041. 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.


 Amy Haynes
 2 years ago
 Views:
Transcription
1 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 we have successfully described an object in freefall and the motion of a projectile, both cases of motion being influenced or driven by the force of gravity. But in both cases the acceleration of the object remained constant. (We described what happened to the object while it was falling, not on what happened to the object once it hit the ground.) This made it unnecessary for us to modify our kinematic definitions or to construct new concepts. However, once we include the concept of force into our study of motion in a general way, by allowing for changes to take place in the magnitude or direction of the force, then we need to anticipate possible changes in the acceleration of the object. The object may speed up, slow down or change direction. The study of motion then expands into dynamics. We shall begin our study of dynamics with the concept of force and the first of the true laws of physics, Newton s Laws of Motion. Later in this and later notes we shall see how these laws can be applied to describe real world problems. The Concept of Force The concept of force is learned early in childhood. We learn that in order to make something move we must push it or pull it; we have to exert a force on it. We also learn that if we jump from a point above the ground then we will drop to the ground (and possibly injure ourselves). In this case something else exerts a force on us. This force we call the force of gravity. In physics, a push or a pull is called a contact force, whereas the force of gravity is called a noncontact force. We shall discuss noncontact forces and the associated concept of a field in a later note. For the moment we focus on contact forces. 1 Force is a Vector If we consider for simplicity a force as a simple pull, then we can quantify the pull in a relative way by observing its effect on something that stretches, like an elastic or spring scale (Figure 41). If a spring is 1 A contact force is actually a manifestation of the electromagnetic force and is not a true, distinct force. It just happens to be easier for teaching purposes to continue using the term contact force for the present. pulled it will stretch by an amount that can be measured with a ruler. If we pull on a spring by a certain amount of muscular action then the spring stretches by a certain amount. If two people each pull by the same amount of muscular action then the spring stretches twice as much as before. Figure 41. Observations with a spring scale indicate that force is a vector. More importantly, if forces of magnitude F 1 and F 2 are applied to the end of the spring scale in arbitrary perpendicular directions as shown in the figure, then the extension of the spring is found to be proportional to F = ( F 1 ) 2 + ( F 2 ) 2. The conclusion to be drawn is that force is a vector. We now consider Newton s Three laws of motion in modern language and discuss the concepts and definitions associated with each. Newton s First Law Newton s first law states: In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line). 041
2 You will be able to witness the effects of Newton s first law for yourself in the experiment Linear Motion. If you place a glider on a horizontal airtrack and release it from rest, it will remain at rest. If you release the glider with some initial velocity, then it will continue to move at a constant velocity (until it encounters the bumper at the end of the track). These observations are consistent with Newton s first law. Law of Inertia Another way of stating the first law is to say if the net force acting on an object is zero, then the acceleration of the object is zero. An object has an attribute that tends to resist a change in its state of motion. This attribute is called inertia. The first law is therefore often called the law of inertia. Inertial Reference Frame In physics, we often make use of the concept of an inertial reference frame. An inertial reference frame is a reference frame in which Newton s first law holds. In other words, an inertial reference frame is one that is not undergoing acceleration itself. A glider, whether stationary or moving with constant velocity on a horizontal airtrack, is an example of an inertial reference frame. Another example of a moreorless inertial reference frame is a position on the surface of the Earth (say at a worktable in the lab). It is true that the Earth is spinning on its axis and is rotating about the Sun, so a position on the surface of the Earth is therefore undergoing two types of acceleration. But both types are very small in relation to the acceleration of most systems under study; in problems in a first year physics course they can mostly be neglected. Inertial Mass We have stated that an object possesses an attribute that resists a change in its state of motion. By state of motion is meant the following: the state of motion of a ball, for example, can be changed by either throwing it or catching it. A ball made of lead is harder to catch than is a ball made of rubber. This attribute is called inertia as we have seen. A lead ball has more inertia than a rubber ball of the same size. Inertia is more familiarly called mass, and in particular, inertial mass. It may be described in these words: Inertial mass is the measure of an object s resistance to a change in motion in response to an external force. If the same force acts on masses m 1 and m 2 and produces the accelerations a 1 and a 2, respectively, then 042 the ratio of the two masses is defined as the inverse ratio of the magnitudes of the accelerations produced by the same force: m 1 = a 2. m 2 a 1 Now if one of these masses happens to be the 1 kg standard mass (described in Note 01) then the mass of the unknown object can be calculated from measurements of the accelerations. 2 Mass is an inherent property of an object, independent of the object s surroundings and of the method used to measure it. Gravitational mass is defined somewhat differently from inertial mass as we shall see. As far as is known an object s inertial and gravitational masses are equal, and are therefore by inference taken to be one and the same property. Newton s Second Law Newton s second law states: The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object s mass. Note that the word object in this statement (and the ones to follow) could be replaced by the word system. Mathematically, the second law means a F m. Writing this expression as an equality and rearranging we have F = ma. [41] Thus the vector sum of forces (net force) on an object equals the product of the object s mass and acceleration. The acceleration of an object is in the same direction as the net force on the object. Since eq[41] is a vector equation these component equations apply in 3D space: = ma x F y = ma y F z = ma z. 2 Interestingly, though mass is a fundamental quantity, the finding of inertial mass involves calculation not measurement with an instrument. As we shall see in due course, the finding of gravitational mass on the other hand involves measurement with an instrument like a calibrated spring scale or a balance.
3 Unit of Force From eq[41] the dimension of force equals the product of the dimensions of mass and acceleration, namely M.L.T 2. Its units are kg.m.s 2. 1 kg.m.s 2 is called a newton. 1 newton (abbreviated N) may be defined in words as the force that produces an acceleration of 1 m.s 2 on a mass of 1 kg y x Once the resultant force on an object of known mass is known then the object s acceleration can be calculated. Let us consider an example. a = 3.66 m/s/s Example Problem 41 Finding the Acceleration of an Object Three forces of magnitude 10.0 N act on a ball of mass 2.00 kg in the directions shown in Figure 42. Calculate the resultant acceleration of the ball. F2 = 10.0 N F3 = 10.0 N 30.0 y 2.00 kg F1 = 10.0 N 30.0 Figure 42. Three forces of magnitude F1, F2 and F3 act on a ball. Solution: This problem is an extension of Example Problem 23. It was shown in that problem that the resultant force vector is of magnitude 7.32 N acting in a direction 30.0 wrt to the ve xaxis (Figure 213). Since we have a = F m a = 7.32(N) 2.00(kg) = 3.66 m.s 2. The acceleration vector points in the same direction as the resultant force vector (Figure 43). x Figure 43. The acceleration of the ball in Figure 42 during the elapsed time the three forces act. WARNING! Force and Acceleration An object undergoes an acceleration only so long as the resultant or net force on the object is also nonzero. In the event that the force is zero the acceleration is also zero. Gravitational Force and Weight We have seen that mass is a fundamental property of an object (being the sum total of the masses of its constituent atoms and molecules). Under ordinary conditions (nonrelativistic speeds) the mass of an object remains constant. An object has the same mass whether measured on the Earth or on the Moon. The weight of an object is different from mass. It is defined in these words: In physics, the weight of an object is defined as the magnitude of the resultant force of gravity on the object. We have seen that when an object is released near the surface of the Earth it always falls downwards with the same acceleration, namely g. In this situation there is only one force acting on the object, the force of gravity. Thus F = Fg. It follows from the second law that Fg = ma = mg, and so the weight of any object of mass m is 043
4 Fg = F g = mg (N). [42] Weight is a positive scalar with the unit newton. Newton s Third Law Newton s Third law states: If two objects interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F 21 exerted by object 2 on object 1, that is, F12 = F21. The idea is illustrated in Figure 44. [43] Figure 44. To every force there is an equal and opposite reaction force. Shown here are the gravitational forces two objects exert on one another. The book has a mass m and is subject to the gravitational force of the Earth. But the book is in contact with the table. Since the Earth pulls downwards on the book and the book is in contact with the table, then the book pushes downwards on the table with the same magnitude of force. Since the book pushes downwards on the table, the table reacts (third law) by pushing upwards on the book. This reaction force (denoted n ) is called a normal force when it is perpendicular (or normal) to a surface. The upshot is that the sum of forces on the book is F = FTB + FEB = n + mg = 0. (Here the notation FTB means the force the table exerts on the book.) Figure 45 is the freebody diagram of the book. A freebody diagram is a diagram showing just the forces acting on the object of interest. The Idea of Tension Tension is a word used to describe the contact force exerted by a rope or a string on whatever it is attched to. A problem involving tension is illustrated in Figure 46. A rope is attached to point W on an immovable wall. A boy at position B pulls on the rope with force FBR in a direction towards the right. Neither wall nor boy actually move. In the process of being pulled, the rope becomes taut and is subject to what is called tension. To explore this idea further with more familiar contact forces consider an object like a book lying at rest on a table (Figure 45). Since the book is stationary, and in an inertial reference frame, it is described by the first law. FWR FRW Boy FTB = n W FRB B FBR 044 FEB = mg book m table Figure 45. Freebody diagram of a book lying at rest on a table in the laboratory. Wall Figure 46. The forces involved when a boy pulls on a rope attached to an immovable wall. Two freebody diagrams are shown here for points W and B. You should be able to reason that the forces shown, namely FBR, FRB, FRW and FWR are all of equal magnitude. F RW and F RB both refer to the same tension in the rope. Tension may be defined in these words:
5 The tension in a rope is the magnitude of the force the rope exerts on whatever it is attached to. Note 04 It is important to note that Figure 46 shows two freebody diagrams for the points W and B. The two forces in the left half of the figure are the forces acting only on W. The two forces on the right half of the figure act only on the point B. An Object in Translational Equilibrium An object at rest or moving with constant velocity is said to be in a state of translational equilibrium. Translational equilibrium is the state of an object that satisfies Newton s first law. 3 The condition of translational equilibrium may be stated mathematically as F = 0. Figure 47a. A traffic light at rest. This means that in 3D space we have the component equations = 0 F y = 0 F z = 0. [44] The book shown in Figure 45 is an example of an object in translational equilibrium. More precisely, since the object is in a state of translational equilibrium and is at rest, it is said to be in a state of static equilibrium. Applications of Newton s Laws In an introductory physics course there are a number of classical problem types. These include the problem of tension in a cable pulling or supporting an object, the working of the Atwood machine and the analysis of objects pushing on one another. We consider these three types in examples. Example Problem 42 A Traffic Light at Rest A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as in Figure 47a. The upper cables make angles of 37.0 and 53.0 with the horizontal. These upper cables are not as strong as the vertical cable, and will break if the tension in them exceeds 100. N. Does the traffic light remain in this situation, or will one of the cables break? Figure 47b. The freebody diagram of the traffic light. Solution: Two points on this diagram are of special interest: the light itself and the knot at which the three cables come together. Both points are in states of static equilibrium (at least they are prior to the instant when the ropes break, if they do break). The freebody diagram of the traffic light itself is drawn in Figure 47b. Figure 47b shows only two forces: the force of gravity acting downwards and the tension T 3 acting upwards. Applying the equilibrium condition to the traffic light in the ydirection F y = 0 gives T 3 F g = 0. This means that 3 In later notes we shall extend this condition to include rotational motion. T 3 = F g = 122 N. 045
6 The force T 3 exerted by the vertical cable balances the force of gravity on the light. As for the knot, its freebody diagram is drawn in Figure 47c, with a set of arbitrarilychosen xand y axes. T 2 = 1.33T 1 = 97.4 N. Both of these values are less than 100. N so the cables will not break. Example Problem 43 The Atwood Machine Figure 47c. The tensions in the ropes act at a common point. The Atwood machine, an example of which is shown in Figure 48, is an apparatus commonly used in introductory physics labs for studying Newton s laws. The version shown here has masses m 1 and m 2 connected together with a rope that passes over a pulley whose friction is assumed to be negligible. 4 We shall assume here that m 1 is less than m 2 so the former should be expected to accelerate upward, the latter downward. Calculate an expression for the magnitude of the acceleration a of the masses and the tension T in the rope. The forces in the ropes can be resolved into their x and ycomponents as listed in the following table: Force xcomponent ycomponent T1 T 1 cos37.0 T 1 sin37.0 T 2 T 2 cos53.0 T 2 sin53.0 T N Eqs[44} applied to the knot give = T 2 cos 53.0 o T 1 cos37.0 o = 0, F y = T 1 sin37.0 o + T 2 sin 53.0 o 122N = 0. Solving the first equation for T 2 gives T 2 in terms of T 1 : cos37.0 o T 2 = T 1 cos53.0 o =1.33T 1. Substituting T 2 into the second of the above equations gives T 1 sin 37.0 o + (1.33T 1 )sin 53.0 o 122N = 0 Figure 48. An Atwood machine. In this note we assume up is positive, down is negative. Solution: We take up as positive, down as negative. Applying Newton s second law to m 1 we have F y = T m 1 g = m 1 a. [45] Applying the second law to m 2 we have so that T 1 = 73.4 N. Finally we substitute back to get T 2 : We assume we can also neglect the moment of inertia of the pulley. In this course, because of a lack of time, we shall have to omit the concept of moment of inertia.
7 F y = T m 2 g = m 2 a. [46] Subtracting eq[46] from eq[45] gives m 1 g g = m 1 a a from which we can solve for the magnitude a: a = m m 2 1 g. m 1 The acceleration of the twoblock system is a = F m 1. Note 04 (b) We now treat each block individually. The freebody diagrams of m 1 and m 2 are drawn in Figures 49b and c where the contact force is denoted P. This expression is general and includes two special cases. If m 2 > m 1 then a is positive and m 1 accelerates upwards and m 2 downwards. If m 1 > m 2 then a is negative and m 1 accelerates downwards, m 2 upwards. Substituting the above expression for a into eq[45] yields T: T = 2m m 1 2 g. m 1 Figure 49b. The freebody diagram of m 1. This expression is general and applies for any value of m 1 and m 2. For example, if m 1 = m 2 then T = mg and a = 0, that is, neither object moves. Example Problem 44 One Block Pushes Another Two blocks of mass m 1 and m 2, with m 1 > m 2, are placed in contact with each other on a surface assumed to be frictionless (Figure 49a). A constant horizontal force F is applied to m 1 as shown. Find (a) the magnitude of the acceleration of the system of two blocks and (b) the magnitude of the contact force between the two blocks. Figure 49c. The freebody diagram of m 2. From Figure 49c the only horizontal force acting on m 2 is the contact force P12 (the force exerted by m 1 on m 2 ), which is directed to the right. Applying the second law to m 2 gives = P 12 = m 2 a. Substituting the expression for a from above gives the magnitude of the contact force requested: Figure 49a. A force is applied to two blocks in contact. Solution: (a) The blocks are in contact and therefore experience the same acceleration produced by F. Thus (system) = F = (m 1 )a. m P 12 = m 2 a = 2 F. m 1 Note that the force on the system as a whole (and on m 1 ) is F but the force on m 2 is less than F. 047
8 To Be Mastered Definitions: force, Newton s Laws of Motion, inertial reference frame Definitions: mass, inertial mass, gravitational mass, weight, tension Definition: weight Definition: tension Definition: freebody diagram 1. State Newton s Laws. Typical Quiz/Test/Exam Questions 2. A puck of mass g rests on a frictionless ice surface. There are two ropes attached to the puck by a pin at the puck s center. Two people pull as hard as they can in a horizontal direction, one person on each rope. If they pull in the same direction as shown, the puck has an acceleration of 1.52 m.s 2 to the right. If the direction of rope 1 is reversed and the people pull in opposite directions, then the puck has an acceleration of m.s 2 to the left. rope 1 puck rope 2 Answer the following questions: (a) What magnitude of force does each rope exert on the puck? (b) What are the corresponding tensions in the ropes? (c) What would be the acceleration of the puck if each person pulls with forces of equal magnitudes in opposite directions? (d) What law(s) of motion do these questions involve? 3. An object of mass 1.0 kg is hanging motionless by a cable from a fixed support (see the figure). Answer the following questions: support cable object (a) What is the weight of the object? (b) What force does the cable exert on the support? (c) What force does the cable exert on the object? (d) What is the acceleration of the object? 048
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
More informationNewton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1
Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is
More informationChapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.
Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationChapter 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?!
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationNewton s Laws of Motion
Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationNewton s Laws of Motion
Physics Newton s Laws of Motion Newton s Laws of Motion 4.1 Objectives Explain Newton s first law of motion. Explain Newton s second law of motion. Explain Newton s third law of motion. Solve problems
More informationLecture Outline Chapter 5. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 5 Physics, 4 th Edition James S. Walker Chapter 5 Newton s Laws of Motion Dynamics Force and Mass Units of Chapter 5 Newton s 1 st, 2 nd and 3 rd Laws of Motion The Vector Nature
More informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problemsolving questions, draw appropriate free body diagrams and use the aforementioned problemsolving method.. Define the following
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationPHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17. February 13, 2013
PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17 February 13, 2013 0.1 A 2.00kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object
More informationPhysics Notes Class 11 CHAPTER 5 LAWS OF MOTION
1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is
More informationSerway_ISM_V1 1 Chapter 4
Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationNewton s Laws. Physics 1425 lecture 6. Michael Fowler, UVa.
Newton s Laws Physics 1425 lecture 6 Michael Fowler, UVa. Newton Extended Galileo s Picture of Galileo said: Motion to Include Forces Natural horizontal motion is at constant velocity unless a force acts:
More informationChapter 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
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationThis week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.
This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical
More information5. Forces and MotionI. Force is an interaction that causes the acceleration of a body. A vector quantity.
5. Forces and MotionI 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
More informationObjective: Equilibrium Applications of Newton s Laws of Motion I
Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (111) Read (4.14.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,
More informationMass, 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
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More informationChapter 5 Newton s Laws of Motion
Chapter 5 Newton s Laws of Motion Sir Isaac Newton (1642 1727) Developed a picture of the universe as a subtle, elaborate clockwork slowly unwinding according to welldefined rules. The book Philosophiae
More informationPhysics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.
Physics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and noncontact forces. Whats a
More informationPhysics 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 informationWorksheet #1 Free Body or Force diagrams
Worksheet #1 Free Body or Force diagrams Drawing FreeBody Diagrams Freebody diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.
More informationChapter 11 Equilibrium
11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of
More informationPHYSICS 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
More informationTwoBody System: Two Hanging Masses
Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationChapter 5. The Laws of Motion
Chapter 5 The Laws of Motion CHAPTER OUTLINE 5.1 The Concept of Force 5.2 Newton s First Law and Inertial Frames 5.3 Mass 5.4 Newton s Second Law 5.5 The Gravitational Force and Weight 5.6 Newton s Third
More informationMULTIPLE 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. 1) Vector A has length 4 units and directed to the north. Vector B has length 9 units and is directed
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationAP Physics Applying Forces
AP Physics Applying Forces This section of your text will be very tedious, very tedious indeed. (The Physics Kahuna is just as sorry as he can be.) It s mostly just a bunch of complicated problems and
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
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
More informationChapter 18 Static Equilibrium
Chapter 8 Static Equilibrium 8. Introduction Static Equilibrium... 8. Lever Law... Example 8. Lever Law... 4 8.3 Generalized Lever Law... 5 8.4 Worked Examples... 7 Example 8. Suspended Rod... 7 Example
More informationPhysics 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
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationNewton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of
Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed
More informationSOLUTIONS 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 informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More information1. 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 informationNewton s Law of Motion
chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating
More informationUNIT 2D. Laws of Motion
Name: Regents Physics Date: Mr. Morgante UNIT 2D Laws of Motion Laws of Motion Science of Describing Motion is Kinematics. Dynamics the study of forces that act on bodies in motion. First Law of Motion
More informationAP 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 informationForces: Equilibrium Examples
Physics 101: Lecture 02 Forces: Equilibrium Examples oday s lecture will cover extbook Sections 2.12.7 Phys 101 URL: http://courses.physics.illinois.edu/phys101/ Read the course web page! Physics 101:
More informationIdeal Cable. Linear Spring  1. Cables, Springs and Pulleys
Cables, Springs and Pulleys ME 202 Ideal Cable Neglect weight (massless) Neglect bending stiffness Force parallel to cable Force only tensile (cable taut) Neglect stretching (inextensible) 1 2 Sketch a
More informationThere are three different properties associated with the mass of an object:
Mechanics Notes II Forces, Inertia and Motion The mathematics of calculus, which enables us to work with instantaneous rates of change, provides a language to describe motion. Our perception of force is
More informationConceptual Questions: Forces and Newton s Laws
Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is
More informationA Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion
A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for
More informationNEWTON 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
More informationTEACHER ANSWER KEY November 12, 2003. Phys  Vectors 11132003
Phys  Vectors 11132003 TEACHER ANSWER KEY November 12, 2003 5 1. A 1.5kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude
More informationForce. 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 informationLAB 6  GRAVITATIONAL AND PASSIVE FORCES
L061 Name Date Partners LAB 6  GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies
More informationDISPLACEMENT AND FORCE IN TWO DIMENSIONS
DISPLACEMENT AND FORCE IN TWO DIMENSIONS Vocabulary Review Write the term that correctly completes the statement. Use each term once. coefficient of kinetic friction equilibrant static friction coefficient
More informationLAB 6: GRAVITATIONAL AND PASSIVE FORCES
55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction
More informationConceptual Physics 11 th Edition
Conceptual Physics 11 th Edition Chapter 5: NEWTON S THIRD LAW OF MOTION This lecture will help you understand: Forces and Interactions Newton s Third Law of Motion Summary of Newton s Laws Vectors Forces
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform
More informationAP Physics Newton's Laws Practice Test
AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a
More informationChapter 5 Newton s Laws of Motion
I do not know what I may appear to the world/ but to myself I seem to have been only like a boy playing on the sea shore, and diverting myself in now and then finding a smoother pebble or a prettier shell
More informationQUESTIONS : CHAPTER5: LAWS OF MOTION
QUESTIONS : CHAPTER5: LAWS OF MOTION 1. What is Aristotle s fallacy? 2. State Aristotlean law of motion 3. Why uniformly moving body comes to rest? 4. What is uniform motion? 5. Who discovered Aristotlean
More informationChapter 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
More informationLecture Presentation Chapter 4 Forces and Newton s Laws of Motion
Lecture Presentation Chapter 4 Forces and Newton s Laws of Motion Suggested Videos for Chapter 4 Prelecture Videos Newton s Laws Forces Video Tutor Solutions Force and Newton s Laws of Motion Class Videos
More informationAP1 Dynamics. Answer: (D) foot applies 200 newton force to nose; nose applies an equal force to the foot. Basic application of Newton s 3rd Law.
1. A mixed martial artist kicks his opponent in the nose with a force of 200 newtons. Identify the actionreaction force pairs in this interchange. (A) foot applies 200 newton force to nose; nose applies
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationPrelab 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 informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More informationChapter 18 Electric Forces and Electric Fields. Key Concepts:
Chapter 18 Lectures Monday, January 25, 2010 7:33 AM Chapter 18 Electric Forces and Electric Fields Key Concepts: electric charge principle of conservation of charge charge polarization, both permanent
More informationLaboratory Report Scoring and Cover Sheet
Laboratory Report Scoring and Cover Sheet Title of Lab _Newton s Laws Course and Lab Section Number: PHY 1103100 Date _23 Sept 2014 Principle Investigator _Thomas Edison CoInvestigator _Nikola Tesla
More informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationB Answer: neither of these. Mass A is accelerating, so the net force on A must be nonzero Likewise for mass B.
CTA1. An Atwood's machine is a pulley with two masses connected by a string as shown. The mass of object A, m A, is twice the mass of object B, m B. The tension T in the string on the left, above mass
More informationForce. A force is a push or a pull. Pushing on a stalled car is an example. The force of friction between your feet and the ground is yet another.
Force A force is a push or a pull. Pushing on a stalled car is an example. The force of friction between your feet and the ground is yet another. Force Weight is the force of the earth's gravity exerted
More informationThe Laws of Motion. web For more information about the airship, visit index.html.
P U Z Z L E R The Spirit of Akron is an airship that is more than 60 m long. When it is parked at an airport, one person can easily support it overhead using a single hand. Nonetheless, it is impossible
More informationConceptual Physics Fundamentals
Conceptual Physics Fundamentals Chapter 4: NEWTON S LAWS OF MOTION Newton s Laws of Motion I was only a scalar until you came along and gave me direction. Barbara Wolfe This lecture will help you understand:
More informationAcceleration due to Gravity
Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision
More informationPhysics 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 8:1510:15 Room:
More informationNewton s Laws of Motion
C HAPTER 4 The great meteor crater in Arizona P sychics and fortunetellers try to predict the future. Such predictions are rarely confirmed, however. There are simply too many unforeseeable circumstances
More informationWeight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)
Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in
More informationB) 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 informationChapter 7 Newton s Laws of Motion
Chapter 7 Newton s Laws of Motion 7.1 Force and Quantity of Matter... 1 Example 7.1 Vector Decomposition Solution... 3 7.1.1 Mass Calibration... 4 7.2 Newton s First Law... 5 7.3 Momentum, Newton s Second
More informationWork Energy & Power. September 2000 Number 05. 1. Work If a force acts on a body and causes it to move, then the force is doing work.
PhysicsFactsheet September 2000 Number 05 Work Energy & Power 1. Work If a force acts on a body and causes it to move, then the force is doing work. W = Fs W = work done (J) F = force applied (N) s = distance
More informationCh 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
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More information2 Newton s First Law of Motion Inertia
2 Newton s First Law of Motion Inertia Conceptual Physics Instructor Manual, 11 th Edition SOLUTIONS TO CHAPTER 2 RANKING 1. C, B, A 2. C, A, B, D 3. a. B, A, C, D b. B, A, C, D 4. a. A=B=C (no force)
More informationUniversal Law of Gravitation
Universal Law of Gravitation Law: Every body exerts a force of attraction on every other body. This force called, gravity, is relatively weak and decreases rapidly with the distance separating the bodies
More informationW02D22 Table Problem Newton s Laws of Motion: Solution
ASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 W0D Table Problem Newton s Laws of otion: Solution Consider two blocks that are resting one on top of the other. The lower block
More informationChapter 4A. Translational Equilibrium. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 4. Translational Equilibrium PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 MOUNTIN CLIMER exerts action forces on crevices and ledges,
More informationUniversity Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples
University Physics 226N/231N Old Dominion University Newton s Laws and Forces Examples Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012odu Wednesday, September
More informationForces. When an object is pushed or pulled, we say that a force is exerted on it.
Forces When an object is pushed or pulled, we say that a force is exerted on it. Forces can Cause an object to start moving Change the speed of a moving object Cause a moving object to stop moving Change
More informationLecture 7 Force and Motion. Practice with Freebody Diagrams and Newton s Laws
Lecture 7 Force and Motion Practice with Freebody Diagrams and Newton s Laws oday we ll just work through as many examples as we can utilizing Newton s Laws and freebody diagrams. Example 1: An eleator
More informationPhysics. Lesson Plan #6 Forces David V. Fansler Beddingfield High School
Physics Lesson Plan #6 Forces David V. Fansler Beddingfield High School Force and Motion Objective Define a force and differentiate between contact forces and longrange forces; Recognize the significance
More information2 Mechanics. Kinematics. Displacement and distance 2.1
2 Mechanics 2.1 Kinematics Assessment statements 2.1.1 Define displacement, velocity, speed and acceleration. 2.1.2 Explain the difference between instantaneous and average values of speed, velocity and
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationFriction and Newton s 3rd law
Lecture 4 Friction and Newton s 3rd law Prereading: 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 informationGeneral Physics Lab: Atwood s Machine
General Physics Lab: Atwood s Machine Introduction One may study Newton s second law using a device known as Atwood s machine, shown below. It consists of a pulley and two hanging masses. The difference
More information