First Assignment Scientific Notation

Chemistry 11. First Assignment Scientific Notation First Assignment Scientific Notation This First Assignment may take between 1 hours depending on your background and prior knowledgeplease follow the instructions carefully. a. Read all the information

More information

A Question about free-body diagrams

A Question about free-body diagrams Free-body Diagrams To help us understand why something moves as it does (or why it remains at rest) it is helpful to draw a free-body diagram. The free-body diagram shows the various forces that act on

More information

Force Vectors and Static Equilibrium

Force Vectors and Static Equilibrium Force Vectors 1 Force Vectors and Static Equilibrium Overview: In this experiment you will hang weights from pulleys over the edge of a small round force table, to exert various forces on a metal ring

More information

Vector components and motion

Vector components and motion Vector components and motion Objectives Distinguish between vectors and scalars and give examples of each. Use vector diagrams to interpret the relationships among vector quantities such as force and acceleration.

More information

Force. The cause of an acceleration or change in an object s motion. Any kind of a push or pull on an object.

Force. The cause of an acceleration or change in an object s motion. Any kind of a push or pull on an object. Force The cause of an acceleration or change in an object s motion. Any kind of a push or pull on an object. Forces do not always give rise to motion. Forces can be equal and opposite. Force is a vector

More information

Lab: Vectors. You are required to finish this section before coming to the lab. It will be checked by one of the lab instructors when the lab begins.

Lab: Vectors. You are required to finish this section before coming to the lab. It will be checked by one of the lab instructors when the lab begins. Lab: Vectors Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Name Partners Pre-Lab You are required to finish this section before coming to the lab. It will be checked by one of the

More information

Chapter 3. Vectors. 3.1 Coordinate Systems 3.2 Vector and Scalar Quantities 3.3 Some Properties of Vectors 3.4 Components of a Vector and Unit Vectors

Chapter 3. Vectors. 3.1 Coordinate Systems 3.2 Vector and Scalar Quantities 3.3 Some Properties of Vectors 3.4 Components of a Vector and Unit Vectors Chapter 3 Vectors 3.1 Coordinate Systems 3.2 Vector and Scalar Quantities 3.3 Some Properties of Vectors 3.4 Components of a Vector and Unit Vectors 1 Vectors Vector quantities Physical quantities that

More information

PHYSICS 231 INTRODUCTORY PHYSICS I

PHYSICS 231 INTRODUCTORY PHYSICS I PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 4 Main points of last lecture Scalars vs. Vectors Vectors A: (A x, A y ) or A & θ Addition/Subtraction Projectile Motion X-direction: a x = 0 (v x = constant)

More information

An object moves back and forth, as shown in the position-time graph. At which points is the velocity positive?

An object moves back and forth, as shown in the position-time graph. At which points is the velocity positive? 1 The slope of the tangent on a position-time graph equals the instantaneous velocity 2 The area under the curve on a velocity-time graph equals the: displacement from the original position to its position

More information

Free Response- Exam Review

Free Response- Exam Review Free Response- Exam Review Name Base your answers to questions 1 through 3 on the information and diagram below and on your knowledge of physics. A 150-newton force, applied to a wooden crate at an angle

More information

Otterbein University Department of Physics Physics Laboratory Partner s Name: EXPERIMENT D FORCE VECTORS

Otterbein University Department of Physics Physics Laboratory Partner s Name: EXPERIMENT D FORCE VECTORS Name: Partner s Name: EXPERIMENT 1500-7 2D FORCE VECTORS INTRODUCTION A vector is represented by an arrow: it has a direction and a magnitude (or length). Vectors can be moved around the page without changing

More information

AP Physics I Summer Work

AP Physics I Summer Work AP Physics I Summer Work 2018 (20 points) Please complete the following set of questions and word problems. Answers will be reviewed in depth during the first week of class followed by an assessment based

More information

9.1. Basic Concepts of Vectors. Introduction. Prerequisites. Learning Outcomes. Learning Style

9.1. Basic Concepts of Vectors. Introduction. Prerequisites. Learning Outcomes. Learning Style Basic Concepts of Vectors 9.1 Introduction In engineering, frequent reference is made to physical quantities, such as force, speed and time. For example, we talk of the speed of a car, and the force in

More information

Vectors. Introduction. Prof Dr Ahmet ATAÇ

Vectors. Introduction. Prof Dr Ahmet ATAÇ Chapter 3 Vectors Vectors Vector quantities Physical quantities that have both n u m e r i c a l a n d d i r e c t i o n a l properties Mathematical operations of vectors in this chapter A d d i t i o

More information

Math Review -- Conceptual Solutions

Math Review -- Conceptual Solutions Math Review Math Review -- Conceptual Solutions 1.) Is three plus four always equal to seven? Explain. Solution: If the numbers are scalars written in base 10, the answer is yes (if the numbers are in

More information

Physics 101 Lecture 5 Newton`s Laws

Physics 101 Lecture 5 Newton`s Laws Physics 101 Lecture 5 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department The Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law qfrictional forces q Examples

More information

UNIT V: Multi-Dimensional Kinematics and Dynamics Page 1

UNIT V: Multi-Dimensional Kinematics and Dynamics Page 1 UNIT V: Multi-Dimensional Kinematics and Dynamics Page 1 UNIT V: Multi-Dimensional Kinematics and Dynamics As we have already discussed, the study of the rules of nature (a.k.a. Physics) involves both

More information

UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES. Objectives. To understand and be able to apply Newton s Third Law

UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES. Objectives. To understand and be able to apply Newton s Third Law UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES Objectives To understand and be able to apply Newton s Third Law To be able to determine the object that is exerting a particular force To understand

More information

Forces I. Newtons Laws

Forces I. Newtons Laws Forces I Newtons Laws Kinematics The study of how objects move Dynamics The study of why objects move Newton s Laws and Forces What is force? What are they? Force A push or a pull Symbol is F Unit is N

More information

MOMENTUM, IMPULSE & MOMENTS

MOMENTUM, IMPULSE & MOMENTS the Further Mathematics network www.fmnetwork.org.uk V 07 1 3 REVISION SHEET MECHANICS 1 MOMENTUM, IMPULSE & MOMENTS The main ideas are AQA Momentum If an object of mass m has velocity v, then the momentum

More information

5. Use the graph below to determine the displacement of the object at the end of the first seven seconds.

5. Use the graph below to determine the displacement of the object at the end of the first seven seconds. Name: Hour: 1. The slope of the tangent on a position-time graph equals the: Sem 1 Exam Review Advanced Physics 2015-2016 2. The area under the curve on a velocity-time graph equals the: 3. The graph below

More information

AP Physics First Nine Weeks Review

AP Physics First Nine Weeks Review AP Physics First Nine Weeks Review 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the

More information

PHYS 1114, Lecture 10, February 8 Contents:

PHYS 1114, Lecture 10, February 8 Contents: PHYS 1114, Lecture 10, February 8 Contents: 1 Example of projectile motion: Man shooting a gun firing a bullet horizontally. 2 Example of projectile motion: Man shooting an arrow at a monkey in a tree.

More information

Experiment 2 Vectors. using the equations: F x = F cos θ F y = F sin θ. Composing a Vector

Experiment 2 Vectors. using the equations: F x = F cos θ F y = F sin θ. Composing a Vector Experiment 2 Vectors Preparation Study for this week's quiz by reviewing the last experiment, reading this week's experiment carefully and by looking up force and vectors in your textbook. Principles A

More information

MODULE 1 DYNAMICS EXTENSION

MODULE 1 DYNAMICS EXTENSION MODULE 1 INTRODUCTION If you took Physics 11, you were introduced to the concepts of vectors and vector arithmetic. You will recall that vectors are used to represent quantities that have both magnitude

More information

AP Physics C Mechanics Summer Assignment

AP Physics C Mechanics Summer Assignment AP Physics C Mechanics Summer Assignment 2018 2019 School Year Welcome to AP Physics C, an exciting and intensive introductory college physics course for students majoring in the physical sciences or engineering.

More information

4. The diagram below represents two concurrent forces.

4. The diagram below represents two concurrent forces. 1. Two 20.-newton forces act concurrently on an object. What angle between these forces will produce a resultant force with the greatest magnitude? A) 0º B) 45º C) 90.º D) 180.º 2. Two forces act concurrently

More information

Chapter 2 A Mathematical Toolbox

Chapter 2 A Mathematical Toolbox Chapter 2 Mathematical Toolbox Vectors and Scalars 1) Scalars have only a magnitude (numerical value) Denoted by a symbol, a 2) Vectors have a magnitude and direction Denoted by a bold symbol (), or symbol

More information

Vector Addition INTRODUCTION THEORY

Vector Addition INTRODUCTION THEORY Vector Addition INTRODUCTION All measurable quantities may be classified either as vector quantities or as scalar quantities. Scalar quantities are described completely by a single number (with appropriate

More information

Vectors a vector is a quantity that has both a magnitude (size) and a direction

Vectors a vector is a quantity that has both a magnitude (size) and a direction Vectors In physics, a vector is a quantity that has both a magnitude (size) and a direction. Familiar examples of vectors include velocity, force, and electric field. For any applications beyond one dimension,

More information

The Concept of Force Newton s First Law and Inertial Frames Mass Newton s Second Law The Gravitational Force and Weight Newton s Third Law Analysis

The Concept of Force Newton s First Law and Inertial Frames Mass Newton s Second Law The Gravitational Force and Weight Newton s Third Law Analysis The Laws of Motion The Concept of Force Newton s First Law and Inertial Frames Mass Newton s Second Law The Gravitational Force and Weight Newton s Third Law Analysis Models using Newton s Second Law Forces

More information

Review of Lectures 1, 2 and 3

Review of Lectures 1, 2 and 3 Physics 22000 General Physics Lecture 4 Applying Newton s Laws Fall 2016 Semester Prof. Matthew Jones 1 Review of Lectures 1, 2 and 3 Algebraic description of linear motion with constant acceleration:

More information

Physics 2A Chapter 4: Forces and Newton s Laws of Motion

Physics 2A Chapter 4: Forces and Newton s Laws of Motion Physics 2A Chapter 4: Forces and Newton s Laws of Motion There is nothing either good or bad, but thinking makes it so. William Shakespeare It s not what happens to you that determines how far you will

More information

I. AXN/RXN W.S. In the example below, the action-reaction pair is shown by the arrows (vectors), and the action-reaction described in words.

I. AXN/RXN W.S. In the example below, the action-reaction pair is shown by the arrows (vectors), and the action-reaction described in words. I. AXN/RXN W.S. In the example below, the action-reaction pair is shown by the arrows (vectors), and the action-reaction described in words. 1. For the remaining situations, discuss with your neighbor

More information

Forces and Newton s Laws Reading Notes. Give an example of a force you have experienced continuously all your life.

Forces and Newton s Laws Reading Notes. Give an example of a force you have experienced continuously all your life. Forces and Newton s Laws Reading Notes Name: Section 4-1: Force What is force? Give an example of a force you have experienced continuously all your life. Give an example of a situation where an object

More information

# x = v f + v & % ( t x = v

# x = v f + v & % ( t x = v Name: Physics Chapter 4 Study Guide ----------------------------------------------------------------------------------------------------- Useful Information: F = ma µ = F fric a = v f " v i t # x = v f

More information

Physics 8 Monday, October 9, 2017

Physics 8 Monday, October 9, 2017 Physics 8 Monday, October 9, 2017 Pick up a HW #5 handout if you didn t already get one on Wednesday. It s due this Friday, 10/13. It contains some Ch9 (work) problems, some Ch10 (motion in a plane) problems,

More information

PHYSICS - CLUTCH CH 01: UNITS & VECTORS.

PHYSICS - CLUTCH CH 01: UNITS & VECTORS. !! www.clutchprep.com Physics is the study of natural phenomena, including LOTS of measurements and equations. Physics = math + rules. UNITS IN PHYSICS We measure in nature. Measurements must have. - For

More information

Chapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion

Chapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors

More information

Chapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc.

Chapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc. Chapter 5 Newton s Laws of Motion Force and Mass Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The Vector Nature of Forces: Forces in Two Dimensions

More information

You may use g = 10 m/s 2, sin 60 = 0.87, and cos 60 = 0.50.

You may use g = 10 m/s 2, sin 60 = 0.87, and cos 60 = 0.50. 1. A child pulls a 15kg sled containing a 5kg dog along a straight path on a horizontal surface. He exerts a force of a 55N on the sled at an angle of 20º above the horizontal. The coefficient of friction

More information

Physics 40 Chapter 3: Vectors

Physics 40 Chapter 3: Vectors Physics 40 Chapter 3: Vectors Cartesian Coordinate System Also called rectangular coordinate system x-and y- axes intersect at the origin Points are labeled (x,y) Polar Coordinate System Origin and reference

More information

Physics 111 Lecture 4 Newton`s Laws

Physics 111 Lecture 4 Newton`s Laws Physics 111 Lecture 4 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com he Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law q Examples Isaac

More information

Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4. Forces and Newton s Laws of Motion. continued Chapter 4 Forces and Newton s Laws of Motion continued Quiz 3 4.7 The Gravitational Force Newton s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other

More information

AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force).

AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force). AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force). 1981M1. A block of mass m, acted on by a force of magnitude F directed horizontally to the

More information

Which, if any, of the velocity versus time graphs below represent the movement of the sliding box?

Which, if any, of the velocity versus time graphs below represent the movement of the sliding box? Review Packet Name: _ 1. A box is sliding to the right along a horizontal surface with a velocity of 2 m/s. There is friction between the box and the horizontal surface. The box is tied to a hanging stone

More information

OpenStax-CNX module: m Vectors. OpenStax College. Abstract

OpenStax-CNX module: m Vectors. OpenStax College. Abstract OpenStax-CNX module: m49412 1 Vectors OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section you will: Abstract View vectors

More information

Scalar Quantities - express only magnitude ie. time, distance, speed

Scalar Quantities - express only magnitude ie. time, distance, speed Chapter 6 - Vectors Scalar Quantities - express only magnitude ie. time, distance, speed Vector Quantities - express magnitude and direction. ie. velocity 80 km/h, 58 displacement 10 km (E) acceleration

More information

Q2. A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book.

Q2. A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book. AP Physics 1- Dynamics Practice Problems FACT: Inertia is the tendency of an object to resist a change in state of motion. A change in state of motion means a change in an object s velocity, therefore

More information

Two Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while

Two Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while Student View Summary View Diagnostics View Print View with Answers Edit Assignment Settings per Student Exam 2 - Forces [ Print ] Due: 11:59pm on Tuesday, November 1, 2011 Note: To underst how points are

More information

Newton s First Law and IRFs

Newton s First Law and IRFs Goals: Physics 207, Lecture 6, Sept. 22 Recognize different types of forces and know how they act on an object in a particle representation Identify forces and draw a Free Body Diagram Solve 1D and 2D

More information

PHYSICS 231 Laws of motion PHY 231

PHYSICS 231 Laws of motion PHY 231 PHYSICS 231 Laws of motion 1 Newton s Laws First Law: If the net force exerted on an object is zero the object continues in its original state of motion; if it was at rest, it remains at rest. If it was

More information

General Physics I Spring Forces and Newton s Laws of Motion

General Physics I Spring Forces and Newton s Laws of Motion General Physics I Spring 2011 Forces and Newton s Laws of Motion 1 Forces and Interactions The central concept in understanding why things move is force. If a tractor pushes or pulls a trailer, the tractor

More information

1. A sphere with a radius of 1.7 cm has a volume of: A) m 3 B) m 3 C) m 3 D) 0.11 m 3 E) 21 m 3

1. A sphere with a radius of 1.7 cm has a volume of: A) m 3 B) m 3 C) m 3 D) 0.11 m 3 E) 21 m 3 1. A sphere with a radius of 1.7 cm has a volume of: A) 2.1 10 5 m 3 B) 9.1 10 4 m 3 C) 3.6 10 3 m 3 D) 0.11 m 3 E) 21 m 3 2. A 25-N crate slides down a frictionless incline that is 25 above the horizontal.

More information

A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units.

A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units. Vectors and Scalars A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude A numerical value with units. Scalar Example Speed Distance Age Heat Number

More information

VECTORS IN 2 DIMENSIONS

VECTORS IN 2 DIMENSIONS Free PowerPoint Templates VECTORS IN 2 DIMENSIONS Sutherland High School Grade 11 2018 SCALAR A physical quantity that has a magnitude and unit only. Example: Mass Time Distance Speed Volume Temperature

More information

Unit 5 Forces I- Newtonʼ s First & Second Law

Unit 5 Forces I- Newtonʼ s First & Second Law Unit 5 orces I- Newtonʼ s irst & Second Law Unit is the NEWTON(N) Is by definition a push or a pull Does force need a Physical contact? Can exist during physical contact(tension, riction, Applied orce)

More information

11. (7 points: Choose up to 3 answers) What is the tension,!, in the string? a.! = 0.10 N b.! = 0.21 N c.! = 0.29 N d.! = N e.! = 0.

11. (7 points: Choose up to 3 answers) What is the tension,!, in the string? a.! = 0.10 N b.! = 0.21 N c.! = 0.29 N d.! = N e.! = 0. A harmonic wave propagates horizontally along a taut string of length! = 8.0 m and mass! = 0.23 kg. The vertical displacement of the string along its length is given by!!,! = 0.1!m cos 1.5!!! +!0.8!!,

More information

Newton s First Law. Newton s Second Law 9/29/11

Newton s First Law. Newton s Second Law 9/29/11 Newton s First Law Any object remains at constant velocity unless acted upon by a net force. AND In order for an object to accelerate, there must be a net force acting on it. Constant velocity could mean

More information

What does the lab partner observe during the instant the student pushes off?

What does the lab partner observe during the instant the student pushes off? Motion Unit Review State Test Questions 1. To create real-time graphs of an object s displacement versus time and velocity versus time, a student would need to use a A motion sensor.b low- g accelerometer.

More information

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²)

Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²) Practice A car starts from rest and travels upwards along a straight road inclined at an angle of 5 from the horizontal. The length of the road is 450 m and the mass of the car is 800 kg. The speed of

More information

G r a d e 1 1 P h y s i c s ( 3 0 s ) Midterm Practice exam

G r a d e 1 1 P h y s i c s ( 3 0 s ) Midterm Practice exam G r a d e 1 1 P h y s i c s ( 3 0 s ) Midterm Practice exam G r a d e 1 1 P h y s i c s ( 3 0 s ) Midterm Practice Exam Instructions The final exam will be weighted as follows: Modules 1 6 100% The format

More information

The Laws of Motion. Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples

The Laws of Motion. Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples The Laws of Motion Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples Gravitational Force Gravitational force is a vector Expressed by Newton s Law of Universal

More information

Vectors Part 1: Two Dimensions

Vectors Part 1: Two Dimensions Vectors Part 1: Two Dimensions Last modified: 20/02/2018 Links Scalars Vectors Definition Notation Polar Form Compass Directions Basic Vector Maths Multiply a Vector by a Scalar Unit Vectors Example Vectors

More information

SECTION 6.3: VECTORS IN THE PLANE

SECTION 6.3: VECTORS IN THE PLANE (Section 6.3: Vectors in the Plane) 6.18 SECTION 6.3: VECTORS IN THE PLANE Assume a, b, c, and d are real numbers. PART A: INTRO A scalar has magnitude but not direction. We think of real numbers as scalars,

More information

PHYS-2010: General Physics I Course Lecture Notes Section V

PHYS-2010: General Physics I Course Lecture Notes Section V PHYS-2010: General Physics I Course Lecture Notes Section V Dr. Donald G. Luttermoser East Tennessee State University Edition 2.5 Abstract These class notes are designed for use of the instructor and students

More information

The net force on a moving object is suddenly reduced to zero. As a consequence, the object

The net force on a moving object is suddenly reduced to zero. As a consequence, the object The net force on a moving object is suddenly reduced to zero. As a consequence, the object (A) stops abruptly (B) stops during a short time interval (C) changes direction (D) continues at a constant velocity

More information

Problem-Solving Strategies

Problem-Solving Strategies Connexions module: m42076 1 Problem-Solving Strategies OpenStax College This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License Abstract Understand and

More information

Vector x-component (N) y-component (N)

Vector x-component (N) y-component (N) Name AP Physics C Summer Assignment 2014 Where calculations are required, show your work. Be smart about significant figures. Print these sheets and hand them in (neatly done) on the first day of class.

More information

Section 1 Changes in Motion. Chapter 4. Preview. Objectives Force Force Diagrams

Section 1 Changes in Motion. Chapter 4. Preview. Objectives Force Force Diagrams Section 1 Changes in Motion Preview Objectives Force Force Diagrams Section 1 Changes in Motion Objectives Describe how force affects the motion of an object. Interpret and construct free body diagrams.

More information

Projectile Motion and 2-D Dynamics

Projectile Motion and 2-D Dynamics Projectile Motion and 2-D Dynamics Vector Notation Vectors vs. Scalars In Physics 11, you learned the difference between vectors and scalars. A vector is a quantity that includes both direction and magnitude

More information

Vectors & scalars: Force as vector Review

Vectors & scalars: Force as vector Review Vectors & scalars: Force as vector Review Name 1. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the

More information

Name: Unit 4 Newton s 1 st & 3 rd Law

Name: Unit 4 Newton s 1 st & 3 rd Law Name: Period: Table #: Unit 4 Newton s 1 st & 3 rd Law 1 UNIT IV: Reading - Force Diagrams The analysis of a problem in dynamics usually involves the selection and analysis of the relevant forces acting

More information

Physics 2211 ABC Quiz #3 Solutions Spring 2017

Physics 2211 ABC Quiz #3 Solutions Spring 2017 Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass

More information

Chapter 5 Newton s Laws of Motion. What determines acceleration on objects?

Chapter 5 Newton s Laws of Motion. What determines acceleration on objects? Chapter 5 Newton s Laws of Motion What determines acceleration on objects? 1 Units of Chapter 5 Force and Mass Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The

More information

Student Exploration: Vectors

Student Exploration: Vectors Name: Date: Student Exploration: Vectors Vocabulary: component, dot product, magnitude, resultant, scalar, unit vector notation, vector Prior Knowledge Question (Do this BEFORE using the Gizmo.) An airplane

More information