Chapter 4 Dynamics: Newton s Laws of Motion


 Rebecca Craig
 2 years ago
 Views:
Transcription
1 Chapter 4 Dynamics: Newton s Laws of Motion
2 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 NormalForce Solving Problems with Newton s Laws: Free Body Diagrams Problem Solving A General Approach
3
4 4 1 Force A force is a push or pull An object at rest needs a force to get it A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity.
5 4 1 Force Force is a vector, having both magnitude and direction. The magnitude of a force can be measured using a spring scale.
6 4 2 Newton s First Law of Motion It may seem as though it takes a force to keep an object moving. Push your book across a table when you stop pushing, it stops moving. But now, throw a ball across the room. The ball keeps moving after you let it go, even though you are not pushing it any more. Why? It doesn t take a force to keep an object moving in a straight line it takes a force to change its motion. Your book stops because the force of friction stops it.
7 4 2 Newton s First Law of Motion This is Newton s first tlaw, which h is often called the law of inertia: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.
8 4 2 Newton s First Law of Motion Conceptual lexample 4 1: Newton s first law. A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What force causes them to do that?
9 4 3 Mass Mass is the measure of inertia of an object, sometimes understood as the quantity of matter in the object. In the SI system, mass is measured in kilograms. Mass is not weight. Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the Moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.
10 4 4 Newton s Second Law of Motion Newton s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.
11 4 4 Newton s Second Law of Motion Force is a vector, so is true along each coordinate axis. The unit of force in the SI system is the newton (N). Note that the pound is a unit of force, not of mass, and can therefore be equated to newtons but notto to kilograms.
12 4 4 Newton s Second Law of Motion Example 4 2: Force to accelerate a fast car. Estimate the net force needed to accelerate (a) a 1000 kg car at ½ g; (b) a 200 g apple at the same rate. Example 4 3: Force to stop a car. What average net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a distance of 55 m?
13 4 5 Newton s Third Law of Motion Any time a force is exerted on an object, that force is caused by another object. Newton s third law: Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.
14 4 5 Newton s Third Law of Motion A key to the correct application of the third law is that the forces are exerted on different objects. Make sure you don t use them as if they were acting on the same object.
15 4 5 Newton s Third Law of Motion Rocket propulsion can also be explained using Newton s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket. Note that the rocket does not need anything to push against.
16 4 5 Newton s Third Law of Motion Conceptual Example 4 4: What exerts the force to move a car? Response: A common answer is that the engine makes the car move forward. But it is not so simple. The engine makes the wheels go around. But tifth the tires are on slick ice or deep mud, they just spin. Friction is needed. On firm ground, the tires push backward against the ground because of friction. By Newton s third law, the ground pushes on the tires in the opposite direction, accelerating the car forward.
17 4 5 Newton s Third Law of Motion Helpful notation: the firstsubscript is the object that the force is being exerted on;the Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.
18 4 5 Newton s Third Law of Motion Conceptual Example 4 5: Third law clarification. Michelangelo s assistant has been assigned the task of moving a block of marble using a sled. He says to his boss, When I exert a forward force on the sled, the sled exerts an equal and opposite force backward. So how can I ever start it moving? No matter how hard I pull, the backward reaction force always equalsmy forward force, so the net force must be zero. I ll never be able to move this load. Is he correct?
19 4 6 Weight the Force of Gravity; and the Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight of an object of mass m is: where
20 4 6 Weight the Force of Gravity; and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? The force exerted perpendicular to a surface is called the normal force. It is exactly as large as needed to balance the force from the object. (If the required force gets too big, something breaks!)
21 4 6 Weight the Force of Gravity; and the Normal Force Example 4 6: Weight, normal force, and a box. A friend has given you a special gift, a box of mass kg with a mystery surprise inside. The box is resting on the smooth (frictionless) horizontal surface of a tbl table. (a) Determine the weight of the box and the normal force exerted onitby the table. (b) Now your friend pushes down on the box with a force of 40.0N. Again determine the normalforce exerted on the box by the table. (c) If your friend pulls upward on the box with a force () y p p of 40.0 N, what now is the normal force exerted on the box by the table?
22
23
24
25 4 6 Weight the Force of Gravity; and the Normal Force Example 4 7: Accelerating the box. What happens when a person pulls upward on the box in the previous example with a force greater than the box s weight, say N?
26
27 4 6 Weight the Force of Gravity; and the Normal Force Example 4 8: Apparent weight loss. A 65 kg woman descends in an elevator that briefly accelerates at 0.20gg downward. She stands on a scale that reads in kg. (a) During this acceleration, what is her weight and what does the scale read? (b) What does the scale read when the elevator descends at a (b) What does the scale read when the elevator descends at a constant speed of 2.0 m/s?
28
29 4 7 Solving Problems with Newton s Laws: Free Body Diagrams 1. Draw a sketch. 2. For one object, draw a free body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one. 3. Resolve vectors into components. 4. Apply Newton s second law to each component. 5. Solve.
30
31 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Example 4 11: Pulling the mystery box. Suppose a friend asks to examine the 10.0 kg box you were given previously, hoping to guess what is inside; and you respond, Sure, pull the box over to you. She then pulls the box by the attached cord along the smooth surface of the table. The magnitude of the force exerted tdby the person is F P = N, and it is exerted at a 30.0 angle as shown. Calculate (a) the acceleration of the box, and (b) the magnitude of the upward force F N exerted by the table on the box.
32
33
34 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Example 4 12: Two boxes connected by a cord. Two boxes, A and B, are connected by a lightweight g cord and are resting on a smooth table. The boxes have masses of 12.0 kg and 10.0 kg. A horizontal force of N is applied to the 10.0 kg 0 box. Find (a) () the acceleration of each box, and (b) the tension in the cord connecting the boxes.
35
36 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Example 4 13: Elevator and counterweight (Atwood s machine). A system of two objects suspended over a pulley by a flexible cable is sometimes referred to as an Atwood s machine. Here, let the mass of the counterweight be 1000 kg. Assume the mass of the empty elevator is 850 kg, and its mass when carrying four passengers is 1150 kg. For the latter case calculate (a) the acceleration of the elevator and (b) the tension in the cable.
37
38 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Conceptual Example 4 14: The advantage of a pulley. A mover is trying to lift a piano (slowly) up to a second story apartment. He is using a rope looped over two pulleys as shown. What force must he exert on the rope to slowly lift the piano s 2000 N weight?
39
40 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Example 4 15: Accelerometer. A small mass m hangs from a thin string and can swing like a pendulum. You attach it above the window of your car as shown. What angle does the string make (a) when the car accelerates at a constant a = 1.20 m/s 2, and (b) when the car moves at constant velocity, v = 90 km/h?
41
42 4 7 Solving Problems with Newton s Laws: Free Body Diagrams Example 4 16: Box slides down an incline. A box of mass m is placed on a smooth incline that A box of mass m is placed on a smooth incline that makes an angle θ with the horizontal. (a) Determine the normal force on the box. (b) Determine the box s acceleration. (c) Evaluate for a mass m = 10 kg and an incline of θ = 30.
43
44 4 8 Problem Solving A General Approach 1. Read the problem carefully; then read it again. 2. Draw a sketch, and then a free body diagram. 3. Choose a convenient coordinate system. 4. List the known and unknown quantities; find relationships bt between the knowns and the unknowns. 5. Estimate the answer. 6. Solve the problem without putting in any numbers (algebraically); once you are satisfied, put the numbers in. 7. Keep track of dimensions. 8. Make sure your answer is reasonable.
45 Summary of Chapter 4 Newton s first law: If the net force on an object is zero, it will remain either at rest or moving in a straight line at constant speed. Newton s second law: Newton s third law: Weight is the gravitational force on an object. Free body diagrams are essential for problem solving. Do one object at a time, make Free body diagrams are essential for problem solving. Do one object at a time, make sure you have all the forces, pick a coordinate system and find the force components, and apply Newton s second law along each axis.
46 5 1 Applications of Newton s Laws Involving Friction Friction is always present when two solid surfaces slide along each other. The microscopic details are not yet fully understood.
47 5 1 Applications of Newton s Laws Involving Friction Slidingfrictioniscalled is called kineticfriction friction. Approximation of the frictional force: F fr = μ k F N. Here, F N is the normal force, and μ k is the coefficient of kinetic friction, which is different for each pair of surfaces.
48 5 1 Applications of Newton s Laws Involving Friction Static friction applies when two surfaces are at rest with respect to each other (such as a book sitting on a table). The static tti fiti frictional lforce is as big as it needs to be to prevent slipping, i up to a maximum value. F fr μ s F N. Usually it is easier to keep an object sliding than it is to get it started.
49 5 1 Applications of Newton s Laws Involving Friction Note that, in general, μ s > μ k.
50 5 1 Applications of Newton s Laws Involving Friction Example 5 1: Friction: static and kinetic. Our 10.0 kg mystery box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is Determine the force of friction acting on the box if a horizontal external applied force is exerted on it of magnitude: (a) 0, (b) 10 N, (c) 20 N, (d) 38 N, and (e) 40 N.
51
52 5 1 Applications of Newton s Laws Involving Friction Conceptual Example 5 2: A box against a wall. You can hold a box against a rough wall and prevent it from slipping down by pressing hard horizontally. How does the application of a horizontal force keep an object from moving vertically?
53 5 1 Applications of Newton s Laws Involving Friction Example 5 3: Pulling against friction. A 10.0 kg box is pulled along a horizontal surface by a force of 40.0 N applied at a 30.0 angle above horizontal. The coefficient of kinetic friction is Calculate the acceleration.
54
55 5 1 Applications of Newton s Laws Involving Friction Conceptual Example 5 4: To push or to pull a sled? Your little sister wants a ride on her sled. If you are on flat ground, will you exert less force if you push her or pull her? Assume the same angle θ in each case.
56
57 5 1 Applications of Newton s Laws Involving Friction Example 5 5: Two boxes and a pulley. Two boxes are connected by a cord running over a pulley. The coefficient of kinetic friction between box A and the table is We ignore the mass of the cord and pulley and any friction in the pulley, which means we can assume that a force applied to one end of the cord will have the same magnitude at the other end. We wish to find the acceleration, a, of the system, which will have the same magnitude for both boxes assuming the cord doesn t stretch. As box B moves down, box A moves to the right.
58
59 5 1 Applications of Newton s Laws Involving Friction Example 5 6: The skier. This skier is descending a 30 slope, at constant g p, speed. What can you say about the coefficient of kinetic friction?
60
61 5 1 Applications of Newton s Laws Involving Friction Example 5 7: A ramp, a pulley, and two boxes. Box A, of mass kg, rests on a surface inclined at 37 to the horizontal. It is connected by a lightweight cord, which passes over a massless and frictionless pulley, to a second box B, which hangs freely as shown. (a) If the coefficient ofstatic friction is 0.40, determine what range ofvalues for mass B will keep the system at rest. (b) If the coefficient of kinetic friction is 0.30, and m B = 10.0 kg, determine the acceleration of the system.
62
63 4. circular motion
64
65 10 1 Angular Quantities In purely rotational motion, all points on the object move in circles around the axis of rotation ( O ). The radius of the circle is R. All points on a straight line drawn through the axis move through the same angle in the same time. The angle θ in radians is defined: l, R where l is the arc length.
66 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again Angular Quantities Example 10 1: Birds of prey in radians. A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 x 10 4 rad. (a) How many degrees is this? (b) (b) How small an object can the bird just distinguish when flying at a height of 100 m?
67
68 10 1 Angular Quantities Angular displacement: The average angular velocity is dfi defined das the total t angular displacement divided by time: The instantaneous angular velocity:
69 10 1 Angular Quantities The angular acceleration is the rate at which the angular velocity changes with time: The instantaneous acceleration:
70 10 1 Angular Quantities Every point on a rotating body has an angular velocity ω and a linear velocity v. They are related:
71 10 1 Angular Quantities Conceptual Example 10 2: Is the lion faster than the horse? On a rotating carousel or merry go round, one child sits on a horse near the outer edge and another child sits on a lion halfway out from the center. (a) () Which child has the greater linear velocity? (b) Which child has the greater angular velocity?
72
73 10 1 Angular Quantities Objects farther from the axis of rotation will move faster.
74 10 1 Angular Quantities If the angular velocity of a rotating object changes, it has a tangential acceleration: Even if the angular velocity is constant, each point on the object has a centripetal acceleration:
75 10 1 Angular Quantities Here is the correspondence between linear and rotational quantities:
76 10 1 Angular Quantities Example 10 3: Angular and linear velocities and accelerations. A carousel is initially at rest. At t = 0 it is given a constant angular acceleration α = rad/s 2,which increases its angular velocity for 8.0 s. At t = 8.0 s, determine the magnitude of the following quantities: (a) the angular velocity of the carousel; (b) the linear velocity of a child located 2.5 m from the center; (c) (d) (e) the tangential (linear) acceleration of that child; the centripetal acceleration of the child; and the total linear acceleration of the child.
77
78
79 10 1 Angular Quantities The frequency is the number of complete revolutions per second: Frequencies are measured in hertz: The period is the time one revolution takes:
80 10 1 Angular Quantities Example 10 4: Hard drive. The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). (a) What is the angular velocity (rad/s) of the platter? (b) If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it? (c) If a single bit requires 0.50 μmof length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?
81
82 Angular Quantities Example 10 5: Given ω as function of time. A disk of radius R = 3.0 m rotates at an angular velocity ω = ( t) rad/s, where t is in seconds. At the instant t = 2.0 s, determine (a) the angular acceleration, and (b) (b) h d d h f h l (b) (b) the speed v and the components of the acceleration a of a point on the edge of the disk.
83
84 5 2 Uniform Circular Motion Kinematics Uniform circular motion: motion in a circle of constant radius at constant speed Instantaneous velocity is always tangent to the circle.
85 5 2 Uniform Circular Motion Kinematics Looking at the change in velocity in the limit that the time interval becomes infinitesimally small, we see that.
86 5 2 Uniform Circular Motion Kinematics This acceleration is called the centripetal, or radial, acceleration, and it points toward the center of the circle.
87 5 2 Uniform Circular Motion Kinematics Example 5 8: Acceleration of a revolving ball. A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius m. The ball makes 2.00 revolutions in a second. What is itscentripetal acceleration?
88
89
90 5 2 Uniform Circular Motion Kinematics Example 5 9: Moon s centripetal acceleration. The Moon s nearly circular orbit about the Earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the Moon toward the Earth.
91
92 5 2 Uniform Circular Motion Kinematics A centrifuge works by spinning very fast. This means there must be a very large centripetal force. The object at A would go in a straight line but for this force; as it is, it winds up at B.
93 5 2 Uniform Circular Motion Kinematics Example 5 10: Ultracentrifuge. The rotor of an ultracentrifuge rotates at 50,000 rpm (revolutions per minute). A particle at the top of a test tube is 6.00 cm from the rotation axis. Calculate its centripetal acceleration, in g s.
94
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 informationChapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.
Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationChapter 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 informationChapter 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
More informationMOTION AND FORCE: DYNAMICS
MOTION AND FORCE: DYNAMICS We ve been dealing with the fact that objects move. Velocity, acceleration, projectile motion, etc. WHY do they move? Forces act upon them, that s why! The connection between
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More information1. Newton s Laws of Motion and their Applications Tutorial 1
1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationChapter 5 Newton s Laws of Motion
Chapter 5 Newton s Laws of Motion Sir Isaac Newton (1642 1727) Developed a picture of the universe as a subtle, elaborate clockwork slowly unwinding according to welldefined rules. The book Philosophiae
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal
More informationPhysics Notes Class 11 CHAPTER 5 LAWS OF MOTION
1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationExplaining Motion:Forces
Explaining Motion:Forces Chapter Overview (Fall 2002) A. Newton s Laws of Motion B. Free Body Diagrams C. Analyzing the Forces and Resulting Motion D. Fundamental Forces E. Macroscopic Forces F. Application
More informationNewton s Laws of Motion (Ch 5)
Newton s Laws of Motion (Ch 5) Force Isaac Newton 16421727 English physicist & mathematician By the age of 31, discovered: laws of motion universal gravitation calculus Eccentric read Coming of Age in
More information2. (P2.1 A) a) A car travels 150 km in 3 hours, what is the cars average speed?
Physics: Review for Final Exam 1 st Semester Name Hour P2.1A Calculate the average speed of an object using the change of position and elapsed time 1. (P2.1 A) What is your average speed if you run 140
More informationPhysics1 Recitation3
Physics1 Recitation3 The Laws of Motion 1) The displacement of a 2 kg particle is given by x = At 3/2. In here, A is 6.0 m/s 3/2. Find the net force acting on the particle. (Note that the force is time
More informationphysics 111N forces & Newton s laws of motion
physics 111N forces & Newton s laws of motion forces (examples) a push is a force a pull is a force gravity exerts a force between all massive objects (without contact) (the force of attraction from the
More informationRotational Dynamics. Luis Anchordoqui
Rotational Dynamics Angular Quantities In purely rotational motion, all points on the object move in circles around the axis of rotation ( O ). The radius of the circle is r. All points on a straight line
More informationRotational Mechanics  1
Rotational Mechanics  1 The Radian The radian is a unit of angular measure. The radian can be defined as the arc length s along a circle divided by the radius r. s r Comparing degrees and radians 360
More informationLesson 5 Rotational and Projectile Motion
Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular
More informationAssignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Assignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE State law of parallelogram of vector addition and derive expression for resultant of two vectors
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationLinear Centripetal Tangential speed acceleration acceleration A) Rω Rω 2 Rα B) Rω Rα Rω 2 C) Rω 2 Rα Rω D) Rω Rω 2 Rω E) Rω 2 Rα Rω 2 Ans: A
1. Two points, A and B, are on a disk that rotates about an axis. Point A is closer to the axis than point B. Which of the following is not true? A) Point B has the greater speed. B) Point A has the lesser
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More information3600 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
More informationPhysics 11 Chapter 4 HW Solutions
Physics 11 Chapter 4 HW Solutions Chapter 4 Conceptual Question: 5, 8, 10, 18 Problems: 3, 3, 35, 48, 50, 54, 61, 65, 66, 68 Q4.5. Reason: No. If you know all of the forces than you know the direction
More informationCHAPTER 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 informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationF 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 250N force is directed horizontally as shown to push a 29kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationANGULAR POSITION. 4. Rotational Kinematics and Dynamics
ANGULAR POSITION To describe rotational motion, we define angular quantities that are analogous to linear quantities Consider a bicycle wheel that is free to rotate about its axle The axle is the axis
More informationIsaac Newton (1642 to 1727) Force. Newton s Three Law s of Motion. The First Law. The First Law. The First Law
Isaac Newton (1642 to 1727) Force Chapter 4 Born 1642 (Galileo dies) Invented calculus Three laws of motion Principia Mathematica. Newton s Three Law s of Motion 1. All objects remain at rest or in uniform,
More informationProblem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s
Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to
More informationUnit 4 Practice Test: Rotational Motion
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
More informationCentripetal Force. 1. Introduction
1. Introduction Centripetal Force When an object travels in a circle, even at constant speed, it is undergoing acceleration. In this case the acceleration acts not to increase or decrease the magnitude
More informationLAB 6  GRAVITATIONAL AND PASSIVE FORCES
L061 Name Date Partners LAB 6  GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationAP Physics Newton's Laws Practice Test
AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a
More informationGround Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. Dr Tay Seng Chuan
PC1221 Fundamentals of Physics I Lectures 9 and 10 he Laws of Motion Dr ay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while lecture
More informationWhat is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact?
Chapter 4: Forces What is a force? Identifying forces. What is the connection between force and motion? How are forces related when two objects interact? Application different forces (field forces, contact
More informationChapter 4: Newton s Laws: Explaining Motion
Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state
More informationNewton s Laws of Motion
Physics Newton s Laws of Motion Newton s Laws of Motion 4.1 Objectives Explain Newton s first law of motion. Explain Newton s second law of motion. Explain Newton s third law of motion. Solve problems
More informationThis week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.
This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationPhysics 11 Assignment KEY Dynamics Chapters 4 & 5
Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problemsolving questions, draw appropriate free body diagrams and use the aforementioned problemsolving method.. Define the following
More information5.2 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
More informationChapter 5: Circular Motion
Page 1 Chapter 5: Circular Motion Rotating Objects: Wheels, moon, earth, CDs, DVDs etc. Rigid bodies. Description of circular motion. Angular Position, Angular Displacement θ r s Angle (in radians) θ =
More informationNewton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1
Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationM OTION. Chapter2 OUTLINE GOALS
Chapter2 M OTION OUTLINE Describing Motion 2.1 Speed 2.2 Vectors 2.3 Acceleration 2.4 Distance, Time, and Acceleration Acceleration of Gravity 2.5 Free Fall 2.6 Air Resistence Force and Motion 2.7 First
More informationNewton s Laws of Motion
Section 3.2 Newton s Laws of Motion Objectives Analyze relationships between forces and motion Calculate the effects of forces on objects Identify force pairs between objects New Vocabulary Newton s first
More informationLAB 6: GRAVITATIONAL AND PASSIVE FORCES
55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction
More informationPhysics 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,
More informationPhys 111 Fall P111 Syllabus
Phys 111 Fall 2012 Course structure Five sections lecture time 150 minutes per week Textbook Physics by James S. Walker fourth edition (Pearson) Clickers recommended Coursework Complete assignments from
More information1. A radian is about: A. 25 ± B. 37 ± C. 45 ± D. 57 ± E. 90 ± ans: D Section: 10{2; Di±culty: E
Chapter 10: ROTATION 1 A radian is about: A 25 ± B 37 ± C 45 ± D 57 ± E 90 ± Section: 10{2; Di±culty: E 2 One revolution is the same as: A 1 rad B 57 rad C ¼=2rad D ¼ rad E 2¼ rad Section: 10{2; Di±culty:
More informationMULTIPLE 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
More information2. A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed? a. 3.2 rad/s c. 52 rad/s b. 26 rad/s d.
Rotational Motion 1. 2 600 rev/min is equivalent to which of the following? a. 2600 rad/s c. 273 rad/s b. 43.3 rad/s d. 60 rad/s 2. A grindstone spinning at the rate of 8.3 rev/s has what approximate angular
More informationA ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum.
MECHANICS: SIMPLE HARMONIC MOTION QUESTIONS THE PENDULUM (2014;2) A pendulum is set up, as shown in the diagram. The length of the cord attached to the bob is 1.55 m. The bob has a mass of 1.80 kg. The
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More information356 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 informationExam Review Tuesday, September 17, Chapter 2: Kinematics in One Dimension
Exam Review Tuesday, September 17, 2013 10:00 PM Chapter 2: Kinematics in One Dimension Example: A juggler throws a ball straight up with an initial speed of 10 m/s. With what speed would she need to throw
More information5. Forces and MotionI. Force is an interaction that causes the acceleration of a body. A vector quantity.
5. Forces and MotionI 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationP113 University of Rochester NAME S. Manly Fall 2013
Final Exam (December 19, 2013) Please read the problems carefully and answer them in the space provided. Write on the back of the page, if necessary. Show all your work. Partial credit will be given unless
More information1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C. PHYS 11: Chap. 2, Pg 2
1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All of the movies A B C PHYS 11: Chap. 2, Pg 2 1 1) A 2) B 3) C 4) A and B 5) A and C 6) B and C 7) All three A B PHYS 11: Chap. 2, Pg 3 C 1) more than
More informationAP 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 information2.2 NEWTON S LAWS OF MOTION
2.2 NEWTON S LAWS OF MOTION Sir Isaac Newton (16421727) made a systematic study of motion and extended the ideas of Galileo (15641642). He summed up Galileo s observation in his three laws of motion
More informationPhysics1 Recitation7
Physics1 Recitation7 Rotation of a Rigid Object About a Fixed Axis 1. The angular position of a point on a wheel is described by. a) Determine angular position, angular speed, and angular acceleration
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More information1 of 7 10/2/2009 1:13 PM
1 of 7 10/2/2009 1:13 PM Chapter 6 Homework Due: 9:00am on Monday, September 28, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationAP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s
AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s Answer the multiple choice questions (2 Points Each) on this sheet with capital
More informationf max s = µ s N (5.1)
Chapter 5 Forces and Motion II 5.1 The Important Stuff 5.1.1 Friction Forces Forces which are known collectively as friction forces are all around us in daily life. In elementary physics we discuss the
More informationCenter of Mass/Momentum
Center of Mass/Momentum 1. 2. An Lshaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the Lshaped
More informationAP 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 informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationPhysics 101 Prof. Ekey. Chapter 5 Force and motion (Newton, vectors and causing commotion)
Physics 101 Prof. Ekey Chapter 5 Force and motion (Newton, vectors and causing commotion) Goal of chapter 5 is to establish a connection between force and motion This should feel like chapter 1 Questions
More informationCurso20122013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationPhysics Midterm Review. MultipleChoice Questions
Physics Midterm Review MultipleChoice Questions 1. A train moves at a constant velocity of 90 km/h. How far will it move in 0.25 h? A. 10 km B. 22.5 km C. 25 km D. 45 km E. 50 km 2. A bicyclist moves
More informationNo Brain Too Small PHYSICS. 2 kg
MECHANICS: ANGULAR MECHANICS QUESTIONS ROTATIONAL MOTION (2014;1) Universal gravitational constant = 6.67 10 11 N m 2 kg 2 (a) The radius of the Sun is 6.96 10 8 m. The equator of the Sun rotates at a
More informationPHYSICS MIDTERM REVIEW
1. The acceleration due to gravity on the surface of planet X is 19.6 m/s 2. If an object on the surface of this planet weighs 980. newtons, the mass of the object is 50.0 kg 490. N 100. kg 908 N 2. If
More informationPhysics 201 Fall 2009 Exam 2 October 27, 2009
Physics 201 Fall 2009 Exam 2 October 27, 2009 Section #: TA: 1. A mass m is traveling at an initial speed v 0 = 25.0 m/s. It is brought to rest in a distance of 62.5 m by a force of 15.0 N. The mass is
More informationMore of Newton s Laws
More of Newton s Laws Announcements: Tutorial Assignments due tomorrow. Pages 1921, 23, 24 (not 22,25) Note Long Answer HW due this week. CAPA due on Friday. Have added together the clicker scores so
More informationROLLING, TORQUE, AND ANGULAR MOMENTUM
Chapter 11: ROLLING, TORQUE, AND ANGULAR MOMENTUM 1 A wheel rolls without sliding along a horizontal road as shown The velocity of the center of the wheel is represented by! Point P is painted on the rim
More information56 Chapter 5: FORCE AND MOTION I
Chapter 5: FORCE AND MOTION I 1 An example of an inertial reference frame is: A any reference frame that is not accelerating B a frame attached to a particle on which there are no forces C any reference
More informationSection Review Answers. Chapter 12
Section Review Answers Chapter 12 Section 1 1. Answers may vary. Students should say in their own words that an object at rest remains at rest and an object in motion maintains its velocity unless it experiences
More informationForce. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1
Department of Physics and Geology Background orce Physical Science 1421 A force is a vector quantity capable of producing motion or a change in motion. In the SI unit system, the unit of force is the Newton
More information041. Newton s First Law Newton s first law states: Sections Covered in the Text: Chapters 4 and 8 F = ( F 1 ) 2 + ( F 2 ) 2.
Force and Motion Sections Covered in the Text: Chapters 4 and 8 Thus far we have studied some attributes of motion. But the cause of the motion, namely force, we have essentially ignored. It is true that
More information1 of 9 10/27/2009 7:46 PM
1 of 9 10/27/2009 7:46 PM Chapter 11 Homework Due: 9:00am on Tuesday, October 27, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy [Return to Standard Assignment View]
More information9 ROTATIONAL DYNAMICS
CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION The magnitude of the torque produced by a force F is given by τ = Fl, where l is the lever arm. When a long pipe is slipped
More informationAngular velocity. Angular velocity measures how quickly the object is rotating. Average angular velocity. Instantaneous angular velocity
Angular velocity Angular velocity measures how quickly the object is rotating. Average angular velocity Instantaneous angular velocity Two coins rotate on a turntable. Coin B is twice as far from the axis
More informationphysics 111N rotational motion
physics 111N rotational motion rotations of a rigid body! suppose we have a body which rotates about some axis! we can define its orientation at any moment by an angle, θ (any point P will do) θ P physics
More informationF13HPhysQ5 Practice
Name: Class: Date: ID: A F13HPhysQ5 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 informationBHS Freshman Physics Review. Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science.
BHS Freshman Physics Review Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science. Galileo (15641642): 1 st true scientist and 1 st person to use
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationRecap. A force is the product of an object s mass and acceleration. Forces are the reason why objects change their velocity. Newton s second law:
Recap A force is the product of an object s mass and acceleration. Forces are the reason why objects change their velocity. Newton s second law: Unit: 1 N = 1 kg m/s 2 Forces are vector quantities, since
More informationTEACHER ANSWER KEY November 12, 2003. Phys  Vectors 11132003
Phys  Vectors 11132003 TEACHER ANSWER KEY November 12, 2003 5 1. A 1.5kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude
More informationConceptual Questions: Forces and Newton s Laws
Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is
More information