# Chapter 14. Oscillations. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc.

Save this PDF as:

Size: px
Start display at page:

Download "Chapter 14. Oscillations. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc."

## Transcription

1 Chapter 14 Oscillations PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition

2 14 Oscillations

3

4

5 Reading Quiz 1. The type of function that describes simple harmonic motion is A. linear B. exponential C. quadratic D. sinusoidal E. inverse

6 Answer 1. The type of function that describes simple harmonic motion is A. linear B. exponential C. quadratic D. sinusoidal E. inverse

7 Reading Quiz 2. A mass is bobbing up and down on a spring. If you increase the amplitude of the motion, how does this affect the time for one oscillation? A. The time increases. B. The time decreases. C. The time does not change.

8 Answer 2. A mass is bobbing up and down on a spring. If you increase the amplitude of the motion, how does this affect the time for one oscillation? A. The time increases. B. The time decreases. C. The time does not change.

9 Reading Quiz 3. If you drive an oscillator, it will have the largest amplitude if you drive it at its frequency. A. special B. positive C. natural D. damped E. pendulum

10 Answer 3. If you drive an oscillator, it will have the largest amplitude if you drive it at its frequency. A. special B. positive C. natural D. damped E. pendulum

11 Equilibrium and Oscillation

12 Linear Restoring Forces and Simple Harmonic Motion Simple harmonic motion (SHM) is the motion of an object subject to a force that is proportional to the object's displacement. One example of SHM is the motion of a mass attached to a spring. In this case, the relationship between the spring force and the displacement is given by Hooke's Law, F = -kx, where k is the spring constant, x is the displacement from the equilibrium length of the spring, and the minus sign indicates that the force opposes the displacement.

13 Linear Restoring Forces and Simple Harmonic Motion

14 Frequency and Period The frequency of oscillation depends on physical properties of the oscillator; it does not depend on the amplitude of the oscillation.

15 Sinusoidal Relationships

16 Each dimension of circular motion is a sinusoidal funtion. Animation of sine and cosine

17 Mathematical Description of Simple Harmonic Motion

18 What is the largest value cos(2pft) can ever have? A. 0 B. 1 C. 2pft D. E. ½

19 What is the largest value cos(2pft) can ever have? A. 0 B. 1 C. 2pft D. E. ½

20 What is the largest value sin(2pft) can ever have? A. 0 B. 1 C. 2pft D. E. ½

21 What is the largest value sin(2pft) can ever have? A. 0 B. 1 C. 2pft D. E. ½

22 Maximum displacement, velocity and acceleration What is the largest displacement possible? A. 0 B. A C. 2pft D. E. ½ A

23 Maximum displacement, velocity and acceleration What is the largest displacement possible? A. 0 B. A C. 2pft D. E. ½ A

24 Maximum displacement, velocity and acceleration What is the largest velocity possible? A. 0 B. 2pf C. 2Apf D. Apf E.

25 Maximum displacement, velocity and acceleration What is the largest velocity possible? A. 0 B. 2pf C. 2Apf D. Apf E.

26 Maximum displacement, velocity and acceleration What is the largest acceleration possible? A. 0 B. 2A(pf) 2 C. 4p 2 Af 2 D. E. 2Apf

27 Maximum displacement, velocity and acceleration What is the largest acceleration possible? A. 0 B. 2A(pf) 2 C. 4p 2 Af 2 D. E. 2Apf

28 Energy in Simple Harmonic Motion As a mass on a spring goes through its cycle of oscillation, energy is transformed from potential to kinetic and back to potential.

29

30 Solving Problems

31 Equations

32 Additional Example Problem Walter has a summer job babysitting an 18 kg youngster. He takes his young charge to the playground, where the boy immediately runs to the swings. The seat of the swing the boy chooses hangs down 2.5 m below the top bar. Push me, the boy shouts, and Walter obliges. He gives the boy one small shove for each period of the swing, in order keep him going. Walter earns \$6 per hour. While pushing, he has time for his mind to wander, so he decides to compute how much he is paid per push. How much does Walter earn for each push of the swing?

33 Additional Example Problem Walter has a summer job babysitting an 18 kg youngster. He takes his young charge to the playground, where the boy immediately runs to the swings. The seat of the swing the boy chooses hangs down 2.5 m below the top bar. Push me, the boy shouts, and Walter obliges. He gives the boy one small shove for each period of the swing, in order keep him going. Walter earns \$6 per hour. While pushing, he has time for his mind to wander, so he decides to compute how much he is paid per push. How much does Walter earn for each push of the swing? T = 2p (l/g) = 3.17 s 3600 s/hr (1 push/3.17s) = 1136 pushes/ hr \$6/hr (1hr/1136 pushes) = \$ / push Or half a penny per push!

34 Checking Understanding A series of pendulums with different length strings and different masses is shown below. Each pendulum is pulled to the side by the same (small) angle, the pendulums are released, and they begin to swing from side to side. 25 Rank the frequencies of the five pendulums, from highest to lowest. A. A E B D C B. D A C B E C. A B C D E D. B E C A D

35 Answer A series of pendulums with different length strings and different masses is shown below. Each pendulum is pulled to the side by the same (small) angle, the pendulums are released, and they begin to swing from side to side. 25 Rank the frequencies of the five pendulums, from highest to lowest. A. A E B D C B. D A C B E C. A B C D E D. B E C A D f = 1/2p (g/l) Frequency is proportional to the inverse of the length. So longer has a lower frequency

36 Example Problem We think of butterflies and moths as gently fluttering their wings, but this is not always the case. Tomato hornworms turn into remarkable moths called hawkmoths whose flight resembles that of a hummingbird. To a good approximation, the wings move with simple harmonic motion with a very high frequency about 26 Hz, a high enough frequency to generate an audible tone. The tips of the wings move up and down by about 5.0 cm from their central position during one cycle. Given these numbers, A. What is the maximum velocity of the tip of a hawkmoth wing? B. What is the maximum acceleration of the tip of a hawkmoth wing?

37 Example Problem We think of butterflies and moths as gently fluttering their wings, but this is not always the case. Tomato hornworms turn into remarkable moths called hawkmoths whose flight resembles that of a hummingbird. To a good approximation, the wings move with simple harmonic motion with a very high frequency about 26 Hz, a high enough frequency to generate an audible tone. The tips of the wings move up and down by about 5.0 cm from their central position during one cycle. Given these numbers, A. What is the maximum velocity of the tip of a hawkmoth wing? B. What is the maximum acceleration of the tip of a hawkmoth wing? v max = 2pfA = 2 p 26Hz 0.05m = 8.17 m/s a max = A (2pf) 2 = (2 p 26Hz) m = 1334 m/s 2

38 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: 1. At which of the above times is the displacement zero? 2. At which of the above times is the velocity zero? 3. At which of the above times is the acceleration zero? 4. At which of the above times is the kinetic energy a maximum? 5. At which of the above times is the potential energy a maximum? 6. At which of the above times is kinetic energy being transformed to potential energy? 7. At which of the above times is potential energy being transformed to kinetic energy?

39 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the displacement zero? A. C, G B. A, E, I C. B, F D. D, H

40 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the displacement zero? A. C, G B. A, E, I C. B, F D. D, H

41 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the velocity zero? A. C, G B. A, E, I C. B, F D. D, H

42 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the velocity zero? A. C, G B. A, E, I C. B, F D. D, H

43 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the acceleration zero? A. C, G B. A, E, I C. B, F D. D, H

44 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: Without ball At which of the above times is the acceleration zero? A. C, G B. A, E, I C. B, F D. D, H

45 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the kinetic energy a maximum? A. C, G B. A, E, I C. B, F D. D, H

46 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the kinetic energy a maximum? A. C, G B. A, E, I C. B, F D. D, H

47 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the potential energy a maximum? A. C, G B. A, E, I C. B, F D. D, H

48 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is the potential energy a maximum? A. C, G B. A, E, I C. B, F D. D, H

49 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is kinetic energy being transformed to potential energy? A. C, G B. A, E, I C. B, F D. D, H

50 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is kinetic energy being transformed to potential energy? A. C, G B. A, E, I C. B, F D. D, H

51 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is potential energy being transformed to kinetic energy? A. C, G B. A, E, I C. B, F D. D, H

52 Example Problem A ball on a spring is pulled down and then released. Its subsequent motion appears as follows: At which of the above times is potential energy being transformed to kinetic energy? A. C, G B. A, E, I C. B, F D. D, H

53 Example Problem A pendulum is pulled to the side and released. Its subsequent motion appears as follows: 1. At which of the above times is the displacement zero? 2. At which of the above times is the velocity zero? 3. At which of the above times is the acceleration zero? 4. At which of the above times is the kinetic energy a maximum? 5. At which of the above times is the potential energy a maximum? 6. At which of the above times is kinetic energy being transformed to potential energy? 7. At which of the above times is potential energy being transformed to kinetic energy?

54 Example Problem A pendulum is pulled to the side and released. Its subsequent motion appears as follows: 1. At which of the above times is the displacement zero? C, G 2. At which of the above times is the velocity zero? A, E, I 3. At which of the above times is the acceleration zero? C, G 4. At which of the above times is the kinetic energy a maximum? C, G 5. At which of the above times is the potential energy a maximum? A, E, I 6. At which of the above times is kinetic energy being transformed to potential energy? D, H 7. At which of the above times is potential energy being transformed to kinetic energy? B, F

55

56 Prediction Why is the slinky stretched more at the top than the bottom? A. The slinky is probably not in good shape and has been overstretched at the top. B. The slinky could be designed that way and if he holds it the other way around, it ll be denser at the top than the bottom. C. There s more mass pulling on the top loop so it has to stretch more to have a upward force kx equal to the weight mg.

57 Prediction Why is the slinky stretched more at the top than the bottom? A. The slinky is probably not in good shape and has been overstretched at the top. B. The slinky could be designed that way and if he holds it the other way around, it ll be denser at the top than the bottom. C. There s more mass pulling on the top loop so it has to stretch more to have an upward force kx equal to the weight mg.

58

59 Prediction How will the slinky fall? A. The entire thing will fall to the ground w/ an acceleration of g. B. The center of mass will fall w/ an acceleration of g as the slinky compresses making it look like the bottom doesn t fall as fast. C. The bottom will hover stationary in the air as the top falls until the top hits the bottom. D. Other watch video

60 Prediction How will the slinky fall? A. The entire thing will fall to the ground w/ an acceleration of g. B. The center of mass will fall w/ an acceleration of g as the slinky compresses making it look like the bottom doesn t fall as fast. C. The bottom will hover stationary in the air as the top falls until the top hits the bottom. D. Other

61 Why does this happen?

62

### Practice Test SHM with Answers

Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one

### Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines

Simple Harmonic Motion(SHM) Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period (T) Time for one complete

### A 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

### Oscillations: Mass on a Spring and Pendulums

Chapter 3 Oscillations: Mass on a Spring and Pendulums 3.1 Purpose 3.2 Introduction Galileo is said to have been sitting in church watching the large chandelier swinging to and fro when he decided that

### Simple Harmonic Motion

Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights

### AP Physics C. Oscillations/SHM Review Packet

AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

### 1 of 10 11/23/2009 6:37 PM

hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction

### Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations

Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring

### AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

### 226 Chapter 15: OSCILLATIONS

Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

### Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of this system is: k m therefore, k

Physics 1C Midterm 1 Summer Session II, 2011 Solutions 1. If F = kx, then k m is (a) A (b) ω (c) ω 2 (d) Aω (e) A 2 ω Solution: F = kx is Hooke s law for a mass and spring system. Angular frequency of

### Chapter 13, example problems: x (cm) 10.0

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

### Physics 231 Lecture 15

Physics 31 ecture 15 Main points of today s lecture: Simple harmonic motion Mass and Spring Pendulum Circular motion T 1/f; f 1/ T; ω πf for mass and spring ω x Acos( ωt) v ωasin( ωt) x ax ω Acos( ωt)

### both double. A. T and v max B. T remains the same and v max doubles. both remain the same. C. T and v max

Q13.1 An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object s maximum speed

### AP Physics - Chapter 8 Practice Test

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

### Hooke s Law and Simple Harmonic Motion

Hooke s Law and Simple Harmonic Motion OBJECTIVE to measure the spring constant of the springs using Hooke s Law to explore the static properties of springy objects and springs, connected in series and

### Physics 1120: Simple Harmonic Motion Solutions

Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured

### 1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.

practice wave test.. Name Use the text to make use of any equations you might need (e.g., to determine the velocity of waves in a given material) MULTIPLE CHOICE. Choose the one alternative that best completes

### 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

### Physics 41 HW Set 1 Chapter 15

Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,

### 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

### Unit 3 Work and Energy Suggested Time: 25 Hours

Unit 3 Work and Energy Suggested Time: 25 Hours PHYSICS 2204 CURRICULUM GUIDE 55 DYNAMICS Work and Energy Introduction When two or more objects are considered at once, a system is involved. To make sense

### THE NOT SO SIMPLE PENDULUM

INTRODUCTION: THE NOT SO SIMPLE PENDULUM This laboratory experiment is used to study a wide range of topics in mechanics like velocity, acceleration, forces and their components, the gravitational force,

### Lab M1: The Simple Pendulum

Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of

### Prelab Exercises: Hooke's Law and the Behavior of Springs

59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically

### PHYS 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

### PENDULUM PERIODS. First Last. Partners: student1, student2, and student3

PENDULUM PERIODS First Last Partners: student1, student2, and student3 Governor s School for Science and Technology 520 Butler Farm Road, Hampton, VA 23666 April 13, 2011 ABSTRACT The effect of amplitude,

### Simple Harmonic Motion Experiment. 1 f

Simple Harmonic Motion Experiment In this experiment, a motion sensor is used to measure the position of an oscillating mass as a function of time. The frequency of oscillations will be obtained by measuring

### HOOKE S LAW AND SIMPLE HARMONIC MOTION

HOOKE S LAW AND SIMPLE HARMONIC MOTION Alexander Sapozhnikov, Brooklyn College CUNY, New York, alexs@brooklyn.cuny.edu Objectives Study Hooke s Law and measure the spring constant. Study Simple Harmonic

### Lesson 11. Luis Anchordoqui. Physics 168. Tuesday, December 8, 15

Lesson 11 Physics 168 1 Oscillations and Waves 2 Simple harmonic motion If an object vibrates or oscillates back and forth over same path each cycle taking same amount of time motion is called periodic

### AP Physics Energy and Springs

AP Physics Energy and Springs Another major potential energy area that AP Physics is enamored of is the spring (the wire coil deals, not the ones that produce water for thirsty humanoids). Now you ve seen

### Experiment P19: Simple Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor)

PASCO scientific Physics Lab Manual: P19-1 Science Workshop S. H. M. Mass on a Spring Experiment P19: Simple Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor) Concept Time SW Interface Macintosh

### Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum

Updated 2013 (Mathematica Version) M1.1 Introduction. Lab M1: The Simple Pendulum The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are

### Lab 5: Conservation of Energy

Lab 5: Conservation of Energy Equipment SWS, 1-meter stick, 2-meter stick, heavy duty bench clamp, 90-cm rod, 40-cm rod, 2 double clamps, brass spring, 100-g mass, 500-g mass with 5-cm cardboard square

### PHYS 2425 Engineering Physics I EXPERIMENT 9 SIMPLE HARMONIC MOTION

PHYS 2425 Engineering Physics I EXPERIMENT 9 SIMPLE HARMONIC MOTION I. INTRODUCTION The objective of this experiment is the study of oscillatory motion. In particular the springmass system and the simple

### A) F = k x B) F = k C) F = x k D) F = x + k E) None of these.

CT16-1 Which of the following is necessary to make an object oscillate? i. a stable equilibrium ii. little or no friction iii. a disturbance A: i only B: ii only C: iii only D: i and iii E: All three Answer:

### Simple Pendulum 10/10

Physical Science 101 Simple Pendulum 10/10 Name Partner s Name Purpose In this lab you will study the motion of a simple pendulum. A simple pendulum is a pendulum that has a small amplitude of swing, i.e.,

### ELASTIC FORCES and HOOKE S LAW

PHYS-101 LAB-03 ELASTIC FORCES and HOOKE S LAW 1. Objective The objective of this lab is to show that the response of a spring when an external agent changes its equilibrium length by x can be described

### PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in

### Sample lab procedure and report. The Simple Pendulum

Sample lab procedure and report The Simple Pendulum In this laboratory, you will investigate the effects of a few different physical variables on the period of a simple pendulum. The variables we consider

### Physics 9 Fall 2009 Homework 2 - Solutions

Physics 9 Fall 009 Homework - s 1. Chapter 7 - Exercise 5. An electric dipole is formed from ±1.0 nc charges spread.0 mm apart. The dipole is at the origin, oriented along the y axis. What is the electric

### EXPERIMENT 2 Measurement of g: Use of a simple pendulum

EXPERIMENT 2 Measurement of g: Use of a simple pendulum OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum. Textbook reference: pp10-15 INTRODUCTION: Many things in nature wiggle

### The Pendulum. Experiment #1 NOTE:

The Pendulum Experiment #1 NOTE: For submitting the report on this laboratory session you will need a report booklet of the type that can be purchased at the McGill Bookstore. The material of the course

### Tennessee State University

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

### physics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves

Chapter 20 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide

### Lesson 40: Conservation of Energy

Lesson 40: Conservation of Energy A large number of questions you will do involve the total mechanical energy. As pointed out earlier, the mechanical energy is just the total of all types of energy. In

### 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

### Galileo s Pendulum: An exercise in gravitation and simple harmonic motion

Galileo s Pendulum: An exercise in gravitation and simple harmonic motion Zosia A. C. Krusberg Yerkes Winter Institute December 2007 Abstract In this lab, you will investigate the mathematical relationships

### Exercises on Oscillations and Waves

Exercises on Oscillations and Waves Exercise 1.1 You find a spring in the laboratory. When you hang 100 grams at the end of the spring it stretches 10 cm. You pull the 100 gram mass 6 cm from its equilibrium

### Chapter 8: Potential Energy and Conservation of Energy. Work and kinetic energy are energies of motion.

Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. Consider a vertical spring oscillating with mass m attached to one end. At the extreme ends of travel

### FXA 2008. UNIT G484 Module 2 4.2.3 Simple Harmonic Oscillations 11. frequency of the applied = natural frequency of the

11 FORCED OSCILLATIONS AND RESONANCE POINTER INSTRUMENTS Analogue ammeter and voltmeters, have CRITICAL DAMPING so as to allow the needle pointer to reach its correct position on the scale after a single

### 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

### Chapter 24 Physical Pendulum

Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

### Work, Energy and Power Practice Test 1

Name: ate: 1. How much work is required to lift a 2-kilogram mass to a height of 10 meters?. 5 joules. 20 joules. 100 joules. 200 joules 5. ar and car of equal mass travel up a hill. ar moves up the hill

### HOOKE S LAW AND OSCILLATIONS

9 HOOKE S LAW AND OSCILLATIONS OBJECTIVE To measure the effect of amplitude, mass, and spring constant on the period of a spring-mass oscillator. INTRODUCTION The force which restores a spring to its equilibrium

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

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

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

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

### Chapter 9. is gradually increased, does the center of mass shift toward or away from that particle or does it remain stationary.

Chapter 9 9.2 Figure 9-37 shows a three particle system with masses m 1 3.0 kg, m 2 4.0 kg, and m 3 8.0 kg. The scales are set by x s 2.0 m and y s 2.0 m. What are (a) the x coordinate and (b) the y coordinate

### Instructor Now pick your pencils up and get this important equation in your notes.

Physics 605 Mechanical Energy (Read objectives on screen.) No, I haven t been playing with this toy the whole time you ve been gone, but it is kind of hypnotizing, isn t it? So where were we? Oh yes, we

### Physics 101 Hour Exam 3 December 1, 2014

Physics 101 Hour Exam 3 December 1, 2014 Last Name: First Name ID Discussion Section: Discussion TA Name: Instructions Turn off your cell phone and put it away. Calculators cannot be shared. Please keep

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

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

### Physics 2305 Lab 11: Torsion Pendulum

Name ID number Date Lab CRN Lab partner Lab instructor Physics 2305 Lab 11: Torsion Pendulum Objective 1. To demonstrate that the motion of the torsion pendulum satisfies the simple harmonic form in equation

### Copyright 2011 Casa Software Ltd. www.casaxps.com

Table of Contents Variable Forces and Differential Equations... 2 Differential Equations... 3 Second Order Linear Differential Equations with Constant Coefficients... 6 Reduction of Differential Equations

### Mechanical Vibrations

Mechanical Vibrations A mass m is suspended at the end of a spring, its weight stretches the spring by a length L to reach a static state (the equilibrium position of the system). Let u(t) denote the displacement,

### Energy transformations

Energy transformations Objectives Describe examples of energy transformations. Demonstrate and apply the law of conservation of energy to a system involving a vertical spring and mass. Design and implement

### 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:

### Determination of Acceleration due to Gravity

Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two

### charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the

This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2-D collisions, and center-of-mass, with some problems requiring

### 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

### Oscillations. Vern Lindberg. June 10, 2010

Oscillations Vern Lindberg June 10, 2010 You have discussed oscillations in Vibs and Waves: we will therefore touch lightly on Chapter 3, mainly trying to refresh your memory and extend the concepts. 1

### Standing Waves on a String

1 of 6 Standing Waves on a String Summer 2004 Standing Waves on a String If a string is tied between two fixed supports, pulled tightly and sharply plucked at one end, a pulse will travel from one end

### 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 100 Friction Lab

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

### 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

### 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

### If you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ

Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces

### LAB 6: GRAVITATIONAL AND PASSIVE FORCES

55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction

### 16.2 Periodic Waves Example:

16.2 Periodic Waves Example: A wave traveling in the positive x direction has a frequency of 25.0 Hz, as in the figure. Find the (a) amplitude, (b) wavelength, (c) period, and (d) speed of the wave. 1

### A2 Physics Notes OCR Unit 4: The Newtonian World

A2 Physics Notes OCR Unit 4: The Newtonian World Momentum: - An object s linear momentum is defined as the product of its mass and its velocity. Linear momentum is a vector quantity, measured in kgms -1

### Lesson 39: Kinetic Energy & Potential Energy

Lesson 39: Kinetic Energy & Potential Energy Total Mechanical Energy We sometimes call the total energy of an object (potential and kinetic) the total mechanical energy of an object. Mechanical energy

### Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

### Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the

### Lab 8: Ballistic Pendulum

Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally

### 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 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

### SOLUTIONS TO CONCEPTS CHAPTER 15

SOLUTIONS TO CONCEPTS CHAPTER 15 1. v = 40 cm/sec As velocity of a wave is constant location of maximum after 5 sec = 40 5 = 00 cm along negative x-axis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L

### Review Assessment: Lec 02 Quiz

COURSES > PHYSICS GUEST SITE > CONTROL PANEL > 1ST SEM. QUIZZES > REVIEW ASSESSMENT: LEC 02 QUIZ Review Assessment: Lec 02 Quiz Name: Status : Score: Instructions: Lec 02 Quiz Completed 20 out of 100 points

### Harmonic oscillation springs linked in parallel and in series

Harmonic oscillation TEP Principle The spring constant k for different springs and connections of springs is determined. For different experimental set-ups and suspended mass the oscillation period is

### Wave topics 1. Waves - multiple choice

Wave topics 1 Waves - multiple choice When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object (a) is at its highest point. (b) is at

### POTENTIAL ENERGY AND CONSERVATION OF ENERGY

Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 1 A good eample of kinetic energy is provided by: A a wound clock spring B the raised weights of a grandfather's clock C a tornado D a gallon of gasoline

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

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

### No 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

### AP Physics C Fall Final Web Review

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

### Curso2012-2013 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.

### PHYSICS HIGHER SECONDARY FIRST YEAR VOLUME - II. Revised based on the recommendation of the Textbook Development Committee. Untouchability is a sin

PHYSICS HIGHER SECONDARY FIRST YEAR VOLUME - II Revised based on the recommendation of the Textbook Development Committee Untouchability is a sin Untouchability is a crime Untouchability is inhuman TAMILNADU

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

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

### 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

### 1) 0.33 m/s 2. 2) 2 m/s 2. 3) 6 m/s 2. 4) 18 m/s 2 1) 120 J 2) 40 J 3) 30 J 4) 12 J. 1) unchanged. 2) halved. 3) doubled.

Base your answers to questions 1 through 5 on the diagram below which represents a 3.0-kilogram mass being moved at a constant speed by a force of 6.0 Newtons. 4. If the surface were frictionless, the