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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

Transcription

1 College Physics 140 Chapter 4: Force and Newton s Laws of Motion We will be investigating what makes you move (forces) and how that accelerates objects.

2 Chapter 4: Forces and Newton s Laws of Motion Forces Newton s Three Laws of Motion The Gravitational Force Contact Forces (normal, friction, tension) Application of Newton s Second Law Apparent Weight Air Resistance Fundamental Forces

3 Forces Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies. Over the next few chapters, we will study how bodies interact with one another. Simply, a force is a push or pull on an object.

4 Forces How can a force be measured? One way is with a spring scale. By hanging masses on a spring we find that the spring stretch applied force. The net force is the vector sum of all the forces acting on a body. This means force is a vector quantity. F net = ΣF = F 1 + F 2 + F 3 + The units of force are Newtons (N).

5 Inertia and Equilibrium: Newton s First Law of Motion Newton s 1 st Law (The Law of Inertia): If no force acts on an object, then its speed and direction of motion do not change. Inertia is a measure of an object s resistance to changes in its motion. If the object is at rest, it remains at rest (speed = 0). If the object is in motion, it continues to move in a straight line with the same speed. No force is required to keep a body in straight line motion when effects such as friction are negligible. Therefore, turning requires an acceleration. An object is in translational equilibrium if the net force on it is zero.

6 Net Force, Mass, and Acceleration: Newton s Second Law of Motion Newton s 2nd Law: The acceleration of a body is directly proportional to the net force acting on the body and inversely proportional to the body s mass. Mathematically: a = F net m or F net = ma Some forces you will deal with: Gravitational, Normal, Friction, Centripetal, Tension,...

7 Net Force, Mass, and Acceleration: Newton s Second Law of Motion An object s mass is a measure of its inertia. The more mass, the more force is required to obtain a given acceleration. The net force is just the vector sum of all of the forces acting on the body, often wri]en as ΣF. If a = 0, then ΣF = 0. This body can have: Speed = 0 which is called static equilibrium, or Speed 0, but constant, which is called dynamic equilibrium. F=ma For Newton s Second Law to be valid it must be applied in an inertial reference frame. An inertial reference frame is one where Newton s First law is valid. A non- accelerating reference frame!

8 Interaction Pairs: Newton s Third Law of Motion Newton s 3 rd Law: When 2 bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction. Or, forces come in pairs. Mathematically: F21 = F 12.

9 Interaction Pairs: Newton s Third Law of Motion Example: Consider a box resting on a table. F 1 (a) F 1 is the force of the Earth on the box, what is the interaction partner of this force? The table! F 2 (b) F 2 is the force of the box on the table, what is the interaction partner of this force? The Floor!

10 External forces: Any force on a system from a body outside of the system. F Pulling a box across the floor Force between bodies of a system. F ext Pulling 2 boxes across the floor where the two boxes are a]ached to each other by a rope.

11 Gravitational Forces Gravity is the force between two masses. Gravity is a long- range or field force. No contact is needed between the bodies. The force of gravity is always a]ractive! The force between two objects F G = GMm r 2 G = 6.67 x m 3 /kgs 2 r is the distance between the two masses M 1 and M 2 and G = Nm 2 /kg 2. M 1 F 21 F 12 M 2 F21 = F 12. r Because the Earth is so large the force is really large. As you move away from the Earth, the force gets smaller, but not zero!

12 Gravitational Forces! Let M 1 = mass of the Earth. F = GM E # " r 2 $ &M 2 % Here F = the force the Earth exerts on mass M 2. This is the force known as weight, w.! w = GM E # 2 " r E $ &M 2 = gm 2. % M E = kg r E = 6400 km where g = GM E r E 2 = 9.8 N/kg = 9.8 m/s 2 Near the surface of the Earth

13 Gravitational Forces Example: What is the weight of a 100 kg astronaut on the surface of the Earth (force of the Earth on the astronaut)? How about in low Earth orbit? This is an orbit about 300 km above the surface of the Earth. On Earth: w = mg = 980 N! In low Earth orbit: w = mg(r o ) = m GM E # " R E + h ( ) 2 $ & = 890 N % Their weight is reduced by about 10%. The astronaut is NOT weightless!

14 Gravitational Forces Mass vs. Weight We perceive the force of gravity as our weight. Don t confuse this with mass. Mass is an intrinsic property of ma]er, but weight will change depending on gravity. GMm FG = 2 r Since the moon has 1/6 the mass of the Earth, it has 1/6 the force of gravity. This means you will weight 1/6 your weight on earth. If you weight 120 lbs. on earth, then you will weight 20 lbs. on the moon!

15 Contact Forces Contact forces: these forces arise because of an interaction between the atoms in the surfaces in contact. Normal force: this force acts in the direction perpendicular to the contact surface. N Normal force of the ground on the box w N Normal force of the ramp on the box w

16 Contact Forces Example: Consider a box on a table. y FBD for box N x w Apply Newton s 2 nd law F y = N w = 0 So that N = w = mg This just says the magnitude of the normal force equals the magnitude of the weight; they are not Newton s third law interaction partners.

17 Contact Forces Friction: a contact force parallel to the contact surfaces. Static friction acts to prevent objects from sliding. The force of static friction is modeled as fs µ sn. where µ s is the coefficient of static friction and N is the normal force. Kinetic friction acts to make sliding objects slow down. The force of kinetic friction is modeled as f = µ k k N. where µ k is the coefficient of kinetic friction and N is the normal force.

18 Contact Forces Example (text problem 4.95): A box full of books rests on a wooden floor. The normal force the floor exerts on the box is 250 N. (a) You push horizontally on the box with a force of 120 N, but it refuses to budge. What can you say about the coefficient of friction between the box and the floor? FBD for N y box (1) F y = N w = 0 f s w F x Apply Newton s 2 nd Law (2) F x = F f s = 0

19 Contact Forces Example (text problem 4.95): A box full of books rests on a wooden floor. The normal force the floor exerts on the box is 250 N. (a) You push horizontally on the box with a force of 120 N, but it refuses to budge. What can you say about the coefficient of friction between the box and the floor? From (2): F = f s = µ s N µ s = F N = 0.48 This is the minimum value of µ s, so µ s > (b) If you must push horizontally on the box with 150 N force to start it sliding, what is the coefficient of static friction? Again from (2): F = f s = µ s N µ s = F N = 0.60

20 Contact Forces Example (text problem 4.95): A box full of books rests on a wooden floor. The normal force the floor exerts on the box is 250 N. (c) Once the box is sliding, you only have to push with a force of 120 N to keep it sliding. What is the coefficient of kinetic friction? y FBD for box N F x Apply Newton s 2 nd Law (1) F y = N w = 0 (2) F x = F f k = 0 f k w From 2: F = f k = µ k N µ k = F N = 120 N 250 N = 0.48

21 Contact Forces Consider a box of mass m that is at rest on an incline. Its FBD is: F RB y There is one long- range force acting on the box: gravity. w x There is one contact force acting on the box from the ramp. If the net force acting on the box is zero, then the contact force from the ramp must have the same magnitude as the weight force, but be in the opposite direction.

22 Contact Forces The force F RB can be resolved into components that are perpendicular and parallel to the ramp. F RB y N The perpendicular component is what we call the normal force. f s w x The parallel component is the static friction force.

23 Example: Let the box on the ramp have a mass 2.5 kg. If the angle between the incline and the horizontal is 25, what are the magnitudes of the weight force, normal force, and static friction force acting on the box? F RB f s θ y N Apply Newton s 2 nd Law F y = N wcosθ = 0 F x = wsinθ f s = 0 w The forces are: x w = mg = 2.5 kg ( )( 9.8 N/kg) = 24.5 N N = wcosθ = ( 24.5 N)cos25 = 22.2 N f s = wsinθ = ( 24.5 N)sin25 =10.4 N

24 Tension This is the force transmi]ed through a rope from one end to the other. An ideal cord has zero mass, does not stretch, and the tension is the same throughout the cord.

25 Free Body Diagrams: Forces Must be drawn for problems when forces are involved. Must be large so that they are readable. Draw an idealization of the body in question (a dot, a box, ). You will need one free body diagram for each body in the problem that will provide useful information for you to solve the given problem. Indicate only the forces acting on the body. Label the forces appropriately. Do not include the forces that this body exerts on any other body. A coordinate system is a must. Do not include fictitious forces. Remember that ma is itself not a force! You may indicate the direction of the body s acceleration or direction of motion if you wish, but it must be done well off to the side of the free body diagram.

26 Example (text problem 4.77): A pulley is hung from the ceiling by a rope. A block of mass M is suspended by another rope that passes over the pulley and is a]ached to the wall. The rope fastened to the wall makes a right angle with the wall. Neglect the masses of the rope and the pulley. Find the tension in the rope from which the pulley hangs and the angle θ. y FDB for the mass M T x w Apply Newton s 2 nd Law to the mass M. F y = T w = 0 T = w = Mg

27 Example (text problem 4.77): A pulley is hung from the ceiling by a rope. A block of mass M is suspended by another rope that passes over the pulley and is a]ached to the wall. The rope fastened to the wall makes a right angle with the wall. Neglect the masses of the rope and the pulley. Find the tension in the rope from which the pulley hangs and the angle θ. FBD for the pulley: Apply Newton s 2 nd Law: y F x = F cosθ T = 0 T θ F x F y = F sinθ T = 0 T = F cosθ = F sinθ This statement is true only when θ = 45 and T F = 2 T = 2 Mg

28 Example: Find the tension in the cord connecting the two blocks as shown. A force of 10.0 N is applied to the right on block 1. Assume a frictionless surface. The masses are m 1 = 3.00 kg and m 2 = 1.00 kg. block 2 block 1 F Assume that the rope stays taut so that both blocks have the same acceleration.

29 Example: Find the tension in the cord connecting the two blocks as shown. A force of 10.0 N is applied to the right on block 1. Assume a frictionless surface. The masses are m 1 = 3.00 kg and m 2 = 1.00 kg. FBD for block 1: FBD for block 2: y y N 1 N 2 T T F x x w 2 F x Apply Newton s 2 nd Law to each block: = T = m 2 a F y = N 2 w 2 = 0 F x w 1 = F T = m 1 a F y = N 1 w 1 = 0

30 Example: Find the tension in the cord connecting the two blocks as shown. A force of 10.0 N is applied to the right on block 1. Assume a frictionless surface. The masses are m 1 = 3.00 kg and m 2 = 1.00 kg. F T = m 1 a T = m 2 a (1) (2) These two equations contain the unknowns: a and T. To solve for T, a must be eliminated. Solve for a in (2) and substitute in (1). " F T = m 1 a = m 1 $ # " F = m 1 $ # T m 2 F T = 1+ m = " % 1 $ ' # & m 2 T m 2 % ' & % " '+T = 1+ m % 1 $ 'T & # & m 2 10 N 1+ 3 kg = 2.5 N " % $ ' # 1 kg &

31 Apparent Weight Stand on a bathroom scale. y FBD for the person: N w x Apply Newton s 2 nd Law: F y = N w = ma y N mg = ma y The normal force is the force the scale exerts on you. By Newton s 3 rd Law this is also the force (magnitude only) you exert on the scale. A scale will read the normal force. N = m g + a y ( ) is what the scale reads. When a y = 0, N = mg. The scale reads your true weight. When a y 0, N > mg or N < mg.

32 Example (text problem 4.128): A woman of mass 51 kg is standing in an elevator. If the elevator pushes up on her feet with 408 newtons of force, what is the acceleration of the elevator? FBD for woman: y N Apply Newton s 2 nd Law: F y w Given: N = 408 newtons, m = 51 kg, g = 9.8 m/s 2 Unknown: a y x = N w = ma y N mg = ma y (1) Solving (1) for a y : a y = N mg m = 1.8 m/s2 The elevator could be (1) traveling upward with decreasing speed, or (2) traveling downward with increasing speed.

33 Air Resistance A stone is dropped from the edge of a cliff; if air resistance cannot be ignored, the FBD for the stone is: y F d w x Apply Newton s Second Law Fy = Fd w = ma Where F d is the magnitude of the drag force on the stone. This force is directed opposite the object s velocity

34 Assume that F d = bv 2 Air Resistance b is a parameter that depends on the size and shape of the object. Since F d v 2, can the object be in equilibrium? F y = F d w = ma bv 2 mg = 0 yes, when v = v t = mg b

35 Example: A paratrooper with a fully loaded pack has a mass of 120 kg. The force due to air resistance has a magnitude of F d = bv 2 where b = 0.14 N s 2 /m 2. (a) If the paratrooper falls with a speed of 64 m/s, what is the force of air resistance on the paratrooper? FBD: F d = bv 2 = ( 0.14 N s 2 /m 2 )( 64 m/s) 2 = 570 N (b) What is the paratrooper s acceleration? y Apply Newton s Second Law and solve for a. F d x F y = F d w = ma a = F d mg m w (c) What is the paratrooper s terminal speed? F y = F d w = ma = 0 v t = bv t 2 mg = 0 mg b = 92 m/s = 5.1 m/s2

36 Fundamental Forces The four fundamental forces of nature are: Gravity which is the force between two masses; it is the weakest of the four. Strong Force which helps to bind atomic nuclei together; it is the strongest of the four. Weak Force binds quarks together to form baryons and mesons. Electromagnetic is the force that acts between charged particles.

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. 2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was

More information

Chapter 4 Newton s Laws: Explaining Motion

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?!

More information

Chapter 5 Newton s Laws of Motion

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

More information

Chapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.

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

More information

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

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

AP Physics Newton's Laws Practice Test

AP Physics Newton's Laws Practice Test AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a

More information

Forces: Equilibrium Examples

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

More information

Newton 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. 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 information

Newton s Laws of Motion

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

More information

Physics 11 Assignment KEY Dynamics Chapters 4 & 5

Physics 11 Assignment KEY Dynamics Chapters 4 & 5 Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following

More information

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

Chapter 4. Forces and Newton s Laws of Motion. continued Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

More information

Chapter 5 Newton s Laws of Motion

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 information

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 ( )

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

More information

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces. Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a

More information

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

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

More information

Chapter 4 Dynamics: Newton s Laws of Motion

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

More information

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 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

More information

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

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

More information

Newton s Laws of Motion

Newton s Laws of Motion Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first

More information

Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION

Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION 1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is

More information

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

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

More information

Worksheet #1 Free Body or Force diagrams

Worksheet #1 Free Body or Force diagrams Worksheet #1 Free Body or Force diagrams Drawing Free-Body Diagrams Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

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. 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 information

VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

More information

Conceptual Questions: Forces and Newton s Laws

Conceptual 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 information

Newton s Law of Motion

Newton s Law of Motion chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating

More information

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

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

More information

This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.

This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap. This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical

More information

AP Physics - Chapter 8 Practice Test

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

More information

UNIT 2D. Laws of Motion

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

More information

Serway_ISM_V1 1 Chapter 4

Serway_ISM_V1 1 Chapter 4 Serway_ISM_V1 1 Chapter 4 ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Newton s second law gives the net force acting on the crate as This gives the kinetic friction force as, so choice (a) is correct. 2. As

More information

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

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc. Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

More information

Lecture 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. 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 information

7. Kinetic Energy and Work

7. Kinetic Energy and Work Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic

More information

AP1 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.

AP1 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 action-reaction force pairs in this interchange. (A) foot applies 200 newton force to nose; nose applies

More information

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

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

More information

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

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

More information

IMPORTANT NOTE ABOUT WEBASSIGN:

IMPORTANT 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 information

Physics I Honors: Chapter 4 Practice Exam

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

More information

Friction and Newton s 3rd law

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

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

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

More information

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26 Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,

More information

University 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 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/2012-odu Wednesday, September

More information

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

PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true? 1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always

More information

SOLUTIONS TO PROBLEM SET 4

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

More information

Units DEMO spring scales masses

Units DEMO spring scales masses Dynamics the study of the causes and changes of motion Force Force Categories ContactField 4 fundamental Force Types 1 Gravity 2 Weak Nuclear Force 3 Electromagnetic 4 Strong Nuclear Force Units DEMO spring

More information

There are three different properties associated with the mass of an object:

There 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 information

Forces. 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 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 information

Two-Body System: Two Hanging Masses

Two-Body 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 information

B) 286 m C) 325 m D) 367 m Answer: B

B) 286 m C) 325 m D) 367 m Answer: B Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of

More information

Objective: Equilibrium Applications of Newton s Laws of Motion I

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,

More information

Physics 100 Friction Lab

Physics 100 Friction Lab Åsa Bradley SFCC Physics Name: AsaB@spokanefalls.edu 509 533 3837 Lab Partners: Physics 100 Friction Lab Two major types of friction are static friction and kinetic (also called sliding) friction. Static

More information

PHY231 Section 1, Form B March 22, 2012

PHY231 Section 1, Form B March 22, 2012 1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate

More information

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

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

More information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014 Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

More information

The Big Idea. Key Concepts

The Big Idea. Key Concepts The Big Idea Acceleration is caused by force. All forces come in pairs because they arise in the interaction of two objects you can t hit without being hit back! The more force applied, the greater the

More information

At the skate park on the ramp

At the skate park on the ramp At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises

More information

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

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

Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43

Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state

More information

Name Class Period. F = G m 1 m 2 d 2. G =6.67 x 10-11 Nm 2 /kg 2

Name Class Period. F = G m 1 m 2 d 2. G =6.67 x 10-11 Nm 2 /kg 2 Gravitational Forces 13.1 Newton s Law of Universal Gravity Newton discovered that gravity is universal. Everything pulls on everything else in the universe in a way that involves only mass and distance.

More information

Introduction to Newton's Laws of Motion 1642-1726

Introduction to Newton's Laws of Motion 1642-1726 Introduction to Newton's Laws of Motion 1642-1726 Outlook 1.The First Law on inertia states that every object will remain in a state of rest or uniform motion in a straight line unless acted upon by an

More information

Announcements. Dry Friction

Announcements. Dry Friction Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics

More information

Chapter 13, example problems: x (cm) 10.0

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

More information

Physics Midterm Review Packet January 2010

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:

More information

circular motion & gravitation physics 111N

circular 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 information

LAB 6 - GRAVITATIONAL AND PASSIVE FORCES

LAB 6 - GRAVITATIONAL AND PASSIVE FORCES L06-1 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 information

F13--HPhys--Q5 Practice

F13--HPhys--Q5 Practice Name: Class: Date: ID: A F13--HPhys--Q5 Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A vector is a quantity that has a. time and direction.

More information

AP Physics Applying Forces

AP 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 information

Physics. Lesson Plan #6 Forces David V. Fansler Beddingfield High School

Physics. 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 long-range forces; Recognize the significance

More information

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

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

More information

NEWTON S LAWS OF MOTION

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

More information

LAB 6: GRAVITATIONAL AND PASSIVE FORCES

LAB 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 information

Chapter 4: Newton s Laws: Explaining Motion

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

More information

9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J

9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J 1. If the kinetic energy of an object is 16 joules when its speed is 4.0 meters per second, then the mass of the objects is (1) 0.5 kg (3) 8.0 kg (2) 2.0 kg (4) 19.6 kg Base your answers to questions 9

More information

6: Applications of Newton's Laws

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

More information

AP Physics C Fall Final Web Review

AP Physics C Fall Final Web Review Name: Class: _ Date: _ AP Physics C Fall Final Web Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. On a position versus time graph, the slope of

More information

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

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

More information

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

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N) Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in

More information

8. Newton's Law of Gravitation

8. Newton's Law of Gravitation 2 8. Newton's Law Gravitation Rev.nb 8. Newton's Law of Gravitation Introduction and Summary There is one other major law due to Newton that will be used in this course and this is his famous Law of Universal

More information

8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential

8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential 8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy

More information

More of Newton s Laws

More of Newton s Laws More of Newton s Laws Announcements: Tutorial Assignments due tomorrow. Pages 19-21, 23, 24 (not 22,25) Note Long Answer HW due this week. CAPA due on Friday. Have added together the clicker scores so

More information

Q: Who established the law of universal gravitation? A: Newton. Q: What is a spring scale used for? A: To measure weight

Q: Who established the law of universal gravitation? A: Newton. Q: What is a spring scale used for? A: To measure weight Q: Who established the law of universal gravitation? A: Newton Q: What is a spring scale used for? A: To measure weight Q: What is the Law of Universal Gravitation? A: Everything in the universe has gravity.

More information

A) N > W B) N = W C) N < W. speed v. Answer: N = W

A) N > W B) N = W C) N < W. speed v. Answer: N = W CTN-12. Consider a person standing in an elevator that is moving upward at constant speed. The magnitude of the upward normal force, N, exerted by the elevator floor on the person's feet is (larger than/same

More information

Chapter 11 Equilibrium

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

More information

CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From

More information

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Forces Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Definition of Force Force = a push or pull that causes a change

More information

Steps to Solving Newtons Laws Problems.

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

More information

356 CHAPTER 12 Bob Daemmrich

356 CHAPTER 12 Bob Daemmrich Standard 7.3.17: Investigate that an unbalanced force, acting on an object, changes its speed or path of motion or both, and know that if the force always acts toward the same center as the object moves,

More information

Exam 2 Review Questions PHY Exam 2

Exam 2 Review Questions PHY Exam 2 Exam 2 Review Questions PHY 2425 - Exam 2 Section: 4 1 Topic: Newton's First Law: The Law of Inertia Type: Conceptual 1 According to Newton's law of inertia, A) objects moving with an initial speed relative

More information

so the angle between them is zero, θ = 0.

so the angle between them is zero, θ = 0. Section 4.1: ork Done by a Constant Force Tutorial 1 Practice, page 166 1. Given: F 275 N;!d 0.65 m Analysis: Use the equation for work, FΔ. F and Δd are in the same direction, so the angle between them

More information

Ideal Cable. Linear Spring - 1. Cables, Springs and Pulleys

Ideal 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 information

QUESTIONS : CHAPTER-5: LAWS OF MOTION

QUESTIONS : CHAPTER-5: LAWS OF MOTION QUESTIONS : CHAPTER-5: 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 information

PHY121 #8 Midterm I 3.06.2013

PHY121 #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 information

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

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

More information

Chapter 6. Work and Energy

Chapter 6. Work and Energy Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a non-zero speed carries energy

More information

= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k

= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k Week 5 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions o these problems, various details have been changed, so that the answers will come out dierently. The method to ind the solution

More information

Lecture Presentation Chapter 4 Forces and Newton s Laws of Motion

Lecture 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 information

Physics 160 Biomechanics. Newton s Laws

Physics 160 Biomechanics. Newton s Laws Physics 160 Biomechanics Newton s Laws Questions to Think About Why does it take more force to cause an object to start sliding than it does to keep it sliding? Why is a ligament more likely to tear during

More information

Experiment: Static and Kinetic Friction

Experiment: Static and Kinetic Friction PHY 201: General Physics I Lab page 1 of 6 OBJECTIVES Experiment: Static and Kinetic Friction Use a Force Sensor to measure the force of static friction. Determine the relationship between force of static

More information