Physics 172H. Lecture 6 Ball-Spring Model of Solids, Friction. Read

Size: px
Start display at page:

Download "Physics 172H. Lecture 6 Ball-Spring Model of Solids, Friction. Read"

Transcription

1 Physics 172H Lecture 6 Ball-Spring Model of Solids, Friction Read

2 Model of solid: chemical bonds d radial force (N) 0 F linear If atoms don t move too far away from equilibrium, force looks like a spring force!

3 A ball-spring model of a solid Ball-spring model of a solid To model need to know: - spring length s - spring stiffness - mass of an atom

4 Initial conditions for circular motion

5 Length of a bond: diameter of copper atom 1. Number of atoms in one cm 3 density ρ = 8.94 g/cm 3 : molecular weight = g/mole N A molecules g/cm 23 atoms 22 atoms N = = g/mole mole cm 2. Volume per one atom: V Cu 1 cm = = atoms/cm atom 3. Interatomic spacing: d Cu = cm 3 = cm= m=2.27

6 Ball-Spring Model of a Wire How is the stiffness of the wire related to the stiffness of one of the short springs (bonds)?

7 Two Springs in Series Spring constant k Mass M Each spring must supply an upward force equal to Mg, thus, each stretches by s giving a total stretch of 2s, or an effective spring constant of k/2.

8 Two Springs in Parallel Mass M Each spring provides an upward force of Mg/2, so each stretches s/2, giving an effective spring constant of 2k.

9 Stiffness of a Copper Wire 2-meter long Cu wire 8.8 x 10 9 bonds in series 1.94 x chains in parallel Each side = 1 mm The stiffness of the wire is much greater than the effective spring stiffness between atoms due to the large number of chains in parallel compared to the number of bonds in series.

10 Estimating interatomic spring stiffness strain stress = = ΔL L FT A tension stress = Y strain FT A = Y ΔL L Y - Young s modulus depends only on material Larger Y means stiffer wire Compare: Fspring = ks s Fspring s A = ks L A L Fspring L s = k s A A L k s = A Y L

11 Effective interatomic spring stiffness k s = A Y L k s = d d 2 Y Interatomic spring stiffness ks = Yd

12 Limits of applicability of Young s modulus stress = Y strain Plastic deformation FT A = Y ΔL L Elastic region When the stretch of the material exceeds the elastic limit, the linear relation between stress and strain fails, and the material deforms plastically. This is an irreversible process. Aluminum alloy

13 Brick on a table: compression F N Mg If the weight of the brick exceeds a limit, the table will either break (if it s brittle) or bend, (if it s ductile).

14 Friction Exert a force so that the brick moves to the right at a constant speed. What is the net force on the brick?

15 Friction Doesn t Always Oppose Motion Just RELATIVE motion of the frictioning surfaces! Box dropped onto moving conveyor belt. What happens? QUIZ What is the state of motion of the box when the belt force has a horizontal component? If the green v vector is the belt s velocity, what can you say about the velocity of the box at the instant of the diagram? How is it that a sprinter can accelerate? A Decelerating B Accelerating C Steady motion

16 Friction Doesn t Always Oppose Motion Just RELATIVE motion of the frictioning surfaces! Box dropped onto moving conveyor belt. What happens? There are no other objects or agents shown. We are shown ALL the forces involved. BUT F belt includes two components, F N and F k, each acting on the box. The force F k is unbalanced, and so at the moment diagrammed, the box is necessarily accelerating to the right. It will eventually match velocity with the belt, at which point F k will VANISH You can further argue that the existence of the F k component means that there MUST be relative motion between the belt and the box at the instant shown. So the box is moving slower than the belt at this instant. The box s inertia is NOT sufficient to keep it moving slower than the belt (or standing still) that would take an extra agent pulling to the left.

17 Sliding Friction When one object slides on another, the component of force exerted by one object on the other has a component parallel (or antiparallel) to the motion: NOTE the friction always acts against the relative motion. It acts on both the object and the surface. f friction ~ μ k F N μ k is the coefficient of kinetic friction F N is the normal force the perpendicular component of the force that is squeezing the two objects into each other

18 Static Friction If the applied force F applied < μ k F N the object will SLOW DOWN (relative to the surface it s frictioning with.) What is the kinetic friction at this point? The block will eventually come to rest, and THEN, any (sideways) force applied < μ s F N will not cause the block to move (relative to the surface it s touching).. Generally the static friction is a bit greater than the kinetic friction: μ k < μ s Once the static friction breaks, the block will speed up (if the applied force does not change) since the applied force is then somewhat greater than the retarding force of the kinetic friction.

Pin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify.

Pin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify. 4. FORCES in PIN JOINTED STRUCTURES Pin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify. They can be fixed structures

More information

C 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

C 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 information

VELOCITY, ACCELERATION, FORCE

VELOCITY, 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 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 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 information

Serway_ISM_V1 1 Chapter 4

Serway_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 information

2.1 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. 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 information

B) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B

B) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time

More information

physics 111N forces & Newton s laws of motion

physics 111N forces & Newton s laws of motion physics 111N forces & Newton s laws of motion forces (examples) a push is a force a pull is a force gravity exerts a force between all massive objects (without contact) (the force of attraction from the

More information

Chapter 4 - Forces and Newton s Laws of Motion w./ QuickCheck Questions

Chapter 4 - Forces and Newton s Laws of Motion w./ QuickCheck Questions Chapter 4 - Forces and Newton s Laws of Motion w./ QuickCheck Questions 2015 Pearson Education, Inc. Anastasia Ierides Department of Physics and Astronomy University of New Mexico September 8, 2015 Review

More information

Lecture 9. Friction in a viscous medium Drag Force Quantified

Lecture 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 information

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) 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 information

Newton s Laws of Motion

Newton s Laws of Motion Newton s Laws of Motion Newton s Laws and the Mousetrap Racecar Simple version of Newton s three laws of motion 1 st Law: objects at rest stay at rest, objects in motion stay in motion 2 nd Law: force

More information

EQUILIBRIUM AND ELASTICITY

EQUILIBRIUM AND ELASTICITY Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none

More information

Chapter 12 Elasticity

Chapter 12 Elasticity If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences

More information

Prelab Exercises: Hooke's Law and the Behavior of Springs

Prelab Exercises: Hooke's Law and the Behavior of Springs 59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

Forces. Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies.

Forces. 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 information

Lecture 15. Torque. Center of Gravity. Rotational Equilibrium. Cutnell+Johnson:

Lecture 15. Torque. Center of Gravity. Rotational Equilibrium. Cutnell+Johnson: Lecture 15 Torque Center of Gravity Rotational Equilibrium Cutnell+Johnson: 9.1-9.3 Last time we saw that describing circular motion and linear motion is very similar. For linear motion, we have position

More information

Monday 20 May 2013 Afternoon

Monday 20 May 2013 Afternoon Monday 20 May 2013 Afternoon AS GCE PHYSICS A G481/01 Mechanics *G411700613* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships Booklet (sent with general

More information

Force. Force as a Vector Real Forces versus Convenience The System Mass Newton s Second Law. Outline

Force. Force as a Vector Real Forces versus Convenience The System Mass Newton s Second Law. Outline Force Force as a Vector Real Forces versus Convenience The System Mass Newton s Second Law Outline Force as a Vector Forces are vectors (magnitude and direction) Drawn so the vector s tail originates at

More information

Newton s Laws Pre-Test

Newton s Laws Pre-Test Newton s Laws Pre-Test 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 information

AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2001 APPLIED MATHEMATICS HIGHER LEVEL

AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2001 APPLIED MATHEMATICS HIGHER LEVEL M3 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 00 APPLIED MATHEMATICS HIGHER LEVEL FRIDAY, JUNE AFTERNOON,.00 to 4.30 Six questions to be answered. All questions carry equal marks.

More information

This 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. 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 information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal

More information

1. Newton s Laws of Motion and their Applications Tutorial 1

1. Newton s Laws of Motion and their Applications Tutorial 1 1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0

More information

If 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

If 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

Lesson 04: Newton s laws of motion

Lesson 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 information

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)

Weight 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 information

Name: Date: 7. A child is riding a bike and skids to a stop. What happens to their kinetic energy? Page 1

Name: Date: 7. A child is riding a bike and skids to a stop. What happens to their kinetic energy? Page 1 Name: Date: 1. Driving down the road, you hit an insect. How does the force your car exerts on the insect compare to the force the insect exerts on the car? A) The insect exerts no force on the car B)

More information

p = F net t (2) But, what is the net force acting on the object? Here s a little help in identifying the net force on an object:

p = F net t (2) But, what is the net force acting on the object? Here s a little help in identifying the net force on an object: Harmonic Oscillator Objective: Describe the position as a function of time of a harmonic oscillator. Apply the momentum principle to a harmonic oscillator. Sketch (and interpret) a graph of position as

More information

Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion

Physics 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 information

Physics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion)

Physics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion) Physics 101 Prof. Ekey Chapter 5 Force and motion (Newton, vectors and causing commotion) Goal of chapter 5 is to establish a connection between force and motion This should feel like chapter 1 Questions

More information

College Physics 140 Chapter 4: Force and Newton s Laws of Motion

College 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 information

PHYS 211 FINAL FALL 2004 Form A

PHYS 211 FINAL FALL 2004 Form A 1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each

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) The following four forces act on a 4.00 kg object: 1) F 1 = 300 N east F 2 = 700 N north

More information

Forces: Equilibrium Examples

Forces: Equilibrium Examples Physics 101: Lecture 02 Forces: Equilibrium Examples oday s lecture will cover extbook Sections 2.1-2.7 Phys 101 URL: http://courses.physics.illinois.edu/phys101/ Read the course web page! Physics 101:

More information

Chapter (1) Fluids and their Properties

Chapter (1) Fluids and their Properties Chapter (1) Fluids and their Properties Fluids (Liquids or gases) which a substance deforms continuously, or flows, when subjected to shearing forces. If a fluid is at rest, there are no shearing forces

More information

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

Ground 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 information

Teaching Motion with the Air Puck

Teaching Motion with the Air Puck Name: Teaching Motion with the Air Puck Objective: In studying motion of objects, many times it is difficult to quantitatively measure objects on Earth because of ever-present friction issues. Often, our

More information

AP Physics Scoring Guidelines

AP Physics Scoring Guidelines AP Physics 1 2015 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

More information

Glossary of Physics Formulas

Glossary of Physics Formulas Glossary of Physics Formulas 1. Kinematic relations in 1-D at constant velocity Mechanics, velocity, position x - x o = v (t -t o ) or x - x o = v t x o is the position at time = t o (this is the beginning

More information

Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION

Physics 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 information

2.2 NEWTON S LAWS OF MOTION

2.2 NEWTON S LAWS OF MOTION 2.2 NEWTON S LAWS OF MOTION Sir Isaac Newton (1642-1727) made a systematic study of motion and extended the ideas of Galileo (1564-1642). He summed up Galileo s observation in his three laws of motion

More information

3) a 1 = a 2. 5) a 1 = 2 a 2

3) 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 information

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the

More information

Force. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1

Force. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1 Department of Physics and Geology Background orce Physical Science 1421 A force is a vector quantity capable of producing motion or a change in motion. In the SI unit system, the unit of force is the Newton

More information

AP Physics C. Oscillations/SHM Review Packet

AP Physics C. Oscillations/SHM Review Packet AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

More information

Linear and Rotational Kinematics

Linear and Rotational Kinematics Linear and Rotational Kinematics Starting from rest, a disk takes 10 revolutions to reach an angular velocity. If the angular acceleration is constant throughout, how many additional revolutions are required

More information

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.

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. 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 non-contact forces. Whats a

More information

General Physics I Can Statements

General 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 information

Physics 271, Sections H1 & H2 Thursday, Nov 20, 2014

Physics 271, Sections H1 & H2 Thursday, Nov 20, 2014 Physics 271, Sections H1 & H2 Thursday, Nov 20, 2014 Problems #11 Oscillations 1) Consider a mass spring system, with mass M and spring constant k. We put a mass m on top of the mass M. The coefficient

More information

Chapter Test. Teacher Notes and Answers Forces and the Laws of Motion. Assessment

Chapter 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 information

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

More information

People s Physics book 3e Ch 25-1

People s Physics book 3e Ch 25-1 The Big Idea: In most realistic situations forces and accelerations are not fixed quantities but vary with time or displacement. In these situations algebraic formulas cannot do better than approximate

More information

SOLID MECHANICS DYNAMICS TUTORIAL INERTIA FORCES IN MECHANISMS

SOLID 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 information

Newton s Laws of Motion. Chapter 4

Newton 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 information

PHYSICS 111 HOMEWORK#6 SOLUTION. February 22, 2013

PHYSICS 111 HOMEWORK#6 SOLUTION. February 22, 2013 PHYSICS 111 HOMEWORK#6 SOLUTION February 22, 2013 0.1 A block of mass m = 3.20 kg is pushed a distance d = 4.60 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

v kt = N A ρ Au exp (

v kt = N A ρ Au exp ( 4-2 4.2 Determination of the number of vacancies per cubic meter in gold at 900 C (1173 K) requires the utilization of Equations 4.1 and 4.2 as follows: N v N exp Q v N A ρ Au kt A Au exp Q v kt (6.023

More information

AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2000

AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2000 M31 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 2000 APPLIED MATHEMATICS - ORDINARY LEVEL FRIDAY, 23 JUNE - AFTERNOON, 2.00 to 4.30 Six questions to be answered. All questions

More information

Teaching Motion with the Air Puck

Teaching Motion with the Air Puck Name: Teaching Motion with the Air Puck Objective: In studying motion of objects, many times it is difficult to quantitatively measure objects on Earth because of ever-present friction issues. Often, our

More information

Ch.4 Forces. Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66

Ch.4 Forces. Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66 Ch.4 Forces Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66 Forces Forces - vector quantity that changes the velocity

More information

AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that

More information

HW#4b Page 1 of 6. I ll use m = 100 kg, for parts b-c: 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. I ll use m = 100 kg, for parts b-c: 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 information

6: Applications of Newton's Laws

6: Applications of Newton's Laws 6: Applications of Newton's Laws Friction opposes motion due to surfaces sticking together Kinetic Friction: surfaces are moving relative to each other a.k.a. Sliding Friction Static Friction: surfaces

More information

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?

PHY231 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 information

Physics 3 Summer 1989 Lab 7 - Elasticity

Physics 3 Summer 1989 Lab 7 - Elasticity Physics 3 Summer 1989 Lab 7 - Elasticity Theory All materials deform to some extent when subjected to a stress (a force per unit area). Elastic materials have internal forces which restore the size and

More information

SOLUTIONS TO PROBLEM SET 4

SOLUTIONS TO PROBLEM SET 4 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01X Fall Term 2002 SOLUTIONS TO PROBLEM SET 4 1 Young & Friedman 5 26 A box of bananas weighing 40.0 N rests on a horizontal surface.

More information

AP Physics Newton's Laws Practice Test

AP 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 information

PHY231 Section 1, Form B March 22, 2012

PHY231 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 information

CHAPTER 3 NEWTON S LAWS OF MOTION

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 information

MECHANICAL PROPERTIES OF MATERIALS. IE-114 Materials Science and General Chemistry Lecture-6

MECHANICAL PROPERTIES OF MATERIALS. IE-114 Materials Science and General Chemistry Lecture-6 MECHANICAL PROPERTIES OF MATERIALS IE-114 Materials Science and General Chemistry Lecture-6 Overview 1) ELASTIC DEFORMATION - Elastic Behavior - Anelasticity - Elastic Properties of Materials 2) PLASTIC

More information

Springs. Spring can be used to apply forces. Springs can store energy. These can be done by either compression, stretching, or torsion.

Springs. Spring can be used to apply forces. Springs can store energy. These can be done by either compression, stretching, or torsion. Work-Energy Part 2 Springs Spring can be used to apply forces Springs can store energy These can be done by either compression, stretching, or torsion. Springs Ideal, or linear springs follow a rule called:

More information

F = ma. F = mg. Forces. Forces. Free Body Diagrams. Find the unknown forces!! Ex. 1 Ex N. Newton s First Law. Newton s Second Law

F = 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 information

Newton s Law of Motion

Newton 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 information

Strength and Stiffness

Strength and Stiffness Strength and Stiffness Stress = load/area is applied to a material by loading it Strain = deformation/length a change of shape (dimensions and twist angles) is its response Stiffness = stress/strain is

More information

Stress and Strain Fundamentals of Tissue Injury

Stress and Strain Fundamentals of Tissue Injury Readings: and Strain Fundamentals of Tissue Injury Chapter 2 [course text] Nordin & Frankel, Chapter 1 [on reserve] Hall, Chapter 4 [on reserve] 1 Learning Objectives By the end of this lecture, you should

More information

Mechanics of Materials

Mechanics of Materials Mechanics of Materials Notation: a = acceleration A = area (net = with holes, bearing = in contact, etc...) ASD = allowable stress design d = diameter of a hole = calculus symbol for differentiation e

More information

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

More information

CHAPTER 15 FORCE, MASS AND ACCELERATION

CHAPTER 15 FORCE, MASS AND ACCELERATION CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car

More information

Chapter 6: Energy and Oscillations. 1. Which of the following is not an energy unit? A. N m B. Joule C. calorie D. watt E.

Chapter 6: Energy and Oscillations. 1. Which of the following is not an energy unit? A. N m B. Joule C. calorie D. watt E. Chapter 6: Energy and Oscillations 1. Which of the following is not an energy unit? A. N m B. Joule C. calorie D. watt E. kwh 2. Work is not being done on an object unless the A. net force on the object

More information

KEY NNHS Introductory Physics: MCAS Review Packet #1 Introductory Physics, High School Learning Standards for a Full First-Year Course

KEY NNHS Introductory Physics: MCAS Review Packet #1 Introductory Physics, High School Learning Standards for a Full First-Year Course Introductory Physics, High School Learning Standards for a Full First-Year Course I. C O N T E N T S T A N D A R D S Central Concept: Newton s laws of motion and gravitation describe and predict the motion

More information

1206EL - Concepts in Physics. Friday, September 18th

1206EL - Concepts in Physics. Friday, September 18th 1206EL - Concepts in Physics Friday, September 18th Notes There is a WebCT course for students on September 21st More information on library webpage Newton s second law Newton's first law of motion predicts

More information

BROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino

BROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino BROCK UNIVERSITY PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino 1. [10 marks] Clearly indicate whether each statement is TRUE or FALSE. Then provide a clear, brief,

More information

Vectors and the Inclined Plane

Vectors 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 information

= mg [down] =!mg [up]; F! x

= mg [down] =!mg [up]; F! x Section 4.6: Elastic Potential Energy and Simple Harmonic Motion Mini Investigation: Spring Force, page 193 Answers may vary. Sample answers: A. The relationship between F g and x is linear. B. The slope

More information

AP Physics - Chapter 8 Practice Test

AP Physics - Chapter 8 Practice Test AP Physics - Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on

More information

April 07, 2015. Force motion examples.notebook MOTION AND FORCES. GRAVITY: a force that makes any object pull toward another object.

April 07, 2015. Force motion examples.notebook MOTION AND FORCES. GRAVITY: a force that makes any object pull toward another object. Force motion examples.notebook April 07, 2015 MOTION AND FORCES GRAVITY: a force that makes any object pull toward another object Feb 15 12:00 PM 1 FRICTION: a force that acts to slow down moving objects

More information

04-1. 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.

04-1. 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 information

第 1 頁, 共 8 頁 Chap12&Chap13 1. *Chapter 12, Problem 25 In Fig. 12-40, what magnitude of force applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h =

More information

b. Velocity tells you both speed and direction of an object s movement. Velocity is the change in position divided by the change in time.

b. Velocity tells you both speed and direction of an object s movement. Velocity is the change in position divided by the change in time. I. What is Motion? a. Motion - is when an object changes place or position. To properly describe motion, you need to use the following: 1. Start and end position? 2. Movement relative to what? 3. How far

More information

1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true?

1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true? Physics 2A, Sec C00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to ll your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Name: Date: PRACTICE QUESTIONS PHYSICS 201 FALL 2009 EXAM 2

Name: Date: PRACTICE QUESTIONS PHYSICS 201 FALL 2009 EXAM 2 Name: Date: PRACTICE QUESTIONS PHYSICS 201 FALL 2009 EXAM 2 1. A force accelerates a body of mass M. The same force applied to a second body produces three times the acceleration. What is the mass of the

More information

Friction and Newton s 3rd law

Friction and Newton s 3rd law Lecture 4 Friction and Newton s 3rd law Pre-reading: KJF 4.8 Frictional Forces Friction is a force exerted by a surface. The frictional force is always parallel to the surface Due to roughness of both

More information

Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: x (cm) 10.0 Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

More information

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are:

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are: Problem 1. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields as shown in the figure. (b) Repeat part (a), assuming the moving particle is

More information

Newtonian Dynamics. Luis Anchordoqui

Newtonian Dynamics. Luis Anchordoqui Newtonian Dynamics Newton's Laws Now that we have studied how objects move, we can ask the questions: Why do objects start to move? What causes a moving object to change speed or change direction? Sir

More information

Newton s Laws of Motion

Newton 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 information

103 PHYS - CH7 - Part2

103 PHYS - CH7 - Part2 Work due to friction If friction is involved in moving objects, work has to be done against the kinetic frictional force. This work is: W = f d = f d cos180 = f d o f k k k Physics 1 Example f n r θ F

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Kinetic Energy and Work Conservation of Energy is one of Nature s fundamental laws that is not violated. Energy can take on different forms in a given system. This chapter we will discuss work

More information