Example (1): Motion of a block on a frictionless incline plane


 Geoffrey Page
 2 years ago
 Views:
Transcription
1 Firm knowledge of vector analysis and kinematics is essential to describe the dynamics of physical systems chosen for analysis through ewton s second law. Following problem solving strategy will allow you to tackle the problems with greater ease. Problem solving strategy: 1) Write the equation of motion F net = ma. Where, F net is the net force and a is the acceleration vector and is equal to a x i + a y j. 2) Draw a free body diagram (FBD) which shows all forces acting on the object/ objects. Do not draw the components of the force on the FBD. 3) Specify a coordinate system. Take xaxis in direction of the motion and yaxis perpendicular to the motion. 4) Express every force in a vector form. 5) In order to get the resultant force, F net, add all force vectors. 6) From the x and y components of F net, construct your x and y equations of motion. If the acceleration has a component in x direction, the xcomponent of the resultant vector is equal to ma x, otherwise it is equal to zero. Also, if the acceleration has a component in y direction, the ycomponent of the resultant vector is equal to ma y, otherwise it is equal to zero. 7) Depending on the question, solve the equation or the set of equations simultaneously for the unknown. Example (1): Motion of a block on a frictionless incline plane The figure below shows an object of mass m moving on a frictionless inclined plane which makes an angle with the horizontal. a) Find the acceleration of the block in terms of the constants g and. b) If the block started from rest and travelled a distance d, find the final speed of the block and the time it took to cover this distance. m
2 SOLUTIO: a) Our object is an accelerating block on a frictionless incline plane. ow, let s follow stepbystep the problem solving strategy and solve for the acceleration. STEP (1): Write the equation of motion F net = ma. Where, F net is the net force and a is the acceleration vector and is equal to a x i + a y j. STEP (2): Draw a free body diagram (FBD) which shows all forces acting on the object/ objects. Do not draw the components of the forces on the FBD. Based on our problem, we have only one object (the block) and there are two forces acting on the block. The forces are: 1) : Force of gravity due to the earth is pulling the block downward 2) : the normal force due to the surface is pushing the block perpendicular to the plane. STEP (3): Specify a coordinate system. Take x axis in direction of the motion and y axis perpendicular to the motion. The Fig. below shows the motion is in direction of x axis while yaxis is perpendicular to the motion. The forces and acting on the block are also shown. yaxis a i j j i cos sin xaxis
3 STEP (4): Express every force in a vector form. This can be done by resolving every force vector into its components. Therefore, from the geometry of the above figure, vectors and can be written as = j (1) = sin i  cos j (2) STEP (5): In order to get the resultant force, F net, add all force vectors. Based on our problem, equations (1) and (2) can be added, we get F net = + = j + sin i  cos j Since F net = ma and a = a x i + a y j, we can write sin i + (  cos) j = m (a x i + a y j) Where, (F net ) x = sin is the xcomponent of the resultant force (3) (F net ) y =  cos is the ycomponent of the resultant force (4) STEP (6): From the x and y component of F net, construct your x and y equations of motion. If the acceleration has a component in x direction, the xcomponent of the resultant vector is equal to ma x, otherwise it is equal to zero. Also, if the acceleration has a component in y direction, the ycomponent of the resultant vector is equal to ma y, otherwise it is equal to zero. Based on our problem, the motion of the block is in direction of x while there is no acceleration in y direction. Thus, from Eq. (3) and (4) the equations of motions are: sin = ma x and  cos = 0 STEP (7): Depending on the question, solve the set of equations simultaneously for the unknown. As we see, we were able to construct our equations of motion for the block. The acceleration can be found from the first equation, sin = ma x. The second equation has no
4 use in this problem unless we are asked to find the magnitude of the normal force. Thus, with = mg, we get mg sin = ma x. Therefore, a x = g sin Or in vector form a = g sin i ote, maximum acceleration is when = 90 o. This corresponds to a free falling object with a x = g = 9.8 m/s 2. Also, the acceleration does not depend on the mass of the object. b) Since the acceleration is constant, the final speed of the block can be found by using the kinematic equation, v 2 fx = v 2 ix + 2a x d. With v i = 0 and a x = g sin, we get v 2 fx = 2gd sin Therefore, v fx = 2gd sin The time it took the block to cover a distance d can be calculated using the kinematic equation, v fx = v ix + a x t With v ix = 0, v fx = 2gd sin and a x = g sin, we get 2gd sin = (g sin) t t = 2gd sin g sin t = 2d g sin
5 Example (2): Motion of a block on a rough incline plane The figure below shows an object of mass m moving on a rough inclined plane which makes an angle with the horizontal. If the coefficient of kinetic friction between the surface and the block is μ k, find the acceleration of the block in terms of the constants g, and μ k. m SOLUTIO: Problem solving strategy: STEP (1): F net = ma. Where, F net is the net force and a is the acceleration vector and is equal to a x i + a y j. STEP (2): Draw a free body diagram (FBD) which shows all forces acting on the object F f STEP (3) Specify a coordinate system and resolve the forces into x and y components. Take x axis in direction of the motion and yaxis perpendicular to the motion. cos F f a yaxis sin xaxis i j j i
6 STEP (4): Express every force in a vector form. There are three forces acting on the block:, and F f. Therefore, from the geometry of the above figure, the three force vectors can be written as = j (1) = sin i  cos j (2) F f = F f i (3) STEP (5): In order to get the resultant force, F net, add all force vectors, Eq. 1, 2 and 3, F net = + + F f = j + ( sin i cos j ) F f i F net = ( sin F f ) i + ( cos) j (4) STEP (6): Construct your x and y equations of motion. The xcomponent of the resultant vector is equal to ma x and the ycomponent of the resultant vector is equal to ma y. Thus from Eq. (4), the equations of motion are: sin F f = ma x (5) cos = ma y = 0, since the acceleration in y direction is zero. (6) STEP (7): ow, let s solve for the acceleration. Since, F f = μ k = μ k cos, where we used Eq. (6) for the value of. Thus, Eq. (5) becomes, sin μ k cos = ma x With = mg, the magnitude of the acceleration is equal to a x = g (sin μ k cos) Or in vector form a = g (sin μ k cos) i
7 OTE: If the surface is frictionless, i.e. μ k = 0, the magnitude of the acceleration will be reduced to g sin as discussed in example number (1). Also note, the acceleration of the block on a rough plan is less than its acceleration on a smooth plane by the amount μ k g cos.
CHAPTER 3 NEWTON S LAWS OF MOTION
CHAPTER 3 NEWTON S LAWS OF MOTION NEWTON S LAWS OF MOTION 45 3.1 FORCE Forces are calssified as contact forces or gravitational forces. The forces that result from the physical contact between the objects
More informationPhysics 101 Exam 1 NAME 2/7
Physics 101 Exam 1 NAME 2/7 1 In the situation below, a person pulls a string attached to block A, which is in turn attached to another, heavier block B via a second string (a) Which block has the larger
More informationA Review of Vector Addition
Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine
More informationChapter Test. Teacher Notes and Answers Forces and the Laws of Motion. Assessment
Assessment Chapter Test A Teacher Notes and Answers Forces and the Laws of Motion CHAPTER TEST A (GENERAL) 1. c 2. d 3. d 4. c 5. c 6. c 7. c 8. b 9. d 10. d 11. c 12. a 13. d 14. d 15. b 16. d 17. c 18.
More informationB Answer: neither of these. Mass A is accelerating, so the net force on A must be nonzero Likewise for mass B.
CTA1. An Atwood's machine is a pulley with two masses connected by a string as shown. The mass of object A, m A, is twice the mass of object B, m B. The tension T in the string on the left, above mass
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationPHYS101 The Laws of Motion Spring 2014
The Laws of Motion 1. An object of mass m 1 = 55.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m 2
More informationGround Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. Dr Tay Seng Chuan
PC1221 Fundamentals of Physics I Lectures 9 and 10 he Laws of Motion Dr ay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while lecture
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationTwoBody System: Two Hanging Masses
Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.
More informationNewton s Law of Motion
chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating
More informationNewton s Laws of Motion
Physics Newton s Laws of Motion Newton s Laws of Motion 4.1 Objectives Explain Newton s first law of motion. Explain Newton s second law of motion. Explain Newton s third law of motion. Solve problems
More informationTEACHER ANSWER KEY November 12, 2003. Phys  Vectors 11132003
Phys  Vectors 11132003 TEACHER ANSWER KEY November 12, 2003 5 1. A 1.5kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude
More informationForces. Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies.
Forces Now we will discuss the part of mechanics known as dynamics. We will introduce Newton s three laws of motion which are at the heart of classical mechanics. We must note that Newton s laws describe
More informationObjective: Equilibrium Applications of Newton s Laws of Motion I
Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (111) Read (4.14.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,
More informationCollege Physics 140 Chapter 4: Force and Newton s Laws of Motion
College Physics 140 Chapter 4: Force and Newton s Laws of Motion We will be investigating what makes you move (forces) and how that accelerates objects. Chapter 4: Forces and Newton s Laws of Motion Forces
More informationWhat is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact?
Chapter 4: Forces What is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact? Application different forces (field forces, contact
More informationDISPLACEMENT 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 informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problemsolving questions, draw appropriate free body diagrams and use the aforementioned problemsolving method.. Define the following
More informationNewton s Laws PreTest
Newton s Laws PreTest 1.) Consider the following two statements and then select the option below that is correct. (i) It is possible for an object move in the absence of forces acting on the object. (ii)
More informationPH2213 : Examples from Chapter 4 : Newton s Laws of Motion. Key Concepts
PH2213 : Examples from Chapter 4 : Newton s Laws of Motion Key Concepts Newton s First and Second Laws (basically Σ F = m a ) allow us to relate the forces acting on an object (lefthand side) to the motion
More information041. Newton s First Law Newton s first law states: Sections Covered in the Text: Chapters 4 and 8 F = ( F 1 ) 2 + ( F 2 ) 2.
Force and Motion Sections Covered in the Text: Chapters 4 and 8 Thus far we have studied some attributes of motion. But the cause of the motion, namely force, we have essentially ignored. It is true that
More informationHW#4b Page 1 of 6. I ll use m = 100 kg, for parts bc: accelerates upwards, downwards at 5 m/s 2 A) Scale reading is the same as person s weight (mg).
HW#4b Page 1 of 6 Problem 1. A 100 kg person stands on a scale. a.) What would be the scale readout? b.) If the person stands on the scale in an elevator accelerating upwards at 5 m/s, what is the scale
More informationApplication of Newton s Second Law Challenge Problem Solutions
Problem 1: Painter on a Platform Application of Newton s Second Law Challenge Problem Solutions A painter of mass m 1 stands on a platform of mass m 2 and pulls himself up by two ropes that run over massless
More informationAP Physics Newton's Laws Practice Test
AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a
More informationLecture 9. Friction in a viscous medium Drag Force Quantified
Lecture 9 Goals Describe Friction in Air (Ch. 6) Differentiate between Newton s 1 st, 2 nd and 3 rd Laws Use Newton s 3 rd Law in problem solving Assignment: HW4, (Chap. 6 & 7, due 10/5) 1 st Exam Thurs.,
More informationChapter 5 Newton s Laws of Motion
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 informationForces & Newton s Laws. Teacher Packet
AP * PHYSICS B Forces & Newton s Laws eacher Packet AP* is a trademark of the College Entrance Examination Board. he College Entrance Examination Board was not involved in the production of this material.
More informationVersion 001 Quest 3 Forces tubman (20131) 1
Version 001 Quest 3 Forces tubman (20131) 1 This printout should have 19 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. l B Conceptual
More information2. What magnitude of net force is required to give a 135kg refrigerator an acceleration of magnitude 1.40 m/. [189 N]
PAGE 1 OF 14 EMAIL: MIAMIMATHTUTOR@GMAIL.COM CONTACT NUMBER: (786)5564839 PHYSICS I NEWTON S LAWS OF MOTION PRACTICE PROBLEMS 5.1 1. If a net horizontal force of 130 N is applied to a person with mass
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationMotion Lesson 1: Review of Basic Motion
Motion in one and two dimensions: Lesson 1 Seminotes Motion Lesson 1: Review of Basic Motion Note. For these semi notes we will use the bold italics convention to represent vectors. Complete the following
More informationUniversity Physics 226N/231N Old Dominion University. Getting Loopy and Friction
University Physics 226N/231N Old Dominion University Getting Loopy and Friction Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012odu Friday, September 28 2012 Happy
More informationUniversity Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples
University Physics 226N/231N Old Dominion University Newton s Laws and Forces Examples Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012odu Wednesday, September
More informationVectors and the Inclined Plane
Vectors and the Inclined Plane Introduction: This experiment is designed to familiarize you with the concept of force as a vector quantity. The inclined plane will be used to demonstrate how one force
More informationSerway_ISM_V1 1 Chapter 4
Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationPhysics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.
Physics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and noncontact forces. Whats a
More informationMULTIPLE 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) The following four forces act on a 4.00 kg object: 1) F 1 = 300 N east F 2 = 700 N north
More informationf max s = µ s N (5.1)
Chapter 5 Forces and Motion II 5.1 The Important Stuff 5.1.1 Friction Forces Forces which are known collectively as friction forces are all around us in daily life. In elementary physics we discuss the
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationTHE NATURE OF FORCES Forces can be divided into two categories: contact forces and noncontact forces.
SESSION 2: NEWTON S LAWS Key Concepts In this session we Examine different types of forces Review and apply Newton's Laws of motion Use Newton's Law of Universal Gravitation to solve problems Xplanation
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationSpinning Stuff Review
Spinning Stuff Review 1. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50kg object, as shown in the figure below. When released
More informationNewton's laws of motion
Newton's laws of motion Forces Forces as vectors Resolving vectors Explaining motion  Aristotle vs Newton Newton s first law Newton s second law Weight Calculating acceleration Newton s third law Moving
More informationWork. Work = Force distance (the force must be parallel to movement) OR Work = (Force)(cos θ)(distance)
Work Work = Force distance (the force must be parallel to movement) OR Work = (Force)(cos θ)(distance) When you are determining the force parallel to the movement you can do this manually and keep track
More information3. KINEMATICS IN TWO DIMENSIONS; VECTORS.
3. KINEMATICS IN TWO DIMENSIONS; VECTORS. Key words: Motion in Two Dimensions, Scalars, Vectors, Addition of Vectors by Graphical Methods, Tail to Tip Method, Parallelogram Method, Negative Vector, Vector
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationNewton s Laws of Motion
Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first
More informationMOTION AND FORCE: DYNAMICS
MOTION AND FORCE: DYNAMICS We ve been dealing with the fact that objects move. Velocity, acceleration, projectile motion, etc. WHY do they move? Forces act upon them, that s why! The connection between
More informationThis week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.
This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical
More informationNewton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1
Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is
More informationPhysics1 Recitation3
Physics1 Recitation3 The Laws of Motion 1) The displacement of a 2 kg particle is given by x = At 3/2. In here, A is 6.0 m/s 3/2. Find the net force acting on the particle. (Note that the force is time
More informationPH 2211D Spring Force and Motion II. Lecture Chapter 6 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 2211D Spring 2013 Force and Motion II Lecture 1213 Chapter 6 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) Chapter 6 Force and Motion II In this chapter we will cover the following
More information3) a 1 = a 2. 5) a 1 = 2 a 2
ConcepTest Pulley Two masses are connected by a light rope as shown below. What is the 1) a 1 = 1/3 a 2 2) a 1 = ½ a 2 relationship between the magnitude of 3) a 1 = a 2 the acceleration of m 1 to that
More informationLesson 04: Newton s laws of motion
www.scimsacademy.com Lesson 04: Newton s laws of motion If you are not familiar with the basics of calculus and vectors, please read our freely available lessons on these topics, before reading this lesson.
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More informationCh. 5, Force and MotionI
Ch. 5, Force and MotionI Newton s First Law Force Mass Newton s Second Law (Newton s Third Law Next Thursday) Isaac Newton s work represents one of the greatest contributions to science ever made by an
More informationUNIT 2D. Laws of Motion
Name: Regents Physics Date: Mr. Morgante UNIT 2D Laws of Motion Laws of Motion Science of Describing Motion is Kinematics. Dynamics the study of forces that act on bodies in motion. First Law of Motion
More informationProjectile Motion. directions simultaneously. deal with is called projectile motion. ! An object may move in both the x and y
Projectile Motion! An object may move in both the x and y directions simultaneously! The form of twodimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion! The
More informationSOLID MECHANICS DYNAMICS TUTORIAL INERTIA FORCES IN MECHANISMS
SOLID MECHANICS DYNAMICS TUTORIAL INERTIA FORCES IN MECHANISMS This work covers elements of the syllabus for the Engineering Council Exam D225 Dynamics of Mechanical Systems C103 Engineering Science. This
More informationF = ma. F = mg. Forces. Forces. Free Body Diagrams. Find the unknown forces!! Ex. 1 Ex N. Newton s First Law. Newton s Second Law
Forces Free Body Diagrams Push or pull on an object Causes acceleration Measured in Newtons N = Kg m s Shows all forces as vectors acting on an object Vectors always point away from object Used to help
More informationPhysics Notes Class 11 CHAPTER 5 LAWS OF MOTION
1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is
More informationChapter 5 Newton s Laws of Motion
Chapter 5 Newton s Laws of Motion Sir Isaac Newton (1642 1727) Developed a picture of the universe as a subtle, elaborate clockwork slowly unwinding according to welldefined rules. The book Philosophiae
More informationAP Physics Applying Forces
AP Physics Applying Forces This section of your text will be very tedious, very tedious indeed. (The Physics Kahuna is just as sorry as he can be.) It s mostly just a bunch of complicated problems and
More informationF f v 1 = c100(10 3 ) m h da 1h 3600 s b =
14 11. The 2Mg car has a velocity of v 1 = 100km>h when the v 1 100 km/h driver sees an obstacle in front of the car. It takes 0.75 s for him to react and lock the brakes, causing the car to skid. If
More informationChapter 11 Equilibrium
11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of
More informationRecap. A force is the product of an object s mass and acceleration. Forces are the reason why objects change their velocity. Newton s second law:
Recap A force is the product of an object s mass and acceleration. Forces are the reason why objects change their velocity. Newton s second law: Unit: 1 N = 1 kg m/s 2 Forces are vector quantities, since
More informationForce & Motion. Force & Mass. Friction
1 2 3 4 Next Force & Motion The motion of an object can be changed by an unbalanced force. The way that the movement changes depends on the strength of the force pushing or pulling and the mass of the
More informationLab: 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 PreLab You are required to finish this section before coming to the lab. It will be checked by one of the
More informationChapter 5 Problems. = 9ˆ i + 0 ˆ j F 2 F 1. = 8cos62 ˆ i + 8sin62 ˆ j. = (9 8cos62 ) i ˆ + (8sin62 ) ˆ j = i ˆ ˆ j =
Chapter 5 Problems 5.1 Only two horizontal forces act on a 3.0 kg body. One force is 9.0N, acting due east, and the other is 8.0N act 62 degrees North of west. What is the magnitude of the body s acceleration?
More informationChapter 4. Forces I. 4.1 The Important Stuff Newton s First Law Newton s Second Law
Chapter 4 Forces I 4.1 The Important Stuff 4.1.1 Newton s First Law With Newton s Laws we begin the study of how motion occurs in the real world. The study of the causes of motion is called dynamics, or
More informationChapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.
Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationPhysics 201 Fall 2009 Exam 2 October 27, 2009
Physics 201 Fall 2009 Exam 2 October 27, 2009 Section #: TA: 1. A mass m is traveling at an initial speed v 0 = 25.0 m/s. It is brought to rest in a distance of 62.5 m by a force of 15.0 N. The mass is
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More information1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C. PHYS 11: Chap. 2, Pg 2
1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C PHYS 11: Chap. 2, Pg 2 1 1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All three A B PHYS 11: Chap. 2, Pg 3 C 1) more than
More informationPHYS 1111L LAB 2. The Force Table
In this laboratory we will investigate the vector nature of forces. Specifically, we need to answer this question: What happens when two or more forces are exerted on the same object? For instance, in
More informationNewton s Laws of Motion. Chapter 4
Newton s Laws of Motion Chapter 4 Changes in Motion Section 4.1 Force is simply a push or pull It is an interaction between two or more objects Force is a vector so it has magnitude and direction In the
More informationGeneral Physics I Can Statements
General Physics I Can Statements Motion (Kinematics) 1. I can describe motion in terms of position (x), displacement (Δx), distance (d), speed (s), velocity (v), acceleration (a), and time (t). A. I can
More information1.3 Displacement in Two Dimensions
1.3 Displacement in Two Dimensions So far, you have learned about motion in one dimension. This is adequate for learning basic principles of kinematics, but it is not enough to describe the motions of
More informationDynamics Pulleys, Ramps, and Friction
Name School Date Purpose To investigate the vector nature of forces. To practice the use freebody diagrams (FBDs). To learn to apply Newton s Second Law to systems of masses connected by pulleys. Equipment
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationThe Big Idea. Key Concepts
The Big Idea Acceleration is caused by force. All forces come in pairs because they arise in the interaction of two objects you can t hit without being hit back! The more force applied, the greater the
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationRotation, Angular Momentum
This test covers rotational motion, rotational kinematics, rotational energy, moments of inertia, torque, crossproducts, angular momentum and conservation of angular momentum, with some problems requiring
More informationChapter 3 Solutions. Figure 3.7a. (b) Thus (c) velocity: At. Figure 3.7b
Chapter 3 Solutions 3.7.IDENTIFY and Use Eqs. (3.4) and (3.12) to find and as functions of time. The magnitude and direction of and can be found once we know their components. (a) Calculate x and y for
More informationMidterm Exam 1 October 2, 2012
Midterm Exam 1 October 2, 2012 Name: Instructions 1. This examination is closed book and closed notes. All your belongings except a pen or pencil and a calculator should be put away and your bookbag should
More informationSingle and Double plane pendulum
Single and Double plane pendulum Gabriela González 1 Introduction We will write down equations of motion for a single and a double plane pendulum, following Newton s equations, and using Lagrange s equations.
More information2Elastic collisions in
After completing this chapter you should be able to: solve problems about the impact of a smooth sphere with a fixed surface solve problems about the impact of smooth elastic spheres. In this chapter you
More informationAnnouncements. Dry Friction
Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics
More informationWeight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)
Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in
More informationIf you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ
Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces
More information= Σ = PILOT PILOT PLANE PLANE. = m/s 13.1kg kg. SOLUTION The magnitude of the average net force applied to the fist is, therefore,
CHAPTER 4 FORCES AND NEWTON'S LAWS OF MOTION PROBLEMS 1. REASONING AND SOLUTION According to Newton s second law, the acceleration is a = ΣF/m. Since the pilot and the plane have the same acceleration,
More informationPhysics 211 Week 12. Simple Harmonic Motion: Equation of Motion
Physics 11 Week 1 Simple Harmonic Motion: Equation of Motion A mass M rests on a frictionless table and is connected to a spring of spring constant k. The other end of the spring is fixed to a vertical
More informationEQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS
EQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS Today s Objectives: Students will be able to: 1. Analyze the planar kinetics of a rigid body undergoing rotational motion. InClass Activities: Applications
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More informationEQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS
EQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS Today s Objectives: Students will be able to: 1. Analyze the planar kinetics InClass Activities: of a rigid body undergoing rotational motion. Check Homework
More information