# VELOCITY, ACCELERATION, FORCE

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 fast the object s position is changing. The magnitude of the velocity ( v ) indicates the object s speed. The direction of the velocity (dir v ) indicates the object s direction of motion. The velocity at any point is always tangent to the object s path at that point. Thus, the velocity tells you how the object is moving. In particular, the velocity tells you which way and how fast the object is moving. acceleration Acceleration a is a vector, with units of meters per second squared ( m 2 ). Acceleration indicates the rate of change of the object s velocity ( v ); i.e., the acceleration tells you how fast the object s velocity is changing. The component of the acceleration that is parallel to the velocity ( a ) indicates the rate of change of the object s speed. If a is parallel to the velocity, then the object is speeding up; if a is anti-parallel to the velocity, then the object is slowing down. The component of the acceleration that is perpendicular to the velocity ( a ) indicates the rate of change of the object s direction. Thus, the acceleration does not tell you the object s motion. Instead, the acceleration tells you how the object s motion is changing. force Force F is a vector, with units of Newtons (N). m From Newton s Second Law, N = kg 2 s Forces cause acceleration, not velocity. (More precisely, the force at any instant determines the acceleration at that instant, not the velocity.) The component of the force that is parallel to the velocity ( F ) changes the object s speed. If F is parallel to the velocity, then the force speeds the object up; if F is antiparallel to the velocity, then the force slows the object down. The component of the force that is perpendicular to the velocity ( F ) changes the object s direction. Thus, forces do not cause motion; forces cause changes in motion. Forces make objects speed up, slow down, and/or change direction. s

2 NEWTON S LAWS OF MOTION constant speed: v constant changing speed: v changing there is no component of acceleration parallel to the velocity: a there is a component of acceleration 0 parallel to the velocity: a = there is no component of the net force parallel to the velocity: net F = 0 there is a component of the net force parallel to the velocity: net F constant direction: dir v constant there is no component of acceleration perpendicular to the velocity: a = 0 there is no component of the net force perpendicular to the velocity: net F = 0 changing direction: dir v changing there is a component of acceleration perpendicular to the velocity: a there is a component of net force perpendicular to the velocity: net F (1) constant velocity ( v constant) (1) changing velocity ( v changing) (2) constant speed ( v constant) and constant direction (dir v (2) changing speed ( v changing) constant) or changing direction (dir v changing) or both (3) there is no acceleration: a = 0 (3) there is an acceleration: a (4) there is no net force: net F = 0 (4) there is a net force: net F Constant velocity is not a synonym for Changing velocity is not a synonym for constant acceleration or constant force. changing acceleration or changing force. rows (3) and (4) are Newton s first law Newton s second law net external F = ma magnitude of the net force = ma direction of the net force = direction of the acceleration Newton s third law F 12 = F 21 magnitude of the reaction = magnitude of the action direction of the reaction is opposite to the direction of the action To identify the reaction force, simply reverse the subscripts on the action force. The reaction to the force of A on B is the force of B on A. Never associate the reaction with a third object C.

3 SPECIAL FORCES physics weight The weight of an object is the gravitational force of the earth on the object. Therefore, any object that is near the earth and that has nonzero mass will have a weight. magnitude of the weight: w = mg direction of the weight = down (i.e., toward the center of the earth) The Newton s Third Law reaction force to an object s weight is the gravitational force of the object on the earth. Notice that the normal force is not the reaction force to the object s weight. Weight is a conservative force. gravitational potential energy = mgh The apparent weight is the force required to support the object, as determined from Newton s Second Law. But the actual weight is always mg. springs spring F = kx k is the spring constant. A large k indicates a stiff spring. x is not the spring s length. x is the spring s displacement from its natural length. magnitude of the spring force = kx direction of the spring force is pointing back towards the natural length Rather than using the vector equation ( spring F = kx ), it is often simpler to use the formula for the magnitude of the spring force (kx) and then determine the correct sign based on common sense. The Newton s Third Law reaction force to the spring force on an object is the force of the object on the spring. The spring force is a conservative force. 2 spring potential energy = 1 kx 2 rope forces and tension A massless rope has the same tension throughout its length. You will generally assume that ropes are massless unless the problem gives you a reason not to. When a rope is connected to an object, it can potentially exert a force on that object. The rope force acts to prevent the object from detaching from the rope. The direction of the rope force is parallel to the rope. The rope force acts to prevent the object from detaching from the rope, so the direction of the rope force can only be to pull on the object, not to push it. The magnitude of the rope force is equal to the tension of the rope at the point where the rope is connected to the object. The rope force is a reactive force, so there is no special formula for the magnitude of the rope force. The magnitude the rope force is whatever it takes to prevent the object from detaching from the rope, as determined from Newton s second law. The rope tension is not necessarily the weight of the object. If two objects are connected by a massless rope, and if the rope tension is greater than zero, then the magnitudes of the accelerations are the same for both objects; but the directions of the accelerations may be different, so the accelerations may have different signs. The reaction force to the force of the rope on the object is the force of the object on the rope. The rope force is a nonconservative force.

4 SPECIAL FORCES continued physics contact forces: normal force and friction When two objects are in contact, they can potentially exert forces on each other. The force perpendicular to the contact surface is the normal force. The force parallel to the contact surface is the friction force. Only objects in contact with each other can exert normal or friction forces. normal force The normal force acts to prevent an object from moving through a surface. The normal force is a reactive force, so there is no special formula for the magnitude of the normal force. The magnitude of the normal force is whatever it takes to prevent the object from moving through the surface, as determined from Newton s Second Law. The magnitude of the normal force is not necessarily equal to the magnitude of the object s weight. The direction of the normal force is perpendicular to the contact surface. The normal force can only prevent an object from moving through a surface; the normal force cannot prevent an object from moving away from a surface. Therefore, the normal force can only push on the object, not pull it. To determine whether the object loses contact with the surface, or for maximum or minimum problems that involve the point at which the object loses contact with the surface, suppose that the object does not lose contact with the surface. To solve such problems you need an inequality. Use the fact that the normal force can only push, not pull, the object to obtain the inequality n 0 or n 0. Alternatively, suppose that the object does lose contact with the surface. Use the fact that the object can only move away from, not through, the surface to obtain your inequality: a 0 or a 0. The reaction force to the normal force of object 1 on object 2 is the normal force of object 2 on object 1: n 12 = n21. The normal force is a nonconservative force. friction Friction acts to prevent or hinder an object from sliding across a surface. Static friction acts to prevent the object from sliding across the surface; kinetic friction acts to hinder sliding. So static friction applies when sliding is not occurring; kinetic friction applies when sliding is occurring. The direction of friction is parallel to the contact surface, pointing so as to prevent or hinder the object from sliding across the surface. The magnitude of kinetic friction: f k = µ k n The magnitude of static friction: f s µ sn Use the static friction inequality only when the problem involves the maximum static friction. Static friction is a reactive force, so there is no equation for the magnitude of the actual static friction. The actual magnitude of static friction is whatever it takes to prevent the object from sliding across the surface, as determined from Newton s Second Law. To determine whether an object will slide, or for maximum or minimum problems that involve the point at which the object just begins to slide, you should assume that the object does not slide. To solve such problems you need an inequality; use f s µ sn. The reaction force to the frictional force of object 1 on object 2 is the frictional force of object 2 on object 1. Friction is a nonconservative force.

5 how to solve mechanics problems using net F = ma 1. Create a separate free-body diagram for each object. You should usually treat everything whose mass is mentioned as a separate object. In the diagram for each object, identify all the forces acting on that object: First, identify the object s weight; then, identify contact forces from everything that is touching the object. In first semester physics, weight (the gravitational force of the earth on the object) is the only noncontact force; so, aside from the object s weight, if two objects are not in contact then they cannot be exerting forces on each other. A diagram should include only the forces on a single object it should not include any of the forces exerted by that object. If a group of objects are moving together with the same acceleration (both magnitude and direction), you can create a separate free-body diagram for this combined object. In your diagram, include all the external forces on the combined object; do not include the internal forces. 2. Choose axes and positive directions. Choose axes that are parallel or antiparallel to as many of the forces and accelerations as possible. It is permissible to use different axes for different objects in the same problem. 3. Break each force into components, based on your axes; include signs. You should usually break a force into components even when the magnitude of the overall force is unknown, using a variable for the magnitude of the overall force. 4. Write down Newton s Second Law separately for each object, and separately for each component: net F1 x = m1a1 x, net F1 y = m1a1 y, net F2 x = m2a2x, net F2 y = m2a2 y, etc. If possible, try to start by working with an equation with only one unknown. 5. For each instance of Newton s Second Law, add all the relevant individual forces on the left side of the equation. 6. Where possible, substitute numbers or expressions for each force; include signs for each substitution. When applicable, use special formulas for the magnitudes of particular forces: magnitude of weight = mg f k = µ k n magnitude of the spring force = k x 6. Where possible, substitute numbers or expressions for each mass. Where possible, substitute numbers or expressions for each acceleration; include signs for each substitution. Do not substitute g for a. If the object has a constant velocity component, then that component of acceleration is 0. If the object is permanently motionless in a component, then the object has a constant velocity (of 0) in that component, so that component of acceleration is For multiple object problems, identify which forces, accelerations, or other variables are the same for the different objects, and which variables may be different. Use the same symbol for variables that are the same; use different symbols (via subscripts) for variables that are different. Watch out for variables that are the same in magnitude but opposite in sign. When two objects are connected, the magnitudes of their accelerations will be equal; it is your job to determine whether the signs of the accelerations will be the same or opposite. For a massless rope, the magnitude of the tension is the same everywhere in the rope. When two objects are in contact, the contact force of object 1 on object 2 will be equal in magnitude but opposite in direction to the contact force of object 2 on object 1 (Newton s third law). 8. To get as many equations as unknowns, you may need to use other equations, such as net τ=iα, or net W nc = E. 9. When you have as many equations as unknowns, reduce the number of variables by solving one of the equations for a variable and substituting for that variable into the remaining equations; repeat as many times as necessary.

6 what condition holds? problems 1. Determine the condition that you will be assuming, and the inequality that follows from that assumption. The condition you assume can be either the condition that is specified in the problem or the opposite of the condition specified in the problem. For example, if the question is asking whether A happens, you might assume either that A happens or that A doesn t happen. You should assume a condition that will give you an inequality to write down. For problems that ask whether an object will slide along a surface, you should always assume that the object does not slide, since this will allow you to use static friction, which obeys the inequality f s µ sn. (If you assumed that the object does slide, you would have to use kinetic friction, which does not obey an inequality.) For problems that ask whether an object will lose contact with a surface, you can assume that the object does not lose contact with the surface; use the fact that the normal force can only push, not pull, the object to obtain the inequality n 0 or n 0. Alternatively, you can suppose that the object does lose contact with the surface; use the fact that the object can only move away from, not through, the surface to obtain the inequality a 0 or a Go through the usual steps to step up a mechanics problem, using the condition you assumed in step one. Solve the equation or system of equations for the unknown variables. 3. Compare the values obtained in step two with your inequality from step one. If your values from step two are consistent with the inequality, then the condition you assumed in step one is the condition that will actually occur. If your values from step two are inconsistent with the inequality, then the condition that will actually occur is the opposite of the condition that you assumed in step one.

7 maximum or minimum problems 1. Determine the condition that you will be assuming, and the inequality that follows from that assumption. The condition you assume can be either the condition that is specified in the problem or the opposite of the condition specified in the problem. For example, if the question is asking for the maximum x such that A happens, you might assume either that A happens or that A doesn t happen. You should assume a condition that will give you an inequality to write down. For maximum or minimum problems that involve the point at which the object just begins to slide, you should always assume that the object does not slide, since this will allow you to use static friction, which obeys the inequality f s µ sn. (If you assumed that the object does slide, you would have to use kinetic friction, which does not obey an inequality.) For maximum or minimum problems that involve the point at which the object loses contact with a surface, you can assume that the object does not lose contact with the surface; use the fact that the normal force can only push, not pull, the object to obtain the inequality n 0 or n 0. Alternatively, you can suppose that the object does lose contact with the surface; use the fact that the object can only move away from, not through, the surface to obtain the inequality a 0 or a Go through the usual steps to step up a mechanics problem, using the condition you assumed in step one. 3. Solve the inequality from step one for one of the variables (say, x). Create a new inequality by substituting the expression for x into your Newton s second law equation and replacing the = sign with or. Remember that the new inequality refers to the condition you assumed in step one. How to determine whether to replace = sign with or : (a) Determine whether you are substituting in a minimum or maximum value for x. (b) Determine whether x has a direct or an inverse relationship to the equation side you are substituting into. (c) Determine whether the substitution for x will minimize or maximize the equation side that you are substituting into. For example, if x has a direct relationship to the equation side, then substituting a maximum for x will maximize the equation side; but if x has an inverse relation to the equation side, then substituting a maximum for x will minimize the equation side. (d) If the equation side is being maximized, indicate that it will be greater than or equal to the other side; if the equation side is being minimized, indicate that it will be less than or equal to the other side. (Of course, if your original inequality involved < or > signs, rather than or, then you would use < or > for the new inequality as well.) 4. Solve the new inequality from step three for the variable the question is asking about. This will give you an inequality that is based on the condition you assumed in step one. If the condition you assumed in step one is the condition that was specified in the problem, this inequality from step four gives the answer to the question. Otherwise, go on to step five. 5. If the condition you assumed in step one is the opposite of the condition that was specified in the problem, create a new inequality by reversing the inequality from step four. This will give you an inequality that is based on the condition specified in the problem. This inequality from step five gives you the answer to the question.

8 how to solve mechanics problems about circular motion horizontal circles 1. Start a free-body diagram. Identify the object with a point. Identify the center of the circle with another point to the left or right of the object. The object s direction of motion is then out of the page or into the page, so you cannot draw the circle itself. 2. Choose your positive x-axis to be horizontal, pointing toward the center of the circle, and your y-axis to be vertical. The x-axis is the centripetal axis. (The z-axis, perpendicular to the page, is the tangential axis.) 3. Identify all the forces on the object and label them on your free body diagram. On a horizontal surface, the friction force (if any) is toward the center of the circle. On a banked surface, draw a dotted line representing the angle of inclination of the bank. Draw the normal force perpendicular to this surface, and the friction force (if any) parallel to this surface. 4. Break each force into components, based on your axes; include signs. 2 mv 5. Apply Newton s Second Law separately to the x- and y-components. Use a x = r (for the centripetal acceleration); be careful to get the right sign. Use a y = 0 (since the object is not moving vertically). vertical circles 1. Start a free-body diagram. Draw the circle. Identify the object with a point on the circle. Identify the center of the circle with another point. The object s direction of motion is then clockwise or counterclockwise in the plane of the page. 2. Choose your axes, a tangential axis and a centripetal axis. Choose positive directions. 3. Identify all the forces on the object and label them on your free-body diagram. 4. Apply Newton s Second Law separately to the centripetal and tangential components. 2 mv Use a c = (for the centripetal acceleration); be careful to get the right sign. For r uniform circular motion, use a T = 0 (for the tangential acceleration). 5. Remember that the normal force always points away from the surface, towards the object.

### 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

### 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,

### 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

### 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

### Chapter 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

### 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

### 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

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

CTA-1. An Atwood's machine is a pulley with two masses connected by a string as shown. The mass of object A, m A, is twice the mass of object B, m B. The tension T in the string on the left, above mass

### 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

### 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

### 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

### 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

### 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

### 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

### 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,

### PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be

### 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

### 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

### 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

### 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

### 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

### Physics 211 Lecture 4

Physics 211 Lecture 4 Today's Concepts: Newton s Laws a) Acceleration is caused by forces b) Force changes momentum c) Forces always come in pairs d) Good reference frames Mechanics Lecture 4, Slide 1

### 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

### 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

### Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

### 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

### Physics 2101, First Exam, Fall 2007

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

### 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

### 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:

### 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

### 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

### 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

### 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

### 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

### 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.

### 11. Rotation Translational Motion: Rotational Motion:

11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational

### FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

### 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

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The following four forces act on a 4.00 kg object: 1) F 1 = 300 N east F 2 = 700 N north

### W02D2-2 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

### Chapter 4 Dynamics: Newton s Laws of Motion

Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

### CHAPTER 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

### 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

### University Physics 226N/231N Old Dominion University. Getting Loopy and Friction

University Physics 226N/231N Old Dominion University Getting Loopy and Friction Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012-odu Friday, September 28 2012 Happy

### 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

### 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

### 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

### STATIC AND KINETIC FRICTION

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

### 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

### 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:

### 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

### 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

### 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

### DISPLACEMENT AND FORCE IN TWO DIMENSIONS

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

### Problem Set 5 Work and Kinetic Energy Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physics Physics 8.1 Fall 1 Problem Set 5 Work and Kinetic Energy Solutions Problem 1: Work Done by Forces a) Two people push in opposite directions on

### 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

### Newton s Law of Motion

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

### Chapter 6. Work and Energy

Chapter 6 Work and Energy ENERGY IS THE ABILITY TO DO WORK = TO APPLY A FORCE OVER A DISTANCE= Example: push over a distance, pull over a distance. Mechanical energy comes into 2 forms: Kinetic energy

### 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

### 1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

### 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

### Mechanics 1: Conservation of Energy and Momentum

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

### = 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

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

### Work, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions

Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.

### WORK DONE BY A CONSTANT FORCE

WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newton-meter (Nm) = Joule, J If you exert a force of

### Work 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

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

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

### 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

### 5.2 Rotational Kinematics, Moment of Inertia

5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

### Chapter 6 Work and Energy

Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

### 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

### 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

### PHYS 101 Lecture 10 - Work and kinetic energy 10-1

PHYS 101 Lecture 10 - Work and kinetic energy 10-1 Lecture 10 - Work and Kinetic Energy What s important: impulse, work, kinetic energy, potential energy Demonstrations: block on plane balloon with propellor

### 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

### 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

### 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.

### 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

### 3600 s 1 h. 24 h 1 day. 1 day

Week 7 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

### TOP VIEW. FBD s TOP VIEW. Examination No. 2 PROBLEM NO. 1. Given:

RLEM N. 1 Given: Find: vehicle having a mass of 500 kg is traveling on a banked track on a path with a constant radius of R = 1000 meters. t the instant showing, the vehicle is traveling with a speed of

### 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

### 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

### 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,

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

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

### Review D: Potential Energy and the Conservation of Mechanical Energy

MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.01 Fall 2005 Review D: Potential Energy and the Conservation of Mechanical Energy D.1 Conservative and Non-conservative Force... 2 D.1.1 Introduction...

### G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD

### Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

### 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

### 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

### 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

### Physics Honors: Chapter 7 Practice Test

Physics Honors: Chapter 7 Practice Test Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. When an object is moving with uniform circular motion,

### 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

### 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?!

### PHYSICS 149: Lecture 4

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

### Name: Partners: Period: Coaster Option: 1. In the space below, make a sketch of your roller coaster.

1. In the space below, make a sketch of your roller coaster. 2. On your sketch, label different areas of acceleration. Put a next to an area of negative acceleration, a + next to an area of positive acceleration,

### Conservation of Energy Workshop. Academic Resource Center

Conservation of Energy Workshop Academic Resource Center Presentation Outline Understanding Concepts Kinetic Energy Gravitational Potential Energy Elastic Potential Energy Example Conceptual Situations

### 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