q = tan -1 (R y /R x )

Size: px
Start display at page:

Download "q = tan -1 (R y /R x )"

Transcription

1 Vector Addition Using Vector Components = + R x = A x + B x B y R y = A y + B y R = (R x 2 + R y 2 ) 1/2 B x q = tan -1 (R y /R x )

2 Example 1.7: Vector has a magnitude of 50 cm and direction of 30º, and vector has a magnitude of 35 cm and direction 110º (both angles measured ccw from ). What is the resultant vector? Page 19 Adding Vectors Using Components R x = A x + B x = 50 cos(30 ) + 35 cos(110 ) = (-12.0) = 31.3 cm R y = A y + B y = 50 sin(30 ) + 35 sin (110 ) = = 57.9 cm R = (R x 2 + R y 2 ) 1/2 = ( ) 1/2 = 66 cm q = tan -1 (R y /R x ) = tan -1 (57.9/31.3) = 62.

3 Superposition of Forces: Resultant and Components of Force Vectors An example of superposition of forces: y In general, the resultant, or vector sum of forces, is: x θ = tan 1 R y R x direction

4 Motion in a Plane (2D) with Constant Acceleration A General Rule: Two sets of quantities are treated separately/independently. All the x-components of the quantities are related to each other in one set of kinematic equations: v x t = v 0x + a x t...(2.6) All the y-components of the quantities are related to each other in another set of kinematic equations: v y t = v 0y + a y t...(2.6) x t = x 0 + v 0x t a xt 2 (2.10) v 2 x = v 2 0x + 2a x x x 0 (2.11) y t = y 0 + v 0y t a yt 2 (2.10) v 2 y = v 2 0y + 2a y y y 0 (2.11) v av,x = 1 2 [v x t + v 0x ].. (2.7) v av,y = 1 2 [v y t + v 0y ].. (2.7) Important initial steps for solving 2D motion with constant acceleration: Set up a convenient x-y coordinate system. Identify the x and y components of initial position, initial velocity, and acceleration. Apply the rule set above and NEVER mix x-component and y-component quantities in the same kinematic equation.

5 Projectile Motion: The motion in a vertical plane of a point particle, given an initial velocity, under the influence of a constant gravitation acceleration, with other factors such as air friction and wind, etc., all neglected. 3.3 Projectile Motion v y = 0 at the maximum height A Summary of the Parameters (with the given coordinates) Acceleration: a x = 0 a y = - g = m s 2 Initial Conditions: x 0 = 0 y 0 = 0 v 0x = v 0 cos(q 0 ) v 0y = v 0 sin(q 0 ) q 0 constant a y constant v x since a x = 0 Other Examples airplane dropping a package motorcycle running off a cliff rock sliding off the edge of a roof etc. x-components v x t = v 0 cos(q 0 ) x t = v 0 cos(q 0 )t y-components v y t = v 0 sin(q 0 ) gt y t = v 0 sin(q 0 )t 1 2 gt2 v y 2 = (v 0 sin(q 0 )) 2 2gy

6 Projectile Motion x-components v x t = v 0 cos(q 0 ) x t = v 0 cos(q 0 )t y-components v y t = v 0 sin(q 0 ) gt y t = v 0 sin(q 0 )t 1 2 gt2 v y 2 = (v 0 sin(q 0 )) 2 2gy v y = 0 at the maximum height constant a y Examples 3.4&3.5: A home run hit Given: v 0 and q 0 Find: (a) x and y, and, v and q, at t = 2.00 s (b) t max and h max (c) Horizontal range R Solutions: (a) x t = v 0 cos(q 0 )t y t = v 0 sin(q 0 )t 1 2 gt2 v x t = v 0 cos(q 0 ) v y t = v 0 sin(q 0 ) gt v = (v x 2 + v y 2 ) 1 2 θ = tan 1 (v y /v x ) q 0 constant v x since a x = 0 (b) Set v y t = v 0 sin(q 0 ) gt = 0 to get t max = v 0 sin(q 0 )/g. Then, set v 2 y = (v 0 sin(q 0 )) 2 2gy = 0 to get h max = (v 0 sin(q 0 )) 2 /2g. (c) Set y t = v 0 sin(q 0 )t 1 2 gt2 = t(v 0 sin(q 0 ) 1 gt)= 0 2 to get the time of flight t f = 2v 0 sin(q 0 )/g = 2t max. Then, using x t = v 0 cos(q 0 )t to get the range R = 2v 2 0 sin(q 0 )cos(q 0 )/g = v 2 0 sin(2q 0 )/g

7 3.4 Uniform Circular Motion An object moving along a circular path with a constant speed v (magnitude of velocity) Velocity and Acceleration Vectors in Uniform Circular Motion Velocity: Accelerarion: tangent to the circle with constant magnitude v 1 = v 2 = v a rad = v2, always pointing toward the center of the circle. R v = റs v R റa av = v = v റs t R t റv = v R റs v റa = lim = v lim റs = v റv t 0 t R t 0 t R a rad = റa = v R റv = v2 R

8 The Component Form: σ റF = m റa σ F x = ma x and σ F y = ma y Example: An object of mass 5.0 kg is acted upon by two forces, F A and F B. F A is directed toward east and has a magnitude 3.0 N. F B is directed toward north and has a magnitude 4.0 N. (a) Draw diagram that describes this situation. (b) Set up a coordinate system. (c) Calculate the components, the magnitude, and the direction of the net force. (d) Calculate the components and the magnitude of the acceleration. y റF B O റF θ റF A x (a) Sketch a diagram that describes this situation. (b) Set up a coordinate system. (c) F x = F Ax = 3.0 N F y = F By = 4.0 N F = ( ) 1/2 = 5.0 N θ = tan = (d) a x = F x = 3.0 = 0.60 m 5.0 m/s2 a y = F y = 4.0 = 0.80 m/s2 m 5.0 a = ( ) 1/2 = 1.0 m/s 2 or a = F/m = 1.0 m/s 2

9 Newton s Second Law: in vector form σ റF = m റa in component form σ F x = ma x σ F y = ma y Strategy for Solving Newton s Law Problems Isolate the bodies in a system. Analyze all the forces acting on each body and draw one free-body diagram for each body. Based on the free-body diagram, set up a most convenient x-y coordinate system. Break each force into components using this coordinates. For each body, sum up all the x-components of the forces to an equation: σ F x = ma x. For each body, sum up all the y-components of the forces to an equation: σ F y = ma y. Use these equations to solve for unknown quantities. Example 1: A box of known mass m is resting on a leveled table surface. Find all the forces acting on this box and their actionreaction counterparts. y n W m Two forces act on the box: weight (known) normal force W = mg n Sum up the y component forces: n + ( mg) = 0. Therefore, n = mg.

10 Example: Box of mass m on a frictionless incline Given: m and q Find: n and a y n Solutions: Weight: W = mg W x = mgsinq W y = mgcosq x-axis: mgsinq = ma a = gsinq y-axis: n mgcosq = 0 n = mgcosq x q q mg Another Question: Near the bottom of the incline, the box is given an initial velocity of a known magnitude v 0 pointing up the incline. What distance will it slide before it turns around and slides downward? Solution: The acceleration is given above a = gsinq Use the kinematic equation v 2 2 v 2 1 = 2a(x 2 x 1 ) (x 2 x 1 ) = v 2 1 /2a = v 2 0 /2gsinq The distance that it will slide up the incline is v 2 0 /2gsinq.

11 Example: Box of mass m is pushed up an incline by a force F parallel to the incline. The coefficient of kinetic friction between the box and the incline is μ k. y f k n F x Given: F, m, μ k, and q Find: n and a Solutions: Weight and its components W = mg W x = mgsinq W y = mgcosq x-axis: F - mgsinq - f k = ma f k = μ k n = μ k mgcosq q q mg a = (F - mgsinq - μ k mg)/m y-axis: n mgcosq = 0 n = mgcosq What if some other quantities are given and you are asked to calculate some different quantities? Consider Problem 9 on Term Exam 1 from 2015.

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

Chapter 4: Newton s Second Law F = m a. F = m a (4.2)

Chapter 4: Newton s Second Law F = m a. F = m a (4.2) Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.

More information

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,

More information

MOTION IN TWO OR THREE DIMENSIONS

MOTION IN TWO OR THREE DIMENSIONS MOTION IN TWO OR THREE DIMENSIONS 3 Sections Covered 3.1 : Position & velocity vectors 3.2 : The acceleration vector 3.3 : Projectile motion 3.4 : Motion in a circle 3.5 : Relative velocity 3.1 Position

More information

Normal Force. W = mg cos(θ) Normal force F N = mg cos(θ) F N

Normal Force. W = mg cos(θ) Normal force F N = mg cos(θ) F N Normal Force W = mg cos(θ) Normal force F N = mg cos(θ) Note there is no weight force parallel/down the include. The car is not pressing on anything causing a force in that direction. If there were a person

More information

Physics C: Mechanics 2015 Scoring Guidelines

Physics C: Mechanics 2015 Scoring Guidelines AP Physics C: Mechanics 015 Scoring Guidelines 015 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central

More information

Distance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is:

Distance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is: Chapter 1 Kinematics 1.1 Basic ideas r(t) is the position of a particle; r = r is the distance to the origin. If r = x i + y j + z k = (x, y, z), then r = r = x 2 + y 2 + z 2. v(t) is the velocity; v =

More information

Motion in Two or Three Dimensions

Motion in Two or Three Dimensions Chapter 3 Motion in Two or Three Dimensions PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 3 To use vectors

More information

UNIT 2E. Forces on Inclined Planes

UNIT 2E. Forces on Inclined Planes Name: Regents Physics Date: Mr. Morgante UNIT 2E Forces on Inclined Planes 1. Frictionless Plane Forces on An Inclined Plane +y +y m VS. +x +x m 2. Free Body Diagram (FBD) m= mass=10kg F N +y = 30 F g

More information

Circular Motion and Gravitation

Circular Motion and Gravitation Chapter 6 Circular Motion and Gravitation To understand the dynamics of circular motion. To study the application of circular motion as it applies to Newton's law of gravitation. To examine the idea of

More information

Chapter 4. Motion in Two Dimensions

Chapter 4. Motion in Two Dimensions Chapter 4 Motion in Two Dimensions Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail Will treat projectile motion and uniform circular motion

More information

Dynamics Review Checklist

Dynamics Review Checklist Dynamics Review Checklist Newton s Laws 2.1.1 Explain Newton s 1 st Law (the Law of Inertia) and the relationship between mass and inertia. Which of the following has the greatest amount of inertia? (a)

More information

Chapter 3. Kinematics in Two Dimensions

Chapter 3. Kinematics in Two Dimensions Chapter 3 Kinematics in Two Dimensions 3.1 Trigonometry 3.1 Trigonometry sin! = h o h cos! = h a h tan! = h o h a 3.1 Trigonometry tan! = h o h a tan50! = h o 67.2m h o = tan50! ( 67.2m) = 80.0m 3.1 Trigonometry!

More information

A+B. Scalar quantities are described by magnitude only (examples: distance, speed, temperature, energy, and mass).

A+B. Scalar quantities are described by magnitude only (examples: distance, speed, temperature, energy, and mass). Honors Physics Examination I Review Questions #1-#11 - Vectors & Measurements vector quantity is specified by magnitude and direction (examples: displacement, velocity, acceleration, momentum, and weight).

More information

Newton s 3 Laws of Motion

Newton s 3 Laws of Motion Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet 3. F = F 1 on 2 2 on 1 Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of

More information

Mechanics 1 Revision notes

Mechanics 1 Revision notes Mechanics 1 Revision notes 1. Kinematics in one and two dimensions EQUATIONS FOR CONSTANT ACCELERATION ARE NOT GIVEN Learn Them! v = u + at s = ut + 1 at s = vt 1 at s = 1 (u + v)t v = u + as s : displacement

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.0T Fall Term 2004 Problem Set 3: Newton's Laws of Motion, Motion: Force, Mass, and Acceleration, Vectors in Physics Solutions Problem

More information

Unit 2: Vector Dynamics

Unit 2: Vector Dynamics Multiple Choice Portion Unit 2: Vector Dynamics 1. Which one of the following best describes the motion of a projectile close to the surface of the Earth? (Assume no friction) Vertical Acceleration Horizontal

More information

dt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2

dt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2 v = v i + at a dv dt = d2 x dt 2 A sphere = 4πr 2 x = x i + v i t + 1 2 at2 x = r cos(θ) V sphere = 4 3 πr3 v 2 = v 2 i + 2a x F = ma R = v2 sin(2θ) g y = r sin(θ) r = x 2 + y 2 tan(θ) = y x a c = v2 r

More information

Review 3: Forces. 1. Which graph best represents the motion of an object in equilibrium? A) B) C) D)

Review 3: Forces. 1. Which graph best represents the motion of an object in equilibrium? A) B) C) D) 1. Which graph best represents the motion of an object in equilibrium? A) B) C) D) 2. A rock is thrown straight up into the air. At the highest point of the rock's path, the magnitude of the net force

More information

EQUATIONS OF MOTION: CYLINDRICAL COORDINATES

EQUATIONS OF MOTION: CYLINDRICAL COORDINATES Today s Objectives: Students will be able to: 1. Analyze the kinetics of a particle using cylindrical coordinates. EQUATIONS OF MOTION: CYLINDRICAL COORDINATES In-Class Activities: Check Homework Reading

More information

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B.

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B. 2003 B1. (15 points) A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown above. One end of the rope is held by Student A of mass 70 kg, who is at rest on

More information

Dynamics II Motion in a Plane. Review Problems

Dynamics II Motion in a Plane. Review Problems Dynamics II Motion in a Plane Review Problems Problem 1 A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N thrust

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You are standing in a moving bus, facing forward, and you suddenly fall forward as the

More information

Physics A - PHY 2048C

Physics A - PHY 2048C Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment

More information

Problem: Projectile (CM-1998)

Problem: Projectile (CM-1998) Physics C -D Kinematics Name: ANSWER KEY AP Review Packet Vectors have both magnitude and direction displacement, velocity, acceleration Scalars have magnitude only distance, speed, time, mass Unit vectors

More information

Kinematics. Vector solutions. Vectors

Kinematics. Vector solutions. Vectors Kinematics Study of motion Accelerated vs unaccelerated motion Translational vs Rotational motion Vector solutions required for problems of 2- directional motion Vector solutions Possible solution sets

More information

PHYS 100 Midterm Exam Review Session

PHYS 100 Midterm Exam Review Session PHYS 100 Midterm Exam Review Session y x F net on A = m a A A v = v + a t x 0x x x = x + v + a t 1 0 0x ( ) ( ) v = v + a x x x 0x x 0 x Physics 100 Midterm Review, Slide 1 Midterm Exam TODAY (Mar 9):

More information

March 10, P12 Inclined Planes.notebook. Physics 12. Inclined Planes. Push it Up Song

March 10, P12 Inclined Planes.notebook. Physics 12. Inclined Planes. Push it Up Song Physics 12 Inclined Planes Push it Up Song 1 Bell Work A box is pushed up a ramp at constant velocity. Draw a neatly labeled FBD showing all of the forces acting on the box. direction of motion θ F p F

More information

1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant

1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant 1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity

More information

Department of Natural Sciences Clayton State University. Physics 1111 Quiz 1

Department of Natural Sciences Clayton State University. Physics 1111 Quiz 1 Physics 1111 Quiz 1 January 14, 008 Name SOLUTION 1. If the velocity of the object, v, is related to time, t, according to the relation v = A + B t, the constant, A, has the dimension of which of the following?

More information

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh. 1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach

More information

CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS

CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS General properties of vectors displacement vector position and velocity vectors acceleration vector equations of motion in 2- and 3-dimensions Projectile motion

More information

Friction is always opposite to the direction of motion.

Friction is always opposite to the direction of motion. 6. Forces and Motion-II Friction: The resistance between two surfaces when attempting to slide one object across the other. Friction is due to interactions at molecular level where rough edges bond together:

More information

Physics 111. Lecture 10 (Walker: 5.5-6) Free Body Diagram Solving 2-D Force Problems Weight & Gravity. February 18, Quiz Monday - Chaps.

Physics 111. Lecture 10 (Walker: 5.5-6) Free Body Diagram Solving 2-D Force Problems Weight & Gravity. February 18, Quiz Monday - Chaps. Phsics 111 Lecture 10 (Walker: 5.5-6) Free Bod Diagram Solving -D Force Problems Weight & Gravit Februar 18, 009 Quiz Monda - Chaps. 4 & 5 Lecture 10 1/6 Third Law Review A small car is pushing a larger

More information

Newton s Laws and Free-Body Diagrams General Physics I

Newton s Laws and Free-Body Diagrams General Physics I Newton s Laws and Free-Body Diagrams In the next few sections, we will be exploring some of the most fundamental laws of our universe, laws that govern the relationship actions and motion. These laws are

More information

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14 Final Review: Chapters 1-11, 13-14 These are selected problems that you are to solve independently or in a team of 2-3 in order to better prepare for your Final Exam 1 Problem 1: Chasing a motorist This

More information

Chapter 3 Vectors in Physics

Chapter 3 Vectors in Physics Chapter 3 Vectors in Physics Is 1+1 always =2? Not true for vectors. Direction matters. Vectors in opposite directions can partially cancel. Position vectors, displacement, velocity, momentum, and forces

More information

PHYS 131 MIDTERM November 1 st, 2012

PHYS 131 MIDTERM November 1 st, 2012 PHYS 131 MIDTERM November 1 st, 2012 The exam comprises two parts: 8 short-answer questions, and 5 problems. Calculators are allowed, as well as a formula sheet (one-side of an 8½ x 11 sheet) of your own

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

PH211 Chapter 10 Solutions

PH211 Chapter 10 Solutions PH Chapter 0 Solutions 0.. Model: We will use the particle model for the bullet (B) and the running student (S). Solve: For the bullet, K B = m v = B B (0.00 kg)(500 m/s) = 50 J For the running student,

More information

Exam 3 Practice Solutions

Exam 3 Practice Solutions Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

More information

Base your answers to questions 5 and 6 on the information below.

Base your answers to questions 5 and 6 on the information below. 1. A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second

More information

PHYSICS 218 EXAM 2 Tuesday, October 26, 2010

PHYSICS 218 EXAM 2 Tuesday, October 26, 2010 PHYSICS 218 EXAM 2 Tuesday, October 26, 2010 NAME: SECTION: 513 514 515 516 Note: 513 Recitation & lab Wed 8:00-10:50 am 514 Recitation & lab Wed 11:30 am - 2:20 pm 515 Recitation & lab Wed 3:00-5:50 pm

More information

CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS

CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS OBJECTIVES After studying the material of this chapter, the student should be able to: represent the magnitude and direction of a vector using a protractor

More information

5. The graph represents the net force acting on an object as a function of time. During which time interval is the velocity of the object constant?

5. The graph represents the net force acting on an object as a function of time. During which time interval is the velocity of the object constant? 1. A 0.50-kilogram cart is rolling at a speed of 0.40 meter per second. If the speed of the cart is doubled, the inertia of the cart is A) halved B) doubled C) quadrupled D) unchanged 2. A force of 25

More information

Chapter Four Holt Physics. Forces and the Laws of Motion

Chapter Four Holt Physics. Forces and the Laws of Motion Chapter Four Holt Physics Forces and the Laws of Motion Physics Force and the study of dynamics 1.Forces - a. Force - a push or a pull. It can change the motion of an object; start or stop movement; and,

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

10. The vectors are V 1 = 6.0i + 8.0j, V 2 = 4.5i 5.0j. (a) For the magnitude of V 1 we have 2 1x + V 1y2 ) 1/2 = [( 6.0) 2 + (8.0) 2 ] 1/2 = 10.0.

10. The vectors are V 1 = 6.0i + 8.0j, V 2 = 4.5i 5.0j. (a) For the magnitude of V 1 we have 2 1x + V 1y2 ) 1/2 = [( 6.0) 2 + (8.0) 2 ] 1/2 = 10.0. 10. The vectors are V 1 = 6.0i + 8.0j, V 2 = 4.5i 5.0j. (a) For the magnitude of V 1 we have V 1 = (V 2 1x + V 1y2 ) 1/2 = [( 6.0) 2 + (8.0) 2 ] 1/2 = 10.0. We find the direction from tan θ 1 = V 1y /V

More information

Adding Vectors in Two Dimensions

Adding Vectors in Two Dimensions Slide 37 / 125 Adding Vectors in Two Dimensions Return to Table of Contents Last year, we learned how to add vectors along a single axis. The example we used was for adding two displacements. Slide 38

More information

Kinematics and Dynamics

Kinematics and Dynamics AP PHYS 1 Test Review Kinematics and Dynamics Name: Other Useful Site: http://www.aplusphysics.com/ap1/ap1- supp.html 2015-16 AP Physics: Kinematics Study Guide The study guide will help you review all

More information

a. Find the speed of the model airplane. b. On the diagram, draw a vector that shows the resultant velocity of the plane.

a. Find the speed of the model airplane. b. On the diagram, draw a vector that shows the resultant velocity of the plane. Vector diagrams *Vectors should be drawn tip-to-tail *Put arrows on all vectors *Resultant arrow goes toward last open arrow *angle is measured from the starting point a. Find the speed of the model airplane.

More information

5. REASONING AND SOLUTION An object will not necessarily accelerate when two or more forces are applied to the object simultaneously.

5. REASONING AND SOLUTION An object will not necessarily accelerate when two or more forces are applied to the object simultaneously. 5. REASONING AND SOLUTION An object will not necessarily accelerate when two or more forces are applied to the object simultaneously. The applied forces may cancel so the net force is zero; in such a case,

More information

EQUATIONS OF MOTION: CYLINDRICAL COORDINATES (Section 13.6)

EQUATIONS OF MOTION: CYLINDRICAL COORDINATES (Section 13.6) EQUATIONS OF MOTION: CYLINDRICAL COORDINATES (Section 13.6) Today s Objectives: Students will be able to analyze the kinetics of a particle using cylindrical coordinates. APPLICATIONS The forces acting

More information

Chapter 4 Kinematics II: Motion in Two and Three Dimensions

Chapter 4 Kinematics II: Motion in Two and Three Dimensions Chapter 4 Kinematics II: Motion in Two and Three Dimensions Demonstrations: 1) Ball falls down and another falls out 2) Parabolic and straight line motion from two different frames. The truck with a dropping

More information

66 Chapter 6: FORCE AND MOTION II

66 Chapter 6: FORCE AND MOTION II Chapter 6: FORCE AND MOTION II 1 A brick slides on a horizontal surface Which of the following will increase the magnitude of the frictional force on it? A Putting a second brick on top B Decreasing the

More information

Physics 1100: 2D Kinematics Solutions

Physics 1100: 2D Kinematics Solutions Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Physics 1100: 2D Kinematics Solutions 1. In the diagrams below, a ball is on a flat horizontal surface. The initial velocity

More information

Chapter 8. Dynamics II: Motion in a Plane

Chapter 8. Dynamics II: Motion in a Plane Chapter 8. Dynamics II: Motion in a Plane A roller coaster doing a loop-the-loop is a dramatic example of circular motion. But why doesn t the car fall off the track when it s upside down at the top of

More information

Rotational Motion. Rotational Motion. Rotational Motion

Rotational Motion. Rotational Motion. Rotational Motion I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x =

More information

Version PREVIEW Semester 1 Review Slade (22222) 1

Version PREVIEW Semester 1 Review Slade (22222) 1 Version PREVIEW Semester 1 Review Slade () 1 This print-out should have 48 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A

More information

Chapter 3 Acceleration

Chapter 3 Acceleration Chapter 3 Acceleration Slide 3-1 PackBack The first answer gives a good physical picture. The video was nice, and worth the second answer. https://www.youtube.com/w atch?v=m57cimnj7fc Slide 3-2 Slide 3-3

More information

INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION

INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION (Sections 12.1-12.2) Today s Objectives: Students will be able to find the kinematic quantities (position, displacement, velocity, and acceleration)

More information

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

G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice exam G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice exam G r a d e 1 1 P h y s i c s ( 3 0 s ) Final Practice Exam Instructions The final exam will be weighted as follows: Modules 1 6 15 20% Modules

More information

SMU Physics 1313 : Fall 2008 Exam 1

SMU Physics 1313 : Fall 2008 Exam 1 SMU Physics 1313 : all 2008 Exam 1 1. Complete the following statement: The term net force most accurately describes (a) the mass of an object. (b) the inertia of an object. (c) the quantity that causes

More information

EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5)

EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5) EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5) Today s Objectives: Students will be able to apply the equation of motion using normal and tangential coordinates. APPLICATIONS Race

More information

Isaac Newton. What is a force? Newton s Three Laws of Motion. What is the acceleration of the car?

Isaac Newton. What is a force? Newton s Three Laws of Motion. What is the acceleration of the car? Aim: What did Isaac Newton teach us about motion? Do Now: 1. A 2009 Ford Mustang convertible is travelling at constant velocity on Interstate 95 south from Philadelphia to Wilmington Delaware. It passes

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 Copyright 2010 Pearson Education, Inc. Force and Mass Copyright 2010 Pearson Education, Inc. Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion

More information

HATZIC SECONDARY SCHOOL

HATZIC SECONDARY SCHOOL HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT VECTOR DYNAMICS MULTIPLE CHOICE / 45 OPEN ENDED / 75 TOTAL / 120 NAME: 1. Unless acted on by an external net force, an object will stay at rest

More information

Physics A - PHY 2048C

Physics A - PHY 2048C Physics A - PHY 2048C Newton s Laws & Equations of 09/27/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 In uniform circular motion (constant speed), what is the direction

More information

Other Examples of Energy Transfer

Other Examples of Energy Transfer Chapter 7 Work and Energy Overview energy. Study work as defined in physics. Relate work to kinetic energy. Consider work done by a variable force. Study potential energy. Understand energy conservation.

More information

Forces on a banked airplane that travels in uniform circular motion.

Forces on a banked airplane that travels in uniform circular motion. Question (60) Forces on a banked airplane that travels in uniform circular motion. A propeller-driven airplane of mass 680 kg is turning in a horizontal circle with a constant speed of 280 km/h. Its bank

More information

PHYSICS FORMULAS. A. B = A x B x + A y B y + A z B z = A B cos (A,B)

PHYSICS FORMULAS. A. B = A x B x + A y B y + A z B z = A B cos (A,B) PHYSICS FORMULAS A = A x i + A y j Φ = tan 1 A y A x A + B = (A x +B x )i + (A y +B y )j A. B = A x B x + A y B y + A z B z = A B cos (A,B) linear motion v = v 0 + at x - x 0 = v 0 t + ½ at 2 2a(x - x

More information

PHY 1114: Physics I. Quick Question 1. Quick Question 2. Quick Question 3. Quick Question 4. Lecture 5: Motion in 2D

PHY 1114: Physics I. Quick Question 1. Quick Question 2. Quick Question 3. Quick Question 4. Lecture 5: Motion in 2D PHY 1114: Physics I Lecture 5: Motion in D Fall 01 Kenny L. Tapp Quick Question 1 A child throws a ball vertically upward at the school playground. Which one of the following quantities is (are) equal

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

PHYSICS 231 INTRODUCTORY PHYSICS I

PHYSICS 231 INTRODUCTORY PHYSICS I PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 6 Last Lecture: Gravity Normal forces Strings, ropes and Pulleys Today: Friction Work and Kinetic Energy Potential Energy Conservation of Energy Frictional Forces

More information

Department of Natural Sciences Clayton State University. Physics 1111 Quiz 1

Department of Natural Sciences Clayton State University. Physics 1111 Quiz 1 Physics 1111 Quiz 1 August 27, 2007 Name SOLUTION 1. If the displacement of the object, x, is related to time, t, according to the relation x = A t, the constant, A, has the dimension of which of the following?

More information

Physics 111. Applying Newton s Laws. Lecture 9 (Walker: 5.4-5) Newton s Third Law Free Body Diagram Solving 2-D Force Problems Weight & Gravity

Physics 111. Applying Newton s Laws. Lecture 9 (Walker: 5.4-5) Newton s Third Law Free Body Diagram Solving 2-D Force Problems Weight & Gravity Phsics 111 Lecture 9 (Walker: 5.4-5) Newton s Third Law ree Bod Diagram Solving -D orce Problems Weight & Gravit Sept. 1, 009 Quiz Wednesda - Chaps. 3 & 4 Lecture 9 1/6 Newton s Third Law of Motion orces

More information

Chapter 3 Acceleration

Chapter 3 Acceleration Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide

More information

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam.

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam. WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system is always

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

W = 750 m. PHYS 101 SP17 Exam 1 BASE (A) PHYS 101 Exams. The next two questions pertain to the situation described below.

W = 750 m. PHYS 101 SP17 Exam 1 BASE (A) PHYS 101 Exams. The next two questions pertain to the situation described below. PHYS 101 Exams PHYS 101 SP17 Exa BASE (A) The next two questions pertain to the situation described below. A boat is crossing a river with a speed to the water. The river is flowing at a speed W = 750

More information

Tutorial 1. Phys 201 Examples

Tutorial 1. Phys 201 Examples Tutorial 1 Phys 201 Examples 0 TUTORIAL 1. PHYS 201 EXAMPLES 1 Examples PHYS 201 - General Physics Eastern Oregon University TUTORIAL 1. PHYS 201 EXAMPLES 2 Chapter 1 Systems of Measurement Example 1.0:

More information

P. O. D. Station 2. You already have the real time. You found that with your stop watch.

P. O. D. Station 2. You already have the real time. You found that with your stop watch. P. O. D. Station 2 In Station 2 you have to find the real time (t real ), the real acceleration (a real )and the real force (Force real ). Then you have to find the ideal force, the ideal acceleration,

More information

EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES

EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES Today s Objectives: Students will be able to: 1. Apply the equation of motion using normal and tangential coordinates. In-Class Activities: Check

More information

The University of Hong Kong Department of Physics

The University of Hong Kong Department of Physics The University of Hong Kong Department of Physics PHYS2250 Introductory Mechanics Teaching notes September 2017 Course title Introductory Mechanics Aim This course covers the foundation of mechanics in

More information

PHYS 111 K SECOND HOUR EXAM 2015

PHYS 111 K SECOND HOUR EXAM 2015 PHYS 111 K SECOND HOUR EXAM 2015 This is a closed book closed note exam. Do all your writing in your blue book (s) and be sure to put your name on each blue book you use. You will not need nor are permitted

More information

Uniform Circular Motion

Uniform Circular Motion Uniform Circular Motion 2.4 Knowledge and Skills Checklist Do I know that uniform circular motion means that a body is moving in a circular path with constant speed? Do I know that, although the speed

More information

LECTURE 30: Conservation of energy

LECTURE 30: Conservation of energy Lectures Page 1 LECTURE 30: Conservation of energy Select LEARNING OBJECTIVES: i. ii. iii. iv. Differentiate between the vector nature of momentum conservation and the scalar nature of energy conservation.

More information

Potential Energy. Serway 7.6, 7.7;

Potential Energy. Serway 7.6, 7.7; Potential Energy Conservative and non-conservative forces Gravitational and elastic potential energy Mechanical Energy Serway 7.6, 7.7; 8.1 8.2 Practice problems: Serway chapter 7, problems 41, 43 chapter

More information

UNIT-07. Newton s Three Laws of Motion

UNIT-07. Newton s Three Laws of Motion 1. Learning Objectives: UNIT-07 Newton s Three Laws of Motion 1. Understand the three laws of motion, their proper areas of applicability and especially the difference between the statements of the first

More information

Physics for Scientists and Engineers. Chapter 6 Dynamics I: Motion Along a Line

Physics for Scientists and Engineers. Chapter 6 Dynamics I: Motion Along a Line Physics for Scientists and Engineers Chapter 6 Dynamics I: Motion Along a Line Spring, 008 Ho Jung Paik Applications of Newton s Law Objects can be modeled as particles Masses of strings or ropes are negligible

More information

Lecture Outline Chapter 5. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 5. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 5 Physics, 4 th Edition James S. Walker 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

More information

Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. A/Prof Tay Seng Chuan

Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. A/Prof Tay Seng Chuan PC1221 Fundamentals of Physics I Lectures 9 and 10 The Laws of Motion A/Prof Tay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while

More information

Physics 1100: Uniform Circular Motion & Gravity

Physics 1100: Uniform Circular Motion & Gravity Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics 1100: Uniform Circular Motion & Gravity 1. In the diagram below, an object travels over a hill, down a valley, and around a loop the loop at constant

More information

Physics Mechanics. Lecture 11 Newton s Laws - part 2

Physics Mechanics. Lecture 11 Newton s Laws - part 2 Physics 170 - Mechanics Lecture 11 Newton s Laws - part 2 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: Newton s Second Law of

More information

AP Physics. Harmonic Motion. Multiple Choice. Test E

AP Physics. Harmonic Motion. Multiple Choice. Test E AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.

More information

Chapter 10 Momentum, System of Particles, and Conservation of Momentum

Chapter 10 Momentum, System of Particles, and Conservation of Momentum Chapter 10 Momentum, System of Particles, and Conservation of Momentum 10.1 Introduction... 1 10. Momentum (Quantity of Motion) and Impulse... 1 10..1 Average Force, Momentum, and Impulse... 10.. Non-Constant

More information

Dynamics; Newton s Laws of Motion

Dynamics; Newton s Laws of Motion Dynamics; Newton s Laws of Motion Force A force is any kind of push or pull on an object. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The magnitude

More information

t = g = 10 m/s 2 = 2 s T = 2π g

t = g = 10 m/s 2 = 2 s T = 2π g Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the

More information

Chapter 3 Motion in two or three dimensions

Chapter 3 Motion in two or three dimensions Chapter 3 Motion in two or three dimensions Lecture by Dr. Hebin Li Announcements As requested by the Disability Resource Center: In this class there is a student who is a client of Disability Resource

More information