# Announcements. Dry Friction

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 of dry friction Problems involving dry friction Examples Engr221 Chapter 8 1

2 Applications In designing a brake system for a bicycle, car, or any other vehicle, it is important to understand the frictional forces involved. For an applied force on the brake pads, how can we determine the magnitude and direction of the resulting friction force? Applications - continued Consider pushing a box as shown here. How can you determine if it will slide, tilt, or stay in static equilibrium? What physical factors affect the answer to this question? Engr221 Chapter 8 2

3 Characteristics of Dry Friction Friction is defined as a force of resistance acting on a body which prevents or retards slipping of the body relative to a second body. Experiments show that frictional forces act tangent (parallel) to the contacting surface in a direction opposing the relative motion or tendency for motion. For the body shown in the figure to be in equilibrium, the following must be true: F = P, N = W, and Wx = Ph. Characteristics of Dry Friction - continued To study the characteristics of the friction force F, let us assume that tipping does not occur (i.e., h is small or a is large). Then, we gradually increase the magnitude of the force P. Typically, experiments show that the friction force F varies with P, as shown in the right figure above. Engr221 Chapter 8 3

4 Characteristics of Dry Friction - continued The maximum friction force is attained just before the block begins to move (a situation called impending motion ). The value of the force is found using F s = µ s N, where µ s is called the coefficient of static friction. The value of µ s depends on the materials in contact. Once the block begins to move, the frictional force typically drops and is given by F k = µ k N. The value of µ k (coefficient of kinetic friction) is less than µ s. Determining µ s Experimentally A block with weight W is placed on an inclined plane. The plane is slowly tilted until the block just begins to slip. The inclination, θ s, is noted. Analysis of the block just before it begins to move gives (using F s = µ s N): + F y = N W cos θ s = 0 + F X = µ S N W sin θ s = 0 Using these two equations, we get µ s = (W sin θ s ) / (W cos θ s ) = tan θ s This simple experiment allows us to find the µ S between two materials in contact. Engr221 Chapter 8 4

5 Procedure for Analysis Steps for solving equilibrium problems involving dry friction: 1. Draw the necessary free body diagrams. Make sure that you show the friction force in the correct direction (it always opposes the motion or impending motion). 2. Determine the number of unknowns. Do not assume that F = µ S N unless the impending motion condition is given. 3. Apply the equations of equilibrium and appropriate frictional equations to solve for the unknowns. Impending Tipping vs. Slipping For a given weight and height, how can we determine if the block will slide first or tip first? In this case, we have four unknowns (F, N, x, and P) and only three E-of-E. Hence, we have to make an assumption to give us another equation. Then we can solve for the unknowns using the three E-of-E. Finally, we need to check if our assumption was correct. Engr221 Chapter 8 5

6 Impending Tipping vs. Slipping - continued Assume: Slipping occurs Known: F = µ s N Solve: x, P, and N Check: 0 x b/2 Or Assume: Tipping occurs Known: x = b/2 Solve: P, N, and F Check: F µ s N a) Draw a FBD Example A Given: A uniform ladder weighs 20 lb. The vertical wall is smooth (no friction).the floor is rough and µ s = 0.8 Find: The minimum force P needed to move (tip or slide) the ladder. Plan: b) Determine the unknowns c) Make any necessary friction assumptions d) Apply E-of-E (and friction equations, if appropriate) to solve for the unknowns e) Check assumptions, if required Engr221 Chapter 8 6

7 Example A - continued N B 4 ft A FBD of the ladder 4 ft 20 lb P F A 3 ft 3 ft There are four unknowns: N A, F A, N B, and P. Assume that the ladder will tip first so N B = 0 + Σ F Y = N A 20 = 0 ; N A = 20 lb + Σ M A = 20(3) P(4) = 0 ; P = 15 lb + Σ F X = 15 F A = 0 ; F A = 15 lb N A Example A - continued N B 4 ft A FBD of the ladder 4 ft 20 lb P F A 3 ft 3 ft N A Now check the assumption. F max = µ s N A = 0.8 * 20 lb = 16 lb Is F A = 15 lb F max = 16 lb? Yes, hence our assumption of tipping is correct. Engr221 Chapter 8 7

8 Example B Given: Drum weight = 100 lb, µ s = 0.5, a = 3 ft, b = 4 ft Find: The smallest magnitude of P that will cause impending motion (tipping or slipping) of the drum Plan: a) Draw a FBD of the drum b) Determine the unknowns c) Make friction assumptions, as necessary d) Apply E-of-E (and friction equations as appropriate) to solve for the unknowns e) Check assumptions, as required Example B - continued P ft 1.5 ft 4 A FBD of the drum 100 lb 4 ft 0 X N F There are four unknowns: P, N, F and x First, let s assume the drum slips. Then the friction equation is F = µ s N = 0.5 N Engr221 Chapter 8 8

9 Example B - continued P ft 1.5 ft 4 A FBD of the drum 100 lb 4 ft + F X = (4/5) P 0.5 N = 0 + F Y = N (3/5) P 100 = 0 These two equations give: 0 X N F P = 100 lb and N = 160 lb + M O = (3/5) 100 (1.5) (4/5) 100 (4) (x) = 0 Check: x = so OK! Drum slips as assumed at P = 100 lb Questions 1. A friction force always acts to the contact surface. A) Normal B) At 45 C) Parallel D) At the angle of static friction 2. If a block is stationary, then the friction force acting on it is A) µ s N B) = µ s N C) µ s N D) = µ k N Engr221 Chapter 8 9

10 Question 100 lb P(A) P(B) P(C) A 100 lb box with wide base is pulled by a force P and µ s = 0.4 Which force orientation requires the least force to begin sliding? A) A B) B C) C D) Can not be determined Questions 1. A 10 lb block is in equilibrium. What is the magnitude of the friction force between this block and the surface? A) 0 lb B) 1 lb C) 2 lb D) 3 lb µ S = lb 2. The ladder AB is positioned as shown. What is the direction of the friction force on the ladder at B? A) B) C) D) A B Engr221 Chapter 8 10

11 Example Problem The refrigerator has a weight of 180 lb and rests on a tile floor for which µ s = 0.25 Also, the man has a weight of 150 lb and the coefficient of static friction between the floor and his shoes is µ s = 0.6 If he pushes horizontally on the refrigerator, determine if he can move it. If so, does the refrigerator tip or slip? Tips: P = 67.5 lb Slips: P = 45 lbs Man slips at 90 lbs F = 45 lbs Yes, he can move it Textbook Problem 8.53 The 50-lb board is placed across the channel and a 100-lb boy attempts to walk across. If the coefficient of static friction at A and B is µ s = 0.4, determine if he can make the crossing; and if not, how far will he get from A before the board slips? N A = 60.3 lb N B = 86.2 lb d = 6.47 ft No, the board will slip Engr221 Chapter 8 11

12 Example Problem The 5-kg cylinder is suspended from two equal-length cords. The end of each cord is attached to a ring of negligible mass, which passes along a horizontal shaft. If the coefficient of static friction between each ring and the shaft is µ s = 0.5, determine the greatest distance d by which the rings can be separated and still support the cylinder. Textbook Problem 8.44 (HW) The crate has a weight of 300 lb and a center of gravity at G. If the coefficient of static friction between the crate and floor is µ s = 0.4, determine the smallest weight of the man so he can push the crate to the left. The coefficient of static friction between his shoes and the floor is µ s = 0.4. Assume the man exerts only a horizontal force on the crate. W man = 171 lb Engr221 Chapter 8 12

13 Textbook Problem 8.50 (HW) Determine the angle φ at which P should act on the block so that the magnitude of P is as small as possible to begin pulling the block up the incline. What is the corresponding value of P? The block weighs W and the slope α is known. φ= tan -1 µ P = Wsin(φ + α) Textbook Problem 8.58 The carpenter slowly pushes the uniform board horizontally over the top of the saw horse. The board has a uniform weight of 3 lb/ft, and the saw horse has a weight of 15 lb and a center of gravity at G. Determine if the saw horse will stay in position, slip, or tip if the board is pushed forward when d = 14 ft. The coefficients of static friction are shown in the figure. N A = 60.3 lb N B = 86.2 lb d = 6.47 ft No, the board will slip Engr221 Chapter 8 13

14 Summary Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Announcements Engr221 Chapter 8 14

15 Wedges and Belts Today s Objectives Determine the forces on a wedge Determine the tensions in a belt Class Activities Applications Analysis of a wedge Analysis of a belt Questions Applications Wedges are used to adjust the elevation or provide stability for heavy objects such as this large steel vessel. How can we determine the force required to pull the wedge out? When there are no applied forces on the wedge, will it stay in place (i.e., be self-locking) or will it come out on its own? Under what physical conditions will it come out? Engr221 Chapter 8 15

16 Applications - continued Belt drives are commonly used for transmitting power from one shaft to another. How can we decide that the belts will function properly, i.e., without slipping or breaking? Applications - continued In the design of a band brake, it is essential to analyze the frictional forces acting on the band (which acts like a belt). How can we determine the tensions in the cable pulling on the band? How are these tensions, the applied force P and the torque M, related? Engr221 Chapter 8 16

17 Analysis of a Wedge W A wedge is a simple machine in which a small force P is used to lift a large weight W. To determine the force required to push the wedge in or out, it is necessary to draw FBDs of the wedge and the object on top of it. It is easier to start with a FBD of the wedge since you know the direction of its motion. Note that: 1) The friction forces are always in the direction opposite to the motion, or impending motion, of the wedge 2) The friction forces are along the contacting surfaces 3) The normal forces are perpendicular to the contacting surfaces Analysis of a Wedge - continued Next, a FBD of the object on top of the wedge is drawn. Note that: a) at the contacting surfaces between the wedge and the object the forces are equal in magnitude and opposite in direction to those on the wedge b) all other forces acting on the object should be shown To determine the unknowns, we must apply E-of-E, F x = 0 and F y = 0, to the wedge and the object as well as the impending motion frictional equation, F = µ S N Now, of the two FBDs, which one should we start analyzing first? We should start analyzing the FBD in which the number of unknowns are less than or equal to the number of equations. Engr221 Chapter 8 17

18 Analysis of a Wedge - continued W If the object is to be lowered, then the wedge needs to be pulled out. If the value of the force P needed to remove the wedge is positive, then the wedge is self-locking, i.e., it will not come out on its own. However, if the value of P is negative, or zero, then the wedge will come out on its own unless a force is applied to keep the wedge in place. This can happen if the coefficient of friction is small or the wedge angle θ is large. Belt Analysis Belts are used for transmitting power or applying brakes. Friction forces play an important role in determining the various tensions in the belt. The belt tension values are then used for analyzing or designing a belt drive or a brake system. Engr221 Chapter 8 18

19 Belt Analysis - continued Consider a flat belt passing over a fixed curved surface with the total angle of contact equal to β radians. If the belt slips or is just about to slip, then T 2 must be larger than T 1 and the friction forces. Hence, T 2 must be greater than T 1. Detailed analysis (please refer to your textbook) shows that T 2 = T 1 e µ β where µ is the coefficient of static friction between the belt and the surface. Be sure to use radians when using this formula! Given: The load weighs 100 lb and the µ S between surfaces AC and BD is 0.3 Smooth rollers are placed between wedges A and B. Assume the rollers and the wedges have negligible weights. Find: The force P needed to lift the load. Plan: 1. Draw a FBD of wedge A. Why do A first? 2. Draw a FBD of wedge B. Example A 3. Apply the E-of-E to wedge B. Why do B first? 4. Apply the E-of-E to wedge A. Engr221 Chapter 8 19

20 Example A - continued The FBDs of wedges A and B are shown in the figures. Applying the E-of-E to wedge B, we get 100 lb B F 3 = 0.3N 3 N 3 + F X = N 2 sin 10 N 3 = 0 + F Y = N 2 cos N 3 = 0 Solving the above two equations, we get N 2 10º N 2 10º N 2 = lb and N 3 = 18.6 lb P A F 1 = 0.3N 1 Applying the E-of-E to the wedge A, we get + F Y = N cos 10 = 0; N 1 = lb + F X = P sin N 1 = 0; P = 50.3 lb N 1 Example B Given: Blocks A and B weigh 50 lb and 30 lb, respectively. Find: The smallest weight of cylinder D which will cause the loss of static equilibrium. Engr221 Chapter 8 20

21 Example B - continued Plan: 1. Consider two cases: a) both blocks slide together, and b) block B slides over block A 2. For each case, draw a FBD of the block(s). 3. For each case, apply the E-of-E to find the force needed to cause sliding. 4. Choose the smaller P value from the two cases. 5. Use belt friction theory to find the weight of block D. Example B - continued P B 30 lb Case a: blocks slide together. A 50 lb + F Y = N 80 = 0 N = 80 lb + F X = 0.4 (80) P = 0 P = 32 lb N F=0.4 N Engr221 Chapter 8 21

22 Example B - continued 30 lb Case b: + F y = N cos N sin = 0 P 0.6 N 20º N N = 6.20 lb + F x = P ( 26.2 ) cos sin 20 = 0 P = lb Case b has the lowest P and will occur first. Next, using the frictional force analysis of belt, we get W D = P e µ β = e 0.5 ( 0.5 π ) = 12.7 lb Block D weight of 12.7 lb will cause block B to slide over block A. Questions 1. A wedge allows a force P to lift a weight W. A) (large, large) B) (small, small) C) (small, large) D) (large, small) W 2. Considering friction forces and the indicated motion of the belt, how are belt tensions T 1 and T 2 related? A) T 1 > T 2 B) T 1 = T 2 C) T 1 < T 2 D) T 1 = T 2 e µ Engr221 Chapter 8 22

23 1. Determine the direction of the friction force on object B at the contact point between A and B. A) B) C) D) Questions 2. The boy (hanging) in the picture weighs 100 lb and the woman weighs 150 lb. The coefficient of static friction between her shoes and the ground is 0.6. The boy will? A) be lifted up B) slide down C) not be lifted up D) not slide down Questions 1. When determining the force P needed to lift the block of weight W, it is easier to draw a FBD of first. A) the wedge B) the block C) the horizontal ground D) the vertical wall W 2. In the analysis of frictional forces on a flat belt, T 2 = T 1 e µ β In this equation, β equals A) angle of contact in degrees B) angle of contact in radians C) coefficient of static friction D) coefficient of kinetic friction Engr221 Chapter 8 23

24 Summary Determine the forces on a wedge Determine the tensions in a belt Engr221 Chapter 8 24

### EQUATIONS 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 In-Class Activities: of a rigid body undergoing rotational motion. Check Homework

### 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

### 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

### Chapter 17 Planar Kinetics of a Rigid Body: Force and Acceleration

Chapter 17 Planar Kinetics of a Rigid Body: Force and Acceleration 17.1 Moment of Inertia I 2 2 = r dm, 單位 : kg m 或 slug m ft 2 M = Iα resistance to angular acceleration dm = ρdv I = ρ V r 2 dv 17-2 MOMENT

### 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

### SOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. N B = 0.

8 1. The mine car and its contents have a total mass of 6 Mg and a center of gravity at G. If the coefficient of static friction between the wheels and the tracks is m s = 0.4 when the wheels are locked,

### What 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

### 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

### 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

### Physics 107 HOMEWORK ASSIGNMENT #8

Physics 107 HOMEORK ASSIGMET #8 Cutnell & Johnson, 7 th edition Chapter 9: Problems 16, 22, 24, 66, 68 16 A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself

### PHYS101 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

### There are four types of friction, they are 1).Static friction 2) Dynamic friction 3) Sliding friction 4) Rolling friction

2.3 RICTION The property by virtue of which a resisting force is created between two rough bodies that resists the sliding of one body over the other is known as friction. The force that always opposes

### Lecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.8-4.12, second half of section 4.7

Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.8-4.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal

### 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.

### 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

### 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

### 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

### 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

### Physics: 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 buckle-up? A) the first law

### 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

### 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.

### 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

### Chapter 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 well-defined rules. The book Philosophiae

### Physics, Chapter 3: The Equilibrium of a Particle

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1-1958 Physics, Chapter 3: The Equilibrium of a Particle

### 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

### 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

### Announcements. Moment of a Force

Announcements Test observations Units Significant figures Position vectors Moment of a Force Today s Objectives Understand and define Moment Determine moments of a force in 2-D and 3-D cases Moment of

Week 8 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

### Engineering Mechanics Dr. G Saravana Kumar Department of Mechanical Engineering Indian Institute of Technology, Guwahati

Engineering Mechanics Dr. G Saravana Kumar Department of Mechanical Engineering Indian Institute of Technology, Guwahati Module 5 Lecture 12 Application of Friction Part-3 Today, we will see some more

### Physics 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

### 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.

### 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

### Version 001 Quest 3 Forces tubman (20131) 1

Version 001 Quest 3 Forces tubman (20131) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. l B Conceptual

### Mechanics 1. Revision Notes

Mechanics 1 Revision Notes July 2012 MECHANICS 1... 2 1. Mathematical Models in Mechanics... 2 Assumptions and approximations often used to simplify the mathematics involved:... 2 2. Vectors in Mechanics....

### Physics 11 Assignment KEY Dynamics Chapters 4 & 5

Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following

### 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

### A 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

### 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

### 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

### 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,

### 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

### Chapter 4: Newton s Laws: Explaining Motion

Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state

### Resistance in the Mechanical System. Overview

Overview 1. What is resistance? A force that opposes motion 2. In the mechanical system, what are two common forms of resistance? friction and drag 3. What is friction? resistance that is produced when

### Copyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass

Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of

### Physics I Honors: Chapter 4 Practice Exam

Physics I Honors: Chapter 4 Practice Exam Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Which of the following statements does not describe

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

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

### 2Elastic 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

### PH2213 : 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 (left-hand side) to the motion

### f 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

### 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

### Assignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Assignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE State law of parallelogram of vector addition and derive expression for resultant of two vectors

### 2. (b). The newton is a unit of weight, and the quantity (or mass) of gold that weighs 1 newton is m 1 N

QUICK QUIZZS 1. Newton s second law says that the acceleration of an object is directly proportional to the resultant (or net) force acting on. Recognizing this, consider the given statements one at a

### 5. Forces and Motion-I. Force is an interaction that causes the acceleration of a body. A vector quantity.

5. Forces and Motion-I 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will

### Explaining Motion:Forces

Explaining Motion:Forces Chapter Overview (Fall 2002) A. Newton s Laws of Motion B. Free Body Diagrams C. Analyzing the Forces and Resulting Motion D. Fundamental Forces E. Macroscopic Forces F. Application

### Problem 5.25 (Adapted from Engineering Mechanics: Statics by Bedford & Fowler, Addison- Wesley)

Problem 5.24 particle is traveling in a straight line in a horizontal plane. The mass of the particle is 0.10 kg. The acceleration of the particle is described by the following equation: dv 2 a= = Bt dt

### MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 2 BELT DRIVES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL BELT DRIVES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential pulley

### Chapter 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

### 4.2 Free Body Diagrams

CE297-FA09-Ch4 Page 1 Friday, September 18, 2009 12:11 AM Chapter 4: Equilibrium of Rigid Bodies A (rigid) body is said to in equilibrium if the vector sum of ALL forces and all their moments taken about

### Chapter 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

### HW Set II page 1 of 9 PHYSICS 1401 (1) homework solutions

HW Set II page 1 of 9 4-50 When a large star becomes a supernova, its core may be compressed so tightly that it becomes a neutron star, with a radius of about 20 km (about the size of the San Francisco

### Physics 2101, First Exam, Fall 2007

Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the

### Physics 201 Homework 8

Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the

### Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

### Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79

Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life? - car brakes - driving around a turn - walking - rubbing your hands together

### THE NATURE OF FORCES Forces can be divided into two categories: contact forces and non-contact 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 X-planation

### 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

### Class Examples. Mapundi Kondwani Banda. Applied Mathematics Division - Mathematical Sciences Stellenbosch University

Class Examples Mapundi Kondwani Banda MKBanda@sun.ac.za Applied Mathematics Division - Mathematical Sciences Stellenbosch University October 7, 2013 Chapter 15: Problem 15.1 The 12 Mg jump jet is capable

### 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

### 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

### Steps to Solving Newtons Laws Problems.

Mathematical Analysis With Newtons Laws similar to projectiles (x y) isolation Steps to Solving Newtons Laws Problems. 1) FBD 2) Axis 3) Components 4) Fnet (x) (y) 5) Subs 1 Visual Samples F 4 1) F 3 F

### Problem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s

Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to

### 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

### B) 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

### 1) 0.33 m/s 2. 2) 2 m/s 2. 3) 6 m/s 2. 4) 18 m/s 2 1) 120 J 2) 40 J 3) 30 J 4) 12 J. 1) unchanged. 2) halved. 3) doubled.

Base your answers to questions 1 through 5 on the diagram below which represents a 3.0-kilogram mass being moved at a constant speed by a force of 6.0 Newtons. 4. If the surface were frictionless, the

### 56 Chapter 5: FORCE AND MOTION I

Chapter 5: FORCE AND MOTION I 1 An example of an inertial reference frame is: A any reference frame that is not accelerating B a frame attached to a particle on which there are no forces C any reference

### ENGR-1100 Introduction to Engineering Analysis. Lecture 13

ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body

### FRICTION, 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

### B Answer: neither of these. Mass A is accelerating, so the net force on A must be non-zero Likewise for mass B.

CTA-1. 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

### Q5.1. A. tension T 1 B. tension T 2 C. tension T 3 D. two of the above E. T 1, T 2, and T Pearson Education, Inc.

Q5.1 A car engine is suspended from a chain linked at O to two other chains. Which of the following forces should be included in the free-body diagram for the engine? A. tension T 1 B. tension T 2 C. tension

### 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

### 2. What magnitude of net force is required to give a 135-kg refrigerator an acceleration of magnitude 1.40 m/. [189 N]

PAGE 1 OF 14 E-MAIL: MIAMIMATHTUTOR@GMAIL.COM CONTACT NUMBER: (786)556-4839 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

### Isaac Newton (1642 to 1727) Force. Newton s Three Law s of Motion. The First Law. The First Law. The First Law

Isaac Newton (1642 to 1727) Force Chapter 4 Born 1642 (Galileo dies) Invented calculus Three laws of motion Principia Mathematica. Newton s Three Law s of Motion 1. All objects remain at rest or in uniform,

### AAPT UNITED STATES PHYSICS TEAM AIP CEE 2013

F = ma Exam AAPT UNITED STATES PHYSICS TEAM AIP CEE F = ma Contest 5 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = N/kg throughout this contest. You may

### Physics 201 Homework 5

Physics 201 Homework 5 Feb 6, 2013 1. The (non-conservative) force propelling a 1500-kilogram car up a mountain -1.21 10 6 joules road does 4.70 10 6 joules of work on the car. The car starts from rest

### 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)

### 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

### 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

### 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

### Mechanics Cycle 2 Chapter 13+ Chapter 13+ Revisit Torque. Revisit Statics

Chapter 13+ Revisit Torque Revisit: Statics (equilibrium) Torque formula To-Do: Torque due to weight is simple Different forms of the torque formula Cross product Revisit Statics Recall that when nothing

### 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

### A +TB v A + v B = 0. Av A B 2 = m>s = 1.27 m>sc Av B B 2 = 1.27 m>st

15 5. If cylinder is given an initial downward speed of 2 m>s, determine the speed of each cylinder when t = 3 s. Neglect the mass of the pulleys. Free-ody Diagram: The free-body diagram of blocks and

### 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

### 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.,

### Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information

### STATIC AND KINETIC FRICTION

STATIC AND KINETIC FRICTION LAB MECH 3.COMP From Physics with Computers, Vernier Software & Technology, 2000. INTRODUCTION If you try to slide a heavy box resting on the floor, you may find it difficult

### 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

### P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections

4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear

### Mass, energy, power and time are scalar quantities which do not have direction.

Dynamics Worksheet Answers (a) Answers: A vector quantity has direction while a scalar quantity does not have direction. Answers: (D) Velocity, weight and friction are vector quantities. Note: weight and