Unit 4: Science and Materials in Construction and the Built Environment. Chapter 14. Understand how Forces act on Structures

Save this PDF as:

Size: px
Start display at page:

Download "Unit 4: Science and Materials in Construction and the Built Environment. Chapter 14. Understand how Forces act on Structures"

Transcription

1 Chapter 14 Understand how Forces act on Structures 14.1 Introduction The analysis of structures considered here will be based on a number of fundamental concepts which follow from simple Newtonian mechanics; it is necessary that we first review Newton s Laws of Motion. The word Laws is often replaced with Axioms, as they cannot be proved in the normal experimental sense but are self-evident truths which are believed to be correct because all results obtained assuming them to be true agree with experimental observations. In 1687 Sir Isaac Newton published a work that clearly set out the Laws of Mechanics. He proposed the following three laws to govern motion: Newton s Laws of Motion Law 1: Law 2: Law 3: Every-body will continue in a state of rest or uniform motion in a straight line unless acted on by a resultant force. The change in momentum per unit time is proportional to the impressed force, and takes place in the direction of the straight line along the axis in which the force acts. Action and reaction are equal and opposite. Based on these laws we are able to define some basic concepts which will assist us in our analysis of structures. Chapter 14: Understand how Forces act on Structures Page 1

2 14.2 Equilibrium Equilibrium is an unchanging state; it is a state of balance. In the analysis of structures this will be achieved when the total of all the applied forces, reactions and moments equate to zero. In this condition, the structure will be in balance and no motion will occur. We will now consider three types of static equilibrium. Figure 1 shows an object, in this case a ball, placed on three differently shaped surfaces. i Potential Energy Gained ii Potential Energy Lost iii Potential Energy Constant Figure 1: A ball, placed on three differently shaped surfaces (Note: Potential Energy = change in energy if the body is displaced. Potential energy is the energy the body possesses by virtue of its position above a known datum, in this case the apex of the surface on which it rests.) In (iii) we have a neutral equilibrium position. The ball will remain at rest unless acted on by a force. The potential energy of the system is constant. In system (i), any movement of the ball will require a gain in potential energy. When released, the ball will try to achieve equilibrium by returning to its original position. In (ii) any movement will cause the ball to move. The shape of the surface on which it rests will further promote this movement. Relative to its original position, potential energy will be lost. Static equilibrium is achieved by having a zero force resultant. It is perhaps worth noting here that our early analysis of structures will be based wholly on the principles of statics alone. That is, force will be constant with respect to time. Hence we will consider the static analyses of structures. The study of structures subject to forces that vary with time is known as dynamic analyses. Chapter 14: Understand how Forces act on Structures Page 2

3 14.3 Force From Newton s Second Law, and since: Momentum = mass velocity Equation 1 We can derive an expression for force such that: Force = change in momentum per unit time = mass acceleration or F = m a Equation 2 where F = force (N) m = mass (kg) a = acceleration = (ms -2 ) Acceleration is a vector quantity since it has both direction and magnitude. It is a measure of change of speed (velocity) over time taken. We commonly look at the acceleration rates of cars as the time it takes to go from 0 to 60 miles per hour (mph) or 0 to 96 kilometres per hour (km/h), around 5 seconds for a Ferrari. This can be represented differentially as: Equation 3 where a = acceleration dv = change in velocity (a vector quantity, i.e. one that has both direction and magnitude) dt = change in time We also know that velocity is a measure of distance covered over time, e.g. at a velocity (or more familiarly a speed) of 96 km/h a car would cover 96 km in 1 hour or m/s. This can also be represented differentially as: Equation 4 where v = velocity ds = change in distance dt = change in time Chapter 14: Understand how Forces act on Structures Page 3

4 So acceleration can be expressed in terms of change in distance over time taken as, the second derivative of a distance-time graph. Equation 5 Acceleration (and thus velocity) can be rectilinear (in a straight line) or rotational. In order to determine forces on a structure we first need to consider the differences between weight and mass. The weight of an object is defined as the force acting on it due to the influence of a gravitational attraction, or gravity. Thus, attaching an object to a spring balance and noting the extension will enable us to determine its weight. From our knowledge of physics we know that within the elastic range, extension is proportional to force (Hooke s Law), and most spring balances are calibrated to read weight directly. Consider an object of mass m and weight W. If the object is held at a certain height above the earth s surface and is released it will fall to the ground. Its acceleration in this case, will be the acceleration due to gravitational force; this is normally denoted by g and taken to be 9.81 m/s 2. Since from equation 2: Force = mass acceleration The force acting on the object, that is its weight, will be: W = m g Equation 6 where W = weight m = mass g = acceleration due to gravity. Hence, we can derive the force (weight) of various objects by multiplying its mass by its acceleration due to gravity, e.g. an object of mass 1 kg will have a force of 1 kg 9.81 m/s 2 = 9.81 kgm/s 2 or 9.81 Newtons. The units of force are the Newton and are normally denoted as N. (Note: 100g is approximately 1 N The weight of an average apple). It is important to note that the acceleration due to gravity is not actually constant over the whole Earth s surface. This is due to the earth being ellipsoidal in shape. It is also interesting to note that the weight of a body on the Moon will be approximately one-sixth of that on the Earth. The Chapter 14: Understand how Forces act on Structures Page 4

5 Unit 4: Science and Materials in Construction and the Built Environment mass of an object is therefore constant, whereas its weight will vary in magnitude with variations in gravitational intensity g. Having determined the force exerted by an object, some basic geometric properties may be defined. All forces are vector quantities, which means, that they have both magnitude and direction. They may therefore be the subject of vector addition. Consider the situation shown in figure 2. Tractor a 500N Post Figure 2: Force Vectors Tractor b Two tractors (seen here in plan) are used to remove (pull out) a post from the ground by exerting horizontal forces as shown. Both tractors are attached by cables to the post and exert forces of 500N in the directions indicated. In force vector terms we can represent our system as shown in figure 3. The forces are represented by straight lines, which can be drawn to scale, denoting both the direction and the magnitude of the force. Any suitable scale can be used to construct the diagram, however in most cases such a diagram, will not be necessary. (i) (ii) (iii) y x Post Figure 3: Graphical Representation of Forces Chapter 14: Understand how Forces act on Structures Page 5

6 It is possible to achieve the same overall result by replacing the forces exerted by tractors a and b with a single tractor c and therefore replacing the system represented in figure 3(i). In order to determine the direction and magnitude of force required by the single tractor we analyse our initial system. Using elementary geometrical relationships we can determine the magnitude and direction of the vector. This can be calculated using the Pythagoras theorem and standard Sine, Cosine and Tangent relationships. The analysis will be completed using normal Cartesian coordinates as shown graphically in figure 3(ii) and (iii). (Note the bar on top of the letters, for example, indicates a vector quantity.) Therefore to calculate the direction and magnitude of the new vector c we can use simple vector algebra: Direction: Magnitude: Thus we can replace our original system with that shown in figure 4. Tractor c Post 707.1N 45 o Figure 4: Single Force System Similarly we can break down a single force c into its mutually orthogonal components, a and b. From figure 3(iii) we find the vector: in the x direction in the y direction Force vectors can therefore be resolved into a resultant, or broken down into horizontal and vertical components. For this year, we will only consider 2D structures; that is, structures with both breadth and height only. The proposed coordinate system is shown in figure 5. Chapter 14: Understand how Forces act on Structures Page 6

7 y x z Figure 5: Two-Dimensional coordinate system We will apply this coordinate system across the entire structure. The coordinate system will therefore be considered as global. In some methods of analysis the coordinate may be oriented to the individual member axis and will then be considered as a local system. For equilibrium in a 2D system we must ensure that the summation of the forces in the x direction, the summation of the forces in the y direction and the moments about the z axis equate to zero. Or: Equation 7 However, real structures exist in three dimensional (3D) space. In three dimensions our coordinate system will be that shown in figure 6. For stable equilibrium of a rigid 3D body at the origin, we must now consider six equations. Equation 8 Chapter 14: Understand how Forces act on Structures Page 7

8 y x Note: Clockwise moments taken as positive z Figure 6: Three dimensional Coordinate System Therefore, in two dimensional analysis we are only required to solve for three equations in order to ensure static equilibrium of a rigid body. For three dimensional structures the analysis is much more complex, requiring the solution of six equations, and will not form part of this years studies. Practice has shown that, in the formative years of study, it is easier to analyse structures using the global Cartesian coordinates concept and resolving forces into horizontal and vertical components in order to check for equilibrium. This may require the resolution of a number of concurrent forces in order to determine the total horizontal and vertical forces applied at a particular position on the structure. Consider the two forces applied at point T as shown in figure 7. Chapter 14: Understand how Forces act on Structures Page 8

9 + y - x Point T R horizontal R vertical + x P Vertical P horizontal - y Figure 7: Concurrent Forces applied to a joint In order to simplify our analysis we will resolve each force into its horizontal and vertical components and then sum the results to find the resultant horizontal and vertical forces. Hence: For vector (force) R For vector (force) P R vertical = R Sin P vertical = P Cos R horizontal = R Cos P horizontal = P Sin Hence resultant forces are: Resultant vertical force Resultant horizontal force = + R Sin - P Cos = + R Cos - P Sin Note that the positive and the negative signs are generated in normal Cartesian coordinates by the force directions shown in figure 7. Also note that we have dropped the bar convention on the vectors to simplify the equations. We can therefore resolve any number of forces into a single horizontal and a single vertical component by adding all horizontal and vertical forces respectively acting at the point under consideration. Chapter 14: Understand how Forces act on Structures Page 9

10 Practical Example 1 Consider the point J shown in figure 8 and the forces applied to it. Determine the magnitude and direction of the horizontal and vertical forces H and V required to ensure equilibrium. Hence or otherwise, calculate the single force and direction required to ensure equilibrium. Force N 30kN Force K 15kN 45 o Point J 50 o 20 o Force H Force M 10kN 40 o Force V Force L 25kN Figure 8: Forces applied at point J Such problem can be solved mathematically or graphically. Mathematically will involve, solving each component by its horizontal and vertical component and hence add all vertical components and horizontal components by using the Cartesian properties. Graphically will involve drawing two components at a time up to scale and by using the parallelogram of forces one will find the resultant force and direction. For such methods and answers, follow the teachers work during the lesson. Chapter 14: Understand how Forces act on Structures Page 10

11 Exercise 14a Choose the correct answer. Mark a very good in the appropriate box. 1 a) stable A funnel that is balanced upright on a table on its narrow tip is in equilibrium. b) unstable c) neutral 2 a) stable An inverted funnel placed on a table is in equilibrium. b) unstable c) neutral 3 a) stable A funnel lying horizontally on its side at rest on a table is in equilibrium. b) unstable c) neutral 4 a) True b) False Two equal and opposite forces acting at a point are in equilibrium. 5 a) True b) False The resultant of two forces acting at a point can be determined by using the Parallelogram of Forces. 6 There are fundamentally kinds of equilibrium. a) four b) two c) three Chapter 14: Understand how Forces act on Structures Page 11

12 7 Three forces in equilibrium acting at a point can be represented in magnitude and direction by the sides of a triangle taken in order. a) true b) false 8 A pendulum at rest is in equilibrium. a) stable b) unstable c) neutral 9 A force of 3 N acts on a small body pushing it vertically upwards. Simultaneously, another force of 8 N acts on it pushing it vertically downwards. The resultant of the two forces is. a) 5 N downwards b) 5 N upwards c) 11 N downwards d) 11 N upwards 10 Two forces acting at right angles, which have the same effect as a single force, are called. a) resultants b) components c) constituents 11 a) stable A sphere that is at rest on a table is in equilibrium. b) unstable c) neutral 12 a) stable A chalkstick that is balanced upright on a table is in equilibrium. b) unstable c) neutral Chapter 14: Understand how Forces act on Structures Page 12

13 Exercise 14b 1. Determine whether or not a net force exists in the following situations. Description of Motion Net Force: Yes or No? 2. Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Chapter 14: Understand how Forces act on Structures Page 13

14 3. Free-body diagrams for four situations are shown below. The net force is known for each situation. However, the magnitudes of a few of the individual forces are not known. Analyse each situation individually and determine the magnitude of the unknown forces. Then click the button to view the answers. Exercise 14c Choose the correct answer. 1 Which of Newton's Three Laws does the following statement satisfy? The relationship between an object's mass (m), its acceleration (a), and the applied force F is F = ma. Acceleration and force are vectors. This law requires that the direction of the acceleration vector is in the same direction as the force vector. a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above 2 Which of Newton's Three Laws does the following statement satisfy? For every action there is an equal and opposite reaction. a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above Chapter 14: Understand how Forces act on Structures Page 14

15 3 Which of Newton's Three Laws does the following statement satisfy? Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above 4 Which of Newton's three laws does the following example illustrate? If you have a hockey puck sliding along a table, it will eventually come to a stop. a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above 5 Which of Newton's Laws does this situation represent? Imagine a ball moving in a straight line directly toward when another ball collides with it. The moving ball exerts a force on the ball at rest. This causes the ball at rest to accelerate. However, the ball at rest also exerts the same magnitude of force (in the opposite direction) of the moving ball. This will cause the moving ball to decelerate or even move in another direction. a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above Chapter 14: Understand how Forces act on Structures Page 15

16 6 In the following example, what are the forces that are acting on the ball? Check all that apply. If a ball is thrown in the air, it will keep going the same velocity unless a force changes the velocity (speed and direction). a) Air friction b) Gravity c) Resistance of the ground d) Mass of the ball 7 Which law states the need to wear seatbelts? a) Newton s first Law b) Newton s second Law c) Newton s third Law d) All of the above 8 was the scientist who gave us the Laws of Motion a) Albert Einstein b) Michael Faraday c) Isaac Newton d) None of the above 9 What is another name for the Newton's first law of motion? a) Law of acceleration b) Law of velocity c) Law of inertia d) Law of mass Chapter 14: Understand how Forces act on Structures Page 16

17 Exercise 14d 1. A block of mass 2kg is pushed along a table with a constant velocity by a force of 5N. When the push is increased to 9N what is; a) the resultant force b) the acceleration? 2. How much net force is required to accelerate a 1000 kg car at 5m/s 2? 3. If you apply a net force of 1 N on 200g book, what is the acceleration of the book? 4. What is the net force on 200 g ball when it hits a wall with acceleration of 10 m/s 2? 5. What is the mass of an object that has a weight of 115 N on the Moon? The gravity of the Moon is 1/6 of g (which is 9.8 m/s 2 ). 6. What is the normal force acting on a 70kg person on the Moon? 7. A car is moving at a constant velocity of 20 km/h (5.56 m/s). How much net force is required to raise its velocity to 50 km/h (13.89 m/s) in 30 seconds? Suppose the car has a mass of 150 kg. 8. On Planet X, a 70 kg object can be lifted by a force of 400 N. a) What is the acceleration of gravity on Planet X? b) How much force is required if the same object is lifted on Earth? c) Suppose your car was taken to Planet X. If the car has a mass of 1500 kg, what would its weight be? 9. Calculate the weight, in kn, of each of the following two people. a) A young woman with a mass of 70kg. b) A middle-aged man with a mass of 95kg. What would be the weights of each of these people on the moon if the gravitational acceleration on the moon is one-sixth of that on earth? 10. Calculate the mass of a brick of length 215 mm, breadth mm and height 65 mm if its density is 1800 kg/m 3. What would be the weight of this brick? Chapter 14: Understand how Forces act on Structures Page 17

19 Exercise 14e 1. For the system of forces shown in the figure below: a) Calculate the horizontal and vertical components for each of the forces. b) Determine if the given system of forces are in static equilibrium. c) Solve this problem graphically to verify if the answers produced in (a) and (b) match. Force N 19.8kN + y Force K 30.23kN 25 o Point T 40 o 13.5 o 20 o + x Force M 72.8kN Force L 59.6kN Chapter 14: Understand how Forces act on Structures Page 19

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....

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

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

Chapter 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

Newton'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

Physics Exam 1 Review - Chapter 1,2

Physics 1401 - Exam 1 Review - Chapter 1,2 13. Which of the following is NOT one of the fundamental units in the SI system? A) newton B) meter C) kilogram D) second E) All of the above are fundamental

2. (P2.1 A) a) A car travels 150 km in 3 hours, what is the cars average speed?

Physics: Review for Final Exam 1 st Semester Name Hour P2.1A Calculate the average speed of an object using the change of position and elapsed time 1. (P2.1 A) What is your average speed if you run 140

Figure 1.1 Vector A and Vector F

CHAPTER I VECTOR QUANTITIES Quantities are anything which can be measured, and stated with number. Quantities in physics are divided into two types; scalar and vector quantities. Scalar quantities have

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 1 NON-CONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects

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

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

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

Newton 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

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

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

UNIT 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

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

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.

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

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

Summary Notes. to avoid confusion it is better to write this formula in words. time

National 4/5 Physics Dynamics and Space Summary Notes The coloured boxes contain National 5 material. Section 1 Mechanics Average Speed Average speed is the distance travelled per unit time. distance (m)

DISPLACEMENT AND FORCE IN TWO DIMENSIONS

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

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,

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

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

PS-5.1 Explain the relationship among distance, time, direction, and the velocity of an object.

PS-5.1 Explain the relationship among distance, time, direction, and the velocity of an object. It is essential for students to Understand Distance and Displacement: Distance is a measure of how far an

Section Review Answers Chapter 12 Section 1 1. Answers may vary. Students should say in their own words that an object at rest remains at rest and an object in motion maintains its velocity unless it experiences

Equilibrium of Concurrent Forces (Force Table)

Equilibrium of Concurrent Forces (Force Table) Objectives: Experimental objective Students will verify the conditions required (zero net force) for a system to be in equilibrium under the influence of

Forces. Lecturer: Professor Stephen T. Thornton

Forces Lecturer: Professor Stephen T. Thornton Reading Quiz: Which of Newton s laws refers to an action and a reaction acceleration? A) First law. B) Second law. C) Third law. D) This is a trick question.

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

Chapter 4 Newton s Laws: Explaining Motion

Chapter 4 Newton s s Laws: Explaining Motion Newton s Laws of Motion The concepts of force, mass, and weight play critical roles. A Brief History! Where do our ideas and theories about motion come from?!

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

M OTION. Chapter2 OUTLINE GOALS

Chapter2 M OTION OUTLINE Describing Motion 2.1 Speed 2.2 Vectors 2.3 Acceleration 2.4 Distance, Time, and Acceleration Acceleration of Gravity 2.5 Free Fall 2.6 Air Resistence Force and Motion 2.7 First

TEACHER ANSWER KEY November 12, 2003. Phys - Vectors 11-13-2003

Phys - Vectors 11-13-2003 TEACHER ANSWER KEY November 12, 2003 5 1. A 1.5-kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude

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

Chapter 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

Dynamics- Why do objects move as they do? What makes an object at rest, begin to move? What makes a body accelerate or decelerate?

Dynamics- Why do objects move as they do? What makes an object at rest, begin to move? What makes a body accelerate or decelerate? What makes an object move in a circle? Force A Force is simply a push

Center of Mass/Momentum

Center of Mass/Momentum 1. 2. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped

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

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

Physics Midterm Review Packet January 2010

Physics Midterm Review Packet January 2010 This Packet is a Study Guide, not a replacement for studying from your notes, tests, quizzes, and textbook. Midterm Date: Thursday, January 28 th 8:15-10:15 Room:

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

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

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

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.

Newton s Laws of Motion

Kari Eloranta 2015 Jyväskylän Lyseon lukio November 30, 2015 Kari Eloranta 2015 2.2.4 Newton s First Law of Motion Definition of Newton s First Law of Motion (Law of Inertia) An object at rest remains

PHYSICS MIDTERM REVIEW

1. The acceleration due to gravity on the surface of planet X is 19.6 m/s 2. If an object on the surface of this planet weighs 980. newtons, the mass of the object is 50.0 kg 490. N 100. kg 908 N 2. If

Lesson 5 Rotational and Projectile Motion

Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular

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

Concept Review. Physics 1

Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or

Conceptual Physics Review (Chapters 4, 5, & 6)

Conceptual Physics Review (Chapters 4, 5, & 6) Solutions Sample Questions and Calculations. If you were in a spaceship and launched a cannonball into frictionless space, how much force would have to be

Objective: Equilibrium Applications of Newton s Laws of Motion I

Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (1-11) Read (4.1-4.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,

v 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

Newton s Laws of Motion

Newton s Laws of Motion FIZ101E Kazım Yavuz Ekşi My contact details: Name: Kazım Yavuz Ekşi Email: eksi@itu.edu.tr Notice: Only emails from your ITU account are responded. Office hour: Wednesday 10.00-12.00

Introduction to Statics. .PDF Edition Version 1.0. Notebook

Introduction to Statics.PDF Edition Version 1.0 Notebook Helen Margaret Lester Plants Late Professor Emerita Wallace Starr Venable Emeritus Associate Professor West Virginia University, Morgantown, West

NEWTON S LAWS OF MOTION

NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied

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

Described by Isaac Newton

Described by Isaac Newton States observed relationships between motion and forces 3 statements cover aspects of motion for single objects and for objects interacting with another object An object at rest

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

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

Physics of Rocket Flight

Physics of Rocket Flight In order to understand the behaviour of rockets it is necessary to have a basic grounding in physics, in particular some of the principles of statics and dynamics. This section

Chapter 4. Forces and Newton s Laws of Motion

Chapter 4 Forces and Newton s Laws of Motion 4.1 The Concepts of Force and Mass A force is a push or a pull. Contact forces arise from physical contact. Action-at-a-distance forces do not require contact

Unit (Section 3) Represent and analyze the motion of an object graphically. Analyze the speed of two objects in terms of distance and time

Curriculum: Physics A Curricular Unit: One Dimensional Kinematics Instructional Unit: A. Describe the relationship of an object s position, velocity and acceleration over time when it moves in one dimension

Newton's First Law. Newton s Laws. Page 1 of 6

Newton's First Law Newton s Laws In previous units, the variety of ways by which motion can be described (words, graphs, diagrams, numbers, etc.) was discussed. In this unit (Newton's Laws of Motion),

COURSE CONTENT. Introduction. Definition of a Force Effect of Forces Measurement of forces. Newton s Laws of Motion

CHAPTER 13 - FORCES COURSE CONTENT Introduction Newton s Laws of Motion Definition of a Force Effect of Forces Measurement of forces Examples of Forces A force is just a push or pull. Examples: an object

Measurements of Speed. Speed. v = d t. PowerPoint Lectures to accompany Physical Science, 6e

PowerPoint Lectures to accompany Physical Science, 6e Chapter 2 Motion Homework: All the multiple choice questions in Applying the Concepts and Group A questions in Parallel Exercises. Motion is.. A change

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

Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

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

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

Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

3.1 Force, Mass, and Acceleration

Sir Isaac Newton discovered one of the most important relationships in physics: the link between the force on an object, its mass, and its acceleration. In this section, you will learn about force and

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

Gravitation. Gravitation

1 Gravitation Newton s observations A constant center seeking force is required to keep an object moving along a circular path. You know that the moon orbits the earth and hence there should be a force

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

Principles and Laws of Motion

2009 19 minutes Teacher Notes: Ian Walter DipAppChem; TTTC; GDipEdAdmin; MEdAdmin (part) Program Synopsis This program begins by looking at the different types of motion all around us. Forces that cause

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

Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 6. Flow of Fluid and Bernoulli s Equation 7.

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

PHYSICS 149: Lecture 4

PHYSICS 149: Lecture 4 Chapter 2 2.3 Inertia and Equilibrium: Newton s First Law of Motion 2.4 Vector Addition Using Components 2.5 Newton s Third Law 1 Net Force The net force is the vector sum of all

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,

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

Chapter 4 Forces and Newton s Laws of Motion continued Clicker Question 4.3 A mass at rest on a ramp. How does the friction between the mass and the table know how much force will EXACTLY balance the gravity

STATICS. Introduction VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.

Eighth E CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Introduction Lecture Notes: J. Walt Oler Texas Tech University Contents What is Mechanics? Fundamental

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 Exam Q1 Exam, Part A Samples

Physics Exam Q1 Exam, Part A Samples 1. An object starts from rest and accelerates uniformly down an incline. If the object reaches a speed of 40 meters per second in 5 seconds, its average speed is (A)

Lesson 4 Rigid Body Statics. Taking into account finite size of rigid bodies

Lesson 4 Rigid Body Statics When performing static equilibrium calculations for objects, we always start by assuming the objects are rigid bodies. This assumption means that the object does not change

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

Section 3 Newton s Laws of Motion

Section 3 Newton s Laws of Motion Key Concept Newton s laws of motion describe the relationship between forces and the motion of an object. What You Will Learn Newton s first law of motion states that

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

First Semester Learning Targets

First Semester Learning Targets 1.1.Can define major components of the scientific method 1.2.Can accurately carry out conversions using dimensional analysis 1.3.Can utilize and convert metric prefixes

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)

4 Gravity: A Force of Attraction

CHAPTER 1 SECTION Matter in Motion 4 Gravity: A Force of Attraction BEFORE YOU READ After you read this section, you should be able to answer these questions: What is gravity? How are weight and mass different?

Mechanics 1: Conservation of Energy and Momentum

Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation

Motion Lesson 1: Review of Basic Motion

Motion in one and two dimensions: Lesson 1 Semi-notes 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

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

ANALYTICAL METHODS FOR ENGINEERS

UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

Homework 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

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