# Lab 5: Conservation of Energy

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 taped to bottom, motion sensor II, photogate sensor, rubber tube (diameter 2.5 cm), paper tube (diameter 2.5 cm), bubble wrap, 30-cm-long string, vernier calipers. 1 Purpose The purpose of this experiment is to explore conservation of energy in three mechanical systems: a falling mass, a pendulum, and a mass oscillating on a spring. 2 Theory If a mass m moves from its initial position r i to its final position r f under the influence of a force F, the work done by the force is given by ( ) ( ) 1 1 F dr = r i 2 mv2 f 2 mv2. (1) i Equation 1 is obtained using Newton s 2nd law to replace F by ma and then integrating over the path (i.e. trajectory) of the mass. Equation 1 is a completely general result, which generally depends on the path taken by the particle. However, if the result of doing that integral is independent of the path taken by the particle, the force F is said to be a conservative force. Examples of conservative forces include the gravitational force, the ideal spring force, and the electrical force. The quantity appearing in each of the terms on the right hand side of Eq. 1 is called the kinetic energy K = 1 2 mv2. (2) As noted above, the integral in Eq. 1 is independent of path for a conservative force, so in that case we can break it up into the sum of two integrals, one that goes from the starting point r i to some arbitrary reference point, and another that goes from to r f : r i F dr = = r0 r i F dr + F dr F dr (3) ri F dr, (4) 1

2 where we have reversed the starting and ending points of the first integral in Eq. 3, which reverses its sign, to obtain Eq. 4. From Eqs. 1 and 4 we obtain ( ) 1 ri ( ) 1 rf 2 mv2 F dr = 2 mv2 F dr. (5) i The fact that Eq. 5 holds for any choice of points r i and r f means that the the quantity on each side of the equality is independent of the choice of r i and r f. That is, it is a constant for any choice of position r. We call that constant the total energy E: E 1 2 mv2 r f F dr, (6) where the velocity and position correspond to the state of the mass at any given time. We have already designated the first term on the right hand side of Eq. 6 as the kinetic energy; the second term defines the potential energy U: U(r) r F dr, (7) which is a function only of r (and the choice of the reference position ), since we have assumed that F is a conservative force. Thus, we may rewrite Eq. 6 as E = K + U, (8) which expresses the principle of the conservation of energy for conservative forces. In the next two sections, we find explicit expressions for the potential energy of a linear spring and for uniform gravity. 2.1 Linear spring Let s consider an ideal spring that obeys the force law F = ky, where y is the distance the spring is stretched along its length. According to Eq. 7, the spring s potential energy is given by: U s (y) = F (y ) dy = y 0 ky dy y 0 (9) = 1 2 k ( y 2 y 2 0). (10) If we take the reference potential energy to be zero at y 0 = 0, then U(y) = 1 2 ky Uniform gravitational field We now consider a mass m in a uniform gravitational field, whose force is given by F = mg, where the upward direction is taken to be positive. According to Eq. 7, the potential energy of the m in the gravitational field is given by: U g (y) = F (y ) dy = mg dy (11) y 0 y 0 = mg (y y 0 ). (12) 2

3 If we take the reference potential energy to be zero at y 0 = 0, then U(y) = mgy. Note that the gravitational potential energy depends on only on the vertical distance y the mass moves and not on the horizontal distance. Why? 3 Experiment You will investigate the conservation of energy for three different cases: free fall in a uniform gravitational field, a pendulum, and a linear spring. 3.1 Free fall of a mass When an object falls in a uniform gravitational field, it s total energy should be conserved, provided all other forces are small compared to gravity. In this experiment you investigate the free fall of a small rubber tube and of a paper tube of roughly the same size Description A tube of mass m is held horizontally a distance h above the level beam of a photogate sensor. The tube is dropped so that it falls without rotating and its velocity is measured as it passes through the photogate. The total energy at the time it is dropped is compared to the total energy when the tube passes through the photogate Programming Measure the diameter of the tube with the vernier calipers provided, checking for uniformity. If the diameter of the tube is not uniform, discuss this in your error analysis. Program SWS for the digital photogate sensor. In the sensor setup window enter the diameter of the tube. Open the digits display window and choose velocity. Double click in the display area of the digits display to open the display setup window. Program for 3 decimal digits. Repeat the measurement a number of times to make sure you get consistent results Taking Data Move the photogate so that its plane is horizontal and is opposite the base plate that holds the vertical rod supporting the photogate. Adjust the height of the photogate beam to be about 25 cm above the table and place the photogate over the edge of the table next to the vertical rod in the bench clamp. Drop the rubber tube taking care to make sure it doesn t rotate as it falls and remains horizontal as it passes through the photogate beam. Use the vertical rod next to the photogate as a guide for dropping the tube through the photogate without hitting it. Click Record, and using the meter stick drop the tube onto bubble wrap from a height of h = 10 cm above the beam. Measure height to the middle of the tube. Record the velocity through the photogate. You will want to take some practice runs and a few runs for real. Repeat for h = 20 and 30 cm Analysis Compare your measured velocities with hose predicted by conservation of energy. Is there any friction in this experiment? If so, how would it affect your data? Try dropping the paper tube from a height of 50 cm above the photogate beam and analyze the data as before. Is energy conserved? If not, what happens to the energy? Try different heights. 3

4 3.2 Pendulum In this experiment, the motion of the mass is not solely in the same direction as the conservative force, and thus illustrates some new features of energy conservation Description A 100 g mass is hung from a 30 cm string and used as a pendulum. The weight is pulled to one side and let go from various heights. At the lowest point the mass passes through the beam of a photogate sensor and its velocity is measured. The total energy at the beginning of the measurement is compared to the energy at the bottom of the pendulum s trajectory Programming Measure the diameter of the 100-g weight with calipers. Follow the procedures in the previous section to measure the velocity of the mass Taking Data Adjust the photogate on the lab bench so that the legs point up. The photogate beam should be directly below the suspension point of the pendulum. Adjust the height of the suspension point of the pendulum so that the full width of the weight swings through the center of the photogate beam taking care to avoid having grooved portions of the weight pass through the beam (why is this important?). Pull the weight to one side so that the middle of the weight is 10 cm above the level of the beam. Let go and record the velocity of the weight at its lowest point. Repeat for h = 8, 6, and 4 cm. Take care to describe how you measure the change in height of the mass so that you make sure that you are measuring the change in height of the center of mass Analysis How well is energy conserved? Is any deviation from perfect conservation within your experimental uncertainty? Does air resistance appear to play a significant role in this experiment or does it appear to be negligible? Note that the mass has a force exerted on it by the string, but this force does not contribute to the potential energy. Why? 3.3 Gravity and a spring In this experiment you investigate conservation of energy for a case in which there are two conservative force laws, that of a spring and gravity, acting simultaneously Description A 0.5 kg mass m is suspended from a vertical spring. The mass is set into vertical oscillatory motion and its position is measured as a function of time by a motion sensor. The velocity and acceleration are calculated by SWS. The total energy of the mass is compared at different points in the motion. The potential energy of the spring-mass system is due to both gravitational potential energy and the potential energy of the spring. 4

5 3.3.2 Theory The mass m performs simple harmonic motion with an angular frequency given by ω = k/m, where k is the spring constant. Define the coordinate y to be zero when the spring is unstretched, as it is when no mass is attached. Take the downward direction to be negative. In this case the total energy can be written as E = 1 2 mv ky2 + mgy. (13) Here, y is defined so that it is both the position of the spring and the height of the mass. Show that when the mass is attached so that the spring is stretched but not oscillating (the force of gravity and the spring on the mass exactly balance), the total energy is given by E = 1 mgb, (14) 2 where is y = B is the distance the spring is stretched by the mass (B > 0). In this experiment, you will explore conservation of energy when the mass is oscillating. If energy is conserved, the total E in Eq. 13 should be the same at any point in the motion, assuming no friction Programming Program SWS for the motion sensor, using the default values. Open the graph window, choosing position, velocity, and acceleration for the vertical axes.you will probably find the default sampling rate of 20 Hz to be satisfactory, but feel free to experiment Preliminaries Hang the spring over the edge of the bench. Tape the top of the spring to the rod from which it is suspended so that the spring cannot slip off the rod inadvertently. Adjust the height of the spring so that with the 0.5 kg mass attached the bottom of the mass is cm from the floor. Measure the force constant k for the spring. Place the motion sensor on the floor directly beneath the the mass. Check that the face of the motion sensor is horizontal. There is a switch on the motion sensor which sets the width of the acoustic beam of the sensor. You will probably find that the narrower width works the best but feel free to experiment. The motion sensor should be plugged into the interface so that position increases as the mass goes higher. Set the mass into motion by pulling it down a reasonable distance and letting go. Recall that the motion sensor does not record distances less than 0.15 m from its face. Do not set the mass in motion by lifting it up. If you lift it too far it will crash into the motion sensor. After the motion settles down, click Record and do the following. Simultaneously observe the motion of the mass and the graphs of position, velocity, and acceleration. Is the acceleration maximum or minimum when the velocity is zero? When the velocity is maximum is the acceleration maximum or minimum? Observe the spring-mass system. Is there any kinetic energy that is not accounted for by 1 2 mv2? If so, this would be worthwhile estimating quantitatively in your error analysis. 5

6 3.3.5 Experiment and Analysis Set the mass into motion, and when the motion settles down click REC, and click STOP after 3 or 4 cycles of the motion. Using the cross hairs on the position graph, determine the distance the mass has traveled from the highest position (H) to the following lowest position (L) on the position graph. This distance will be 2A, where A is taken to be a positive number. Determine the total energy E for the following 4 positions of the mass during the motion: the highest and lowest positions of the mass utilized in finding the amplitude A, and the two positions of maximum velocity following these highest and lowest positions of the mass. Recall that the coordinate y gives the position of the end of the spring, not the position of the mass. The highest position of the mass occurs when y = y 0 + A and the lowest position of the mass when y = y 0 A. Maximum velocity occurs when y = y When the mass is at the highest chosen position and the kinetic energy is zero, the energy E H will be E H = 1 2 k(y 0 + A) 2 + mg(y 0 + A). (15) 2. When the mass has the maximum down velocity following the highest chosen position of the mass the energy E 01 is given E 01 = 1 2 mv ky2 0 + mgy 0. (16) 3. When the mass is at the lowest chosen point and the kinetic energy is zero, the energy is given by E L = 1 2 k(y 0 A) 2 + mg(y 0 A). (17) 4. When the mass has the maximum up velocity following the lowest chosen position of the mass the energy E 02 is given by E 02 = 1 2 mv ky2 0 + mgy 0. (18) Obtain the velocity from the velocity curve of the graph display. Compare the total energy at these 4 points. Is energy conserved? What factors might introduce error into your measurements and calculations? Questions The analysis presented in this section assume no friction. How will friction affect your experimental results? Do you see evidence of friction in the curve of position vs time? Extra: Copy the record or position, velocity, and acceleration over two or three minutes to an Excel file. Save the file as a CSV file and plot the position, velocity, and acceleration as a function of time using Python. From your plots, determine how much energy is lost per cycle. Is the energy lost per cycle the same throughout the experiment? Is the fraction of energy lost per cycle the same throughout the experiment? 6

7 4 Finishing Up Please return the bench to the condition in which you found it. From the File menu click New and then click Don t Save. Thank you. 7

### 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

### 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

### Lab 7: Rotational Motion

Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

### 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,

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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 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

### 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 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

### 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

### Rotational Kinetic Energy

Objective: The kinetic energy of a rotating disk and falling mass are found; the change in their kinetic energy is compared with the change in potential energy of the falling mass. The conservation of

### Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion

Physics 11 Week 1 Simple Harmonic Motion: Equation of Motion A mass M rests on a frictionless table and is connected to a spring of spring constant k. The other end of the spring is fixed to a vertical

### 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,

### 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

### 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

### 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,

### 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

### 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.

### 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

### 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

### Chapter 4. Kinematics - Velocity and Acceleration. 4.1 Purpose. 4.2 Introduction

Chapter 4 Kinematics - Velocity and Acceleration 4.1 Purpose In this lab, the relationship between position, velocity and acceleration will be explored. In this experiment, friction will be neglected.

### 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

### 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

### 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

### SHM Simple Harmonic Motion revised June 16, 2012

SHM Simple Harmonic Motion revised June 16, 01 Learning Objectives: During this lab, you will 1. communicate scientific results in writing.. estimate the uncertainty in a quantity that is calculated from

### 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

### 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

### 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

### 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

### Experiment 9. The Pendulum

Experiment 9 The Pendulum 9.1 Objectives Investigate the functional dependence of the period (τ) 1 of a pendulum on its length (L), the mass of its bob (m), and the starting angle (θ 0 ). Use a pendulum

### 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

### F mg (10.1 kg)(9.80 m/s ) m

Week 9 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

### 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

### 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

### 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

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

### Experiment: Static and Kinetic Friction

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

### Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information

### 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

### 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,

### 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

### Assignment 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

### 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

### 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 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

### Lab 3 - Projectile Motion Scientific Data Collection and Analysis (with some experimental design)

Partner 1: Lab 3 - Scientific Data Collection and Analysis (with some experimental design) Purpose: This Minilab is designed help you apply the skills you learned in the homework; that is, to collect data

### 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

### 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

### 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

### 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

### PHYSICS 183 Acceleration of Gravity Lab (Picket Fence)

PHYSICS 183 Acceleration of Gravity Lab (Picket Fence) Object: To measure the acceleration of a freely falling body due to gravitational attraction. Apparatus: IBM compatible computer running Windows 98SE,

### Newton s Second Law. Evaluation copy

Newton s Second Law Experiment 4 INTRODUCTION In your discussion of Newton s first law, you learned that when the sum of the forces acting on an object is zero, its velocity does not change. However, when

### 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

### Work and Energy. W =!KE = KE f

Activity 19 PS-2826 Work and Energy Mechanics: work-energy theorem, conservation of energy GLX setup file: work energy Qty Equipment and Materials Part Number 1 PASPORT Xplorer GLX PS-2002 1 PASPORT Motion

### 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

### 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...

### Picket Fence Free Fall

Picket Fence Free Fall Experiment 5 We say an object is in free fall when the only force acting on it is the earth s gravitational force. No other forces can be acting; in particular, air resistance must

### 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 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

### Projectile Motion & Conservation of Energy

Projectile Motion & Conservation of Energy Equipment Qty Item Part Number 1 Mini Launcher ME-6800 1 Metal Sphere Projectile 1 and 2 Meter Sticks 1 Large Metal Rod ME-8741 1 Small Metal Rod ME-8736 1 Support

### 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.

### 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 5 ~ Friction

Purpose: Experiment 5 ~ Friction In this lab, you will make some basic measurements of friction. First you will measure the coefficients of static friction between several combinations of surfaces using

### 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

### 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

### Proving the Law of Conservation of Energy

Table of Contents List of Tables & Figures: Table 1: Data/6 Figure 1: Example Diagram/4 Figure 2: Setup Diagram/8 1. Abstract/2 2. Introduction & Discussion/3 3. Procedure/5 4. Results/6 5. Summary/6 Proving

### CHAPTER 6 WORK AND ENERGY

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

### LAB MECH 16. CALC From Physics with Calculators, Vernier Software & Technology, 2003.

LAB MECH 16. CALC From Physics with Calculators, Vernier Software & Technology, 2003. INTRODUCTION A swinging pendulum keeps a very regular beat. It is so regular, in fact, that for many years the pendulum

### E X P E R I M E N T 8

E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:

### 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

### Introduction to the Vernier Photogate: Part 1 Gate Timing

PHY 7a Introduction to the Vernier Photogate: Part 1 Gate Timing The Vernier Photogate is a general sensor used for measuring speeds, accelerations, and periods of moving objects. It can also be used for

### 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,

### Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1

Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UW-Madison 1 relaxed position F X = -kx > 0 F X = 0 x apple 0 x=0 x > 0 x=0 F X = - kx < 0 x 12/9/09 Physics 201, UW-Madison 2 We know

### Magnetism. ***WARNING: Keep magnets away from computers and any computer disks!***

Magnetism This lab is a series of experiments investigating the properties of the magnetic field. First we will investigate the polarity of magnets and the shape of their field. Then we will explore the

### 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 Acceleration Due to Gravity

1 The Acceleration Due to Gravity Introduction: Acceleration is defined as the rate at which the velocity of a moving object changes with time. Accelerations are always caused by forces. In this laboratory

### Motion 1. 1 Introduction. 2 The Motion Sensor

Motion 1 Equipment: DataStudio, motion sensor mounted about 25 cm above lab bench, Data studio files mot1.ds and mot2.ds. Lab Report: Describe procedures not given in the write up. Submit data graphs where

### STATIC AND KINETIC FRICTION

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

### 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

### Determining the Acceleration Due to Gravity

Chabot College Physics Lab Scott Hildreth Determining the Acceleration Due to Gravity Introduction In this experiment, you ll determine the acceleration due to earth s gravitational force with three different

### 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

### 5.1 The First Law: The Law of Inertia

The First Law: The Law of Inertia Investigation 5.1 5.1 The First Law: The Law of Inertia How does changing an object s inertia affect its motion? Newton s first law states that objects tend to keep doing

### Activity P13: Buoyant Force (Force Sensor)

Name Class Date Activity P13: Buoyant Force (Force Sensor) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Archimedes Principle P13 Buoyant Force.DS P18 Buoyant Force P18_BUOY.SWS Equipment

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### physics 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

### Torque and Rotary Motion

Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straight-forward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,

### Physics 201 Homework 5

Physics 201 Homework 5 Feb 6, 2013 1. The (non-conservative) force propelling a 1500-kilogram car up a mountain -1.21 10 6 joules road does 4.70 10 6 joules of work on the car. The car starts from rest

### 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

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

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

### Solution Derivations for Capa #10

Solution Derivations for Capa #10 1) The flywheel of a steam engine runs with a constant angular speed of 172 rev/min. When steam is shut off, the friction of the bearings and the air brings the wheel

### Rocket Activity Foam Rocket

Rocket Activity Foam Rocket Objective Students will learn about rocket stability and trajectory with rubber band-powered foam rockets. Description Students will construct rockets made from pipe insulating