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

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 from a spring will undergo oscillatory motion if perturbed.. (3 marks) Calculate the effective spring constant of the following arrangement of springs, given that each spring has spring constant k. 3. (4 marks) Draw an arrangement of four springs, each with spring constant k, with an effective spring constant of k.

2 60

3 6 Hooke's Law and the Behavior of Springs Equipment Four 5mm light springs, 5mm tight spring, tapered brass spring, long and short spring support bar with notches, set of masses (0g-000g), digital balance, rubber bands, 30cm ruler, meter stick, laboratory stand with right angle bar clamp, stopwatch. Purpose To use and understand Hooke's law. To examine the behavior of springs and compare the results with Hooke's law. To measure the spring constant of springs using both the static and dynamic methods. To measure the spring constant of springs in parallel and series combinations and compare with theoretical predictions. To examine the behavior of an elastic band and compare the results with Hooke's law. Theory In 678, Robert Hooke investigated the elastic properties of various objects. Hooke measured the extension of the object resulting from the application of a stretching force. The extension of an object is the length that the object is stretched beyond it's resting length. For many objects, including metal wire and coil springs, he observed elastic behavior. Specifically, in a certain range of extension, the material would exert a restoring force opposing the stretching force. In the absence of the stretching force, the material would regain it's original length. He also found that a linear relationship existed between the applied force and the resulting extension in the elastic range. If, for an object, the relationship between applied force and extension is linear, it is said to obey Hooke's law. A spring is a common example of an object that obeys Hooke's Law. Hooke's law for a spring is given by F kx F, () 0 where F is the force exerted by the spring, k is the spring constant, x is the extension of the spring, and Fo is the threshold force of the spring. The threshold force is the minimum force necessary before the spring will begin to stretch. In some springs the coils are pressed together tightly and an initial threshold force is required to separate the coils. In others, the coils are already separated when unextended, so the threshold force is simply zero. Once the coils have separated, the extension is non-zero and Hooke's law applies. There is also a maximum extension above which Hooke's law no longer applies. This limit is known as the elastic limit. Below the elastic limit, the spring deforms elastically, meaning that it will regain it's original shape in the absence of a load. Above the elastic limit, plastic deformation or permanent deformation occurs, Hooke's law is not obeyed, and the original shape of the spring is not regained. In this experiment, we only deal with extensions of springs less than the elastic limit. If a mass, m, is carefully suspended from the free end of a hanging spring so that it is at rest, the spring will stretch to an equilibrium extension, xeq. At this extension, the upward force, F s, exerted by the spring just balances the force of gravity, mg, on the spring. In this situation, illustrated in Figure, we have x mg F kx F. () eq 0 s eq By varying the load on a spring and observing the resulting extension, it is possible to determine the spring constant. We will call this the static method of determining the spring constant. m F s mg Figure If the mass is not at rest, but is suspended from a hanging spring so that there is no horizontal swinging motion, the mass will oscillate in the vertical direction about the equilibrium extension. Suppose the mass is above the equilibrium position, xeq. The force due to gravity is greater than this upward spring force and there will be a downward acceleration. At the equilibrium position, the force of gravity is balanced by the upward spring force, there is no net force and zero acceleration. If the

4 6 mass is below the equilibrium position, then the spring force is greater than the force of gravity and there is an upward acceleration. We can see that there will be a net force acting on the mass which tends to restore it to the equilibrium position. If the spring obeys Hooke's law, the restoring force will be directly proportional to the distance from the equilibrium position. Extension x eq Now, consider a mass that is held at a distance A above the equilibrium position and released. A resulting downward acceleration will be observed. The mass will then overshoot the equilibrium extension and come to rest for an instant at a distance A below the equilibrium position. The mass will accelerate upwards, once again overshooting the equilibrium position to come to rest for an instant at a distance A above the equilibrium position. In a frictionless system, the cycle shown in Figure would continue forever if uninterrupted. This type of motion, in which the acceleration is directly proportional to the distance from the equilibrium position, is called simple harmonic motion. The quantity A, shown in Figure, is the amplitude of the oscillation. The period, T, also shown in Figure, is the time that is required for the mass to undergo one complete cycle. In a real situation, there is internal spring friction as well as resistance due to the surrounding air. With friction, the oscillations are damped, which means the amplitude of the oscillations will decrease with time and the mass will eventually come to a halt at the equilibrium position. In the laboratory setup, the damping is relatively weak and an oscillating mass will only come to rest after a significant period of time. The period of oscillation for a mass hanging from a spring is given by where k is the spring constant of the spring. We can also write T T m, (3) k 4 k m. (4) Equation 4 shows that we can calculate the spring constant by varying the mass and measuring the resulting period of oscillation of a mass suspended from a hanging spring. We will call this the dynamic method of determining the spring constant. It is possible to have multiple spring arrangements and to examine the combined behavior of springs. In particular, we will be investigating two ways of combining springs, a parallel configuration and a series configuration. A parallel configuration of two springs, with spring constants k and k, is shown in Figure 3. We can derive the effective spring constant of this two spring system, meaning that the system of F = k x T x m Figure 3 Figure F = k x two springs can be modeled by a single spring with one spring constant, k'. In this derivation, we will neglect the threshold force of the springs and assume that the springs have the same resting length for simplicity. The total force exerted by the two spring system must be equal to the sum of the forces exerted by each spring. We have F k x k x k x. (5) So, k, the effective spring constant of the system, is given by k k k. (6) Similarly, it can be shown that for a parallel system of n springs, the effective spring constant is given by k k k k 3... k n (7) where k i is the spring constant of the i th spring. A Time

5 63 Figure 4 shows two springs, with spring constants k and k, in a series configuration. For simplicity, the threshold force of the springs and the mass of the springs will be neglected. In the laboratory experiments to be performed here, these are valid approximations. In this case, the total force exerted by the two spring system is not equal to the sum of the forces exerted by each spring. In static equilibrium, the two springs must be exerting the same force, F. From Figure 4, we see that F k x k x. (8) x x m F= k x F= k x In order to find the effective spring constant of the system, we must put the force in terms of the total extension, x. The total extension is given by x x x. (9) We are looking for an expression involving the effective spring constant, k, in the following form From equations 8 and 0, we have Rearranging equation yields, F k x k ( x x ). (0) k ( x x ) k x. () Figure 4 and with equation 8, ( x x ) k k x k k k k x k x, (). (3) Similarly it can be shown that for a system of n springs in series configuration, the effective spring constant is given by where k i is the spring constant of the i th spring.... (4) k k k k k 3 n

6 64 Experimental Procedure. Determine the spring constant of one of the 5mm light springs using the static method. Do this by hanging the spring from the spring support bar and by suspending the weights from the bottom of the spring. Make a table of values of force on the spring and the resulting extension beyond the resting length, together with errors. The mass should remain below 50 grams so that the elastic limit of the spring is not exceeded.. Determine the spring constant of parallel and series arrangements of the 5mm light springs using the static method. It is sufficient to make quick "one data point" measurements of force and extension by suspending a weight on the end of the spring arrangement and measuring a single extension. Do this for arrangements of springs in parallel, 4 springs in parallel, springs in series, and 3 springs in series. Remember to include the mass of the lower spring support bar when calculating the force on the parallel arrangements of springs. 3. Determine how the extension of an elastic band varies with stretching force. In a manner similar to step, make a table of values of force on the band and the resulting extension beyond the resting length. For safety, try not to stretch the elastic band to the point of breakage. 4. Determine the spring constant of one of the 5mm light springs using the dynamic method. Do this by measuring the period of oscillation of various masses suspended on the free end of the spring. The period can be determined by counting the number of oscillations that occur in a length of time measured by the stopwatch. Make a table of values of the period of oscillation and the corresponding mass, with errors. The mass should range from 0 grams to 50 grams. This range is such that the spring can oscillate freely and the elastic limit is not exceeded. 5. Perform any optional investigations as required. Error Analysis Masses measured by the digital balance can be considered to be exact. The stopwatch is subject to errors arising from the reaction time of the person operating the stopwatch. The reaction time can be estimated by double clicking the stopwatch and doubling this to get the error in the time measurement. The error in time measurements can be minimized by timing for a large number of oscillations since the reaction time error is spread over all of the oscillations when propagated to an error in the period. The error in length measurements can be taken to be half of the smallest division of the ruler. There are systematic errors arising from inhomogeneities in the springs (in both coil separation and wire diameter) which cause deviation from ideal behavior. Internal friction in the springs and air resistance contribute to damping which is not accounted for in the theory. Quantities such as the threshold force and the mass of the springs in the analysis of series and parallel configurations of springs have also been neglected.

7 65 The following pages are to be filled out and handed in at the end of this lab session. Hooke's Law and the Behavior of Springs Total Marks = 7 Name: I.D. #: Lab Section: Lab Instructor:. ( marks) Enter numerical values for mass, m, force, F, length, L, and extension, x, of the 5mm light spring as measured in procedure step, together with errors. Proper headings and units should be included in the table. Unextended length of the spring:. ( marks) Plot a graph of F versus x for the 5mm light spring. If the behavior of the spring is described by Equation, then the graph should be linear. Include errors bars on the graph as well as proper axis labeling and a title for the graph. 3. ( mark) From the slope and intercept of the graph, determine the spring constant as well as the threshold force of the spring. Does Hooke's law apply to the spring? Why or why not?

8 66 4. (3 marks) Fill in the blanks with your measurements from procedure step. When calculating the effective spring constants, you must neglect the threshold friction of the system. Assuming that the springs are identical, equations 7 and 4 can be used to predict the effective spring constant using the results of the previous exercise. springs in parallel Data and calculations: 4 springs in parallel Data and calculations: Measured effective spring constant: Predicted effective spring constant: springs in series Data and calculations: Measured effective spring constant: Predicted effective spring constant: 3 springs in series Data and calculations: Measured effective spring constant: Predicted effective spring constant: Measured effective spring constant: Predicted effective spring constant: 5. ( marks) Enter numerical values for mass, m, force, F, length, L, and extension, x, of the elastic band as measured in procedure step 3, together with errors. Proper headings and units should be included in the table.

9 67 Unextended length of the elastic band: 6. ( marks) Plot a graph of F versus x for the elastic band. Compare this graph qualitatively with that of the spring. Does Hooke's law apply to the elastic band? Why or why not?

10 68 7. ( marks) Enter numerical values for mass, m, number of oscillations, N, total time, t, period, T, and period, T, for the 5mm light spring as measured in procedure step 4, together with errors. Proper headings and units should be included in the table. 8. ( marks) Plot a graph of T versus m. If the behavior of the spring is described by Equation 4, then the graph will be linear. Include errors bars on the graph as well as proper axis labeling and a title for the graph. 9. ( marks) From the slope of the graph, determine the spring constant of the spring. Compare the value of the spring constant with that obtained using the static method. 0. ( bonus mark) Determine the threshold force of the 5mm tight spring. Do this by making a data table of force on the spring and the resulting extension in a range around the threshold force (some of the data

11 69 points should be below the threshold force). Enter numerical values for mass, m, force, F, length, L, and extension, x, of the small stiff spring, together with errors. Proper headings and units should be included in the table. Plot a graph of F versus x and extrapolate to find the threshold force of the spring. Unextended length of the spring: Threshold force of the spring:. ( bonus mark) In the analysis leading to Equation 4, the mass of the spring was neglected. We can account for the mass of the spring by modifying Equation 4 to include the effective mass of the system. There is kinetic energy associated with a mass which is oscillating. We wish to find the kinetic energy associated with the oscillating spring. Due to the nature of the spring, each point along the length of an extending spring is moving with a different velocity. A spring, with mass m s, is extending with end point velocity v, as shown in Figure 5. The kinetic energy of this spring is given by E k ( s p r in g ) m s 3 v. (5) m s Since v is the velocity of the hanging mass, the kinetic energy associated with the hanging mass is simply E k ( m a s s ) mv. (6) m v So then the total kinetic energy of the expanding spring system is Figure 5 m E E E m k ( to ta l ) k ( s p r in g ) k ( m a s s ) 3 s v (7) and we can see that the effective mass of the system is m. 3 In order to take into account the mass of the spring in the analysis of the oscillatory motion of the hanging mass, we simply need to re-derive Equation 4 with the corrected effective mass of the system. The result is then m s

12 70 T 4 k m m s 3. (8) We can see that, given a significantly massive spring, the mass of the spring can be calculated from the analysis of it's oscillatory motion. Determine the spring constant and the mass of the tapered brass spring using the dynamic method. Make a table of values of the period of oscillation and the corresponding mass, with errors. The mass should range from 50 grams to 50 grams so that the spring can oscillate freely and the elastic limit is not exceeded. Make sure to weigh the tapered brass spring using the digital balance so that you can compare your results. Enter values for mass, m, number of oscillations, N, total time, t, period, T, and period, T, for the heavy spring, together with errors. Headings and units should be included in the table. Mass of the spring:. ( bonus mark) Plot a graph of T versus m for the tapered brass spring. Include errors bars on the graph as well as proper axis labeling and a title for the graph. From the slope and intercept of the graph, determine the spring constant as well as the mass of the spring using equation 8. Compare the calculated value of the mass of the brass spring with the one that you measured.

### 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

### 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

### 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

### Force. 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

### 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

### LABORATORY 9. Simple Harmonic Motion

LABORATORY 9 Simple Harmonic Motion Purpose In this experiment we will investigate two examples of simple harmonic motion: the mass-spring system and the simple pendulum. For the mass-spring system we

### 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

### Simple Harmonic Motion

Simple Harmonic Motion Objective: In this exercise you will investigate the simple harmonic motion of mass suspended from a helical (coiled) spring. Apparatus: Spring 1 Table Post 1 Short Rod 1 Right-angled

### HOOKE'S LAW AND SIMPLE HARMONIC MOTION OBJECT

5 M19 M19.1 HOOKE'S LAW AND SIMPLE HARMONIC MOTION OBJECT The object of this experiment is to determine whether a vertical mass-spring system obeys Hooke's Law and to study simple harmonic motion. THEORY

### THE SPRING CONSTANT. Apparatus: A spiral spring, a set of weights, a weight hanger, a balance, a stop watch, and a twometer

THE SPRING CONSTANT Objective: To determine the spring constant of a spiral spring by Hooe s law and by its period of oscillatory motion in response to a weight. Apparatus: A spiral spring, a set of weights,

### Advanced Higher Physics: MECHANICS. Simple Harmonic Motion

Advanced Higher Physics: MECHANICS Simple Harmonic Motion At the end of this section, you should be able to: Describe examples of simple harmonic motion (SHM). State that in SHM the unbalanced force is

### SIMPLE HARMONIC MOTION

SIMPLE HARMONIC MOTION PURPOSE The purpose of this experiment is to investigate one of the fundamental types of motion that exists in nature - simple harmonic motion. The importance of this kind of motion

### PHYS 202 Laboratory #4. Activity 1: Thinking about Oscillating Systems

SHM Lab 1 Introduction PHYS 202 Laboratory #4 Oscillations and Simple Harmonic Motion In this laboratory, we examine three simple oscillatory systems: a mass on a spring, a pendulum, and a mass on a rubber

### HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 1983 ABSTRACT

HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 983 (Digitized and Revised, Fall 005) ABSTRACT The spring constant of a screen-door spring was determined both statically, by measuring

### 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

### A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for

### PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion

PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion NAME: DATE: SECTION: PARTNERS: OBJECTIVES 1. Verify Hooke s Law and use it to measure the force constant of a spring. 2. Investigate

### Simple Harmonic Motion

Simple Harmonic Motion Simple harmonic motion is one of the most common motions found in nature and can be observed from the microscopic vibration of atoms in a solid to rocking of a supertanker on the

### General Physics Lab: Atwood s Machine

General Physics Lab: Atwood s Machine Introduction One may study Newton s second law using a device known as Atwood s machine, shown below. It consists of a pulley and two hanging masses. The difference

### Centripetal 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

### 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

### 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

### Simple Harmonic Motion Concepts

Simple Harmonic Motion Concepts INTRODUCTION Have you ever wondered why a grandfather clock keeps accurate time? The motion of the pendulum is a particular kind of repetitive or periodic motion called

### STANDING WAVES. Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave.

STANDING WAVES Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave. Apparatus: Magnetic oscillator, string, mass hanger and assorted masses, pulley,

### 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

### GENERAL SCIENCE LABORATORY 1110L Lab Experiment 5 THE SPRING CONSTANT

GENERAL SCIENCE LABORATORY 1110L Lab Experiment 5 THE SPRING CONSTANT Objective: To determine the spring constant of a spiral spring Apparatus: Pendulum clamp, aluminum pole, large clamp, assorted masses,

### 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,

### 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

### 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

### Simple Harmonic Motion

Simple Harmonic Motion 9M Object: Apparatus: To determine the force constant of a spring and then study the harmonic motion of that spring when it is loaded with a mass m. Force sensor, motion sensor,

### 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

### Determination of g using a spring

INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative

### Experiment Type: Open-Ended

Simple Harmonic Oscillation Overview Experiment Type: Open-Ended In this experiment, students will look at three kinds of oscillators and determine whether or not they can be approximated as simple harmonic

### Graphical Presentation of Data

Graphical Presentation of Data Guidelines for Making Graphs Titles should tell the reader exactly what is graphed Remove stray lines, legends, points, and any other unintended additions by the computer

### 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

### Computer Experiment. Simple Harmonic Motion. Kinematics and Dynamics of Simple Harmonic Motion. Evaluation copy

INTRODUCTION Simple Harmonic Motion Kinematics and Dynamics of Simple Harmonic Motion Computer Experiment 16 When you suspend an object from a spring, the spring will stretch. If you pull on the object,

### 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

### Conservation of Energy Physics Lab VI

Conservation of Energy Physics Lab VI Objective This lab experiment explores the principle of energy conservation. You will analyze the final speed of an air track glider pulled along an air track by a

### 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

### Equilibrium. To determine the mass of unknown objects by utilizing the known force requirements of an equilibrium

Equilibrium Object To determine the mass of unknown objects by utilizing the known force requirements of an equilibrium situation. 2 Apparatus orce table, masses, mass pans, metal loop, pulleys, strings,

### EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives

EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives to verify how the distance of a freely-falling body varies with time to investigate whether the velocity

### 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

### Physics 1020 Laboratory #6 Equilibrium of a Rigid Body. Equilibrium of a Rigid Body

Equilibrium of a Rigid Body Contents I. Introduction II. III. IV. Finding the center of gravity of the meter stick Calibrating the force probe Investigation of the angled meter stick V. Investigation of

### 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

### 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

### 1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date)

1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date) Experiment 5 Harmonic motion In this Experiment you will learn that Hooke s Law F = kx can be used to model the interaction

### SOLUTIONS TO PROBLEM SET 4

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

### Physics 3 Summer 1989 Lab 7 - Elasticity

Physics 3 Summer 1989 Lab 7 - Elasticity Theory All materials deform to some extent when subjected to a stress (a force per unit area). Elastic materials have internal forces which restore the size and

### 04-1. 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

### Physics Spring Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance

Physics 182 - Spring 2012 - Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify

### physics 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

### 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

### Vectors and the Inclined Plane

Vectors and the Inclined Plane Introduction: This experiment is designed to familiarize you with the concept of force as a vector quantity. The inclined plane will be used to demonstrate how one force

### Experiment 5: Newton s Second Law

Name Section Date Introduction Experiment : Newton s Second Law In this laboratory experiment you will consider Newton s second law of motion, which states that an object will accelerate if an unbalanced

### 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

### ACTIVITY SIX CONSERVATION OF MOMENTUM ELASTIC COLLISIONS

1 PURPOSE ACTIVITY SIX CONSERVATION OF MOMENTUM ELASTIC COLLISIONS For this experiment, the Motion Visualizer (MV) is used to capture the motion of two frictionless carts moving along a flat, horizontal

### Lab: Vectors. You are required to finish this section before coming to the lab. It will be checked by one of the lab instructors when the lab begins.

Lab: Vectors Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Name Partners Pre-Lab You are required to finish this section before coming to the lab. It will be checked by one of the

### Spring Force Constant Determination as a Learning Tool for Graphing and Modeling

NCSU PHYSICS 205 SECTION 11 LAB II 9 FEBRUARY 2002 Spring Force Constant Determination as a Learning Tool for Graphing and Modeling Newton, I. 1*, Galilei, G. 1, & Einstein, A. 1 (1. PY205_011 Group 4C;

### Physics 1050 Experiment 2. Acceleration Due to Gravity

Acceleration Due to Gravity Prelab Questions These questions need to be completed before entering the lab. Please show all workings. Prelab 1: For a falling ball, which bounces, draw the expected shape

### Center of Mass/Momentum

Center of Mass/Momentum 1. 2. An L-shaped 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 L-shaped

### Springs. Spring can be used to apply forces. Springs can store energy. These can be done by either compression, stretching, or torsion.

Work-Energy Part 2 Springs Spring can be used to apply forces Springs can store energy These can be done by either compression, stretching, or torsion. Springs Ideal, or linear springs follow a rule called:

### AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.

1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach

### Simple Harmonic Motion

Simple Harmonic Motion Restating Hooke s law The equation of motion Phase, frequency, amplitude Simple Pendulum Damped and Forced oscillations Resonance Harmonic Motion A lot of motion in the real world

### 1 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]

### The moment of inertia of a rod rotating about its centre is given by:

Pendulum Physics 161 Introduction This experiment is designed to study the motion of a pendulum consisting of a rod and a mass attached to it. The period of the pendulum will be measured using three different

### Physics 6A Lab Experiment 6

Physics 6A Lab Experiment 6 Biceps Muscle Model APPARATUS Biceps model Large mass hanger with four 1-kg masses Small mass hanger for hand end of forearm bar with five 100-g masses Meter stick Centimeter

### Explaining 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

### 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

### DATA ANALYSIS USING GRAPHS Written by Zikri Yusof

DATA ANALYSIS USING GRAPHS Written by Zikri Yusof Numerous times during the Introductory Physics Laboratory courses, you will be asked to graph your data as part of your analysis. Almost all of these graphs

### Rotational Motion. So far, you have studied translational motion. Here you will explore the physics of rotational motion.

Team: Rotational Motion Rotational motion is everywhere. When you push a door, it rotates. When you pedal a bike, the wheel rotates. When you start an engine, many parts rotate. Electrons rotate in an

### Gravity Pre-Lab 1. Why do you need an inclined plane to measure the effects due to gravity?

AS 101 Lab Exercise: Gravity (Report) Your Name & Your Lab Partner s Name Due Date Gravity Pre-Lab 1. Why do you need an inclined plane to measure the effects due to gravity? 2. What are several advantage

### Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

### The quest to find how x(t) and y(t) depend on t is greatly simplified by the following facts, first discovered by Galileo:

Team: Projectile Motion So far you have focused on motion in one dimension: x(t). In this lab, you will study motion in two dimensions: x(t), y(t). This 2D motion, called projectile motion, consists of

### 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

### THE CONSERVATION OF ENERGY - PENDULUM -

THE CONSERVATION OF ENERGY - PENDULUM - Introduction The purpose of this experiment is to measure the potential energy and the kinetic energy of a mechanical system and to quantitatively compare the two

### 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

### CME Conservation of Mechanical Energy revised May 5, 2015

CME Conservation of Mechanical Energy revised May 5, 2015 Learning Objectives: During this lab, you will 1. learn how to communicate scientific results in writing. 2. estimate the uncertainty in a quantity

### = mg [down] =!mg [up]; F! x

Section 4.6: Elastic Potential Energy and Simple Harmonic Motion Mini Investigation: Spring Force, page 193 Answers may vary. Sample answers: A. The relationship between F g and x is linear. B. The slope

### AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

### 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,

### Standing Waves Physics Lab I

Standing Waves Physics Lab I Objective In this series of experiments, the resonance conditions for standing waves on a string will be tested experimentally. Equipment List PASCO SF-9324 Variable Frequency

### 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.

### 8 SIMPLE HARMONIC MOTION

8 SIMPLE HARMONIC MOTION Chapter 8 Simple Harmonic Motion Objectives After studying this chapter you should be able to model oscillations; be able to derive laws to describe oscillations; be able to use

### 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

### Name: Lab Partner: Section:

Chapter 10 Simple Harmonic Motion Name: Lab Partner: Section: 10.1 Purpose Simple harmonic motion will be examined in this experiment. 10.2 Introduction A periodic motion is one that repeats itself in

### Experiment P007: Acceleration due to Gravity (Free Fall Adapter)

Experiment P007: Acceleration due to Gravity (Free Fall Adapter) EQUIPMENT NEEDED Science Workshop Interface Clamp, right angle Base and support rod Free fall adapter Balls, 13 mm and 19 mm Meter stick

### 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

### 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

### Measurement of the Acceleration Due to Gravity

Measurement of the Acceleration Due to Gravity Phys 303 Lab Experiment 0 Justin M. Sanders January 12, 2004 Abstract Near the surface of the earth, all objects freely fall downward with the same acceleration

### 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

### Ground 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

### 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

### Monday 20 May 2013 Afternoon

Monday 20 May 2013 Afternoon AS GCE PHYSICS A G481/01 Mechanics *G411700613* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships Booklet (sent with general

### AP Physics B Free Response Solutions

AP Physics B Free Response Solutions. (0 points) A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The anchor is suspended by a rope of negligible

### Objective: Work Done by a Variable Force Work Done by a Spring. Homework: Assignment (1-25) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout)

Double Date: Objective: Work Done by a Variable Force Work Done by a Spring Homework: Assignment (1-25) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout) AP Physics B Mr. Mirro Work Done by a Variable

### 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

### 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

### Lab 5: Projectile Motion

Description Lab 5: Projectile Motion In this lab, you will examine the motion of a projectile as it free falls through the air. This will involve looking at motion under constant velocity, as well as motion