CAPEphysics_labs1 - v4 (1).pdf

BISHOP ANSTEY HIGH SCHOOL EAST AND TRINITY COLLEGE EAST (BATCE) Sixth Form TRINCITY, TRINIDAD AND TOBAGO, WEST INDIES

CENTRE NO. 160570

CXC CAPE Physics Unit 1 Lab Manual 2015-2016

c Copyright by Bishop Anstey High School East and Trinity College East

(BATCE) 2015 All Rights Reserved

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Rules and Regulations of the Laboratory 1. All experiments in this laboratory manual must be performed and written scripts for each experiment must be submitted to your class teacher to obtain a practical coursework mark. 2. Commencement of sessions: You are expected to be at your experiment station punctually. 3. Preparation: Laboratory manuals are available at the class website. These manuals contain a description of all the laboratory experiments that must be performed as part of the requirements for CAPE Physics SBAs. Students are required to prepare adequately for their assigned laboratory experiment prior the start of the session. Preparation includes reading the experimental description adequately and performing the necessary research to enable one to perform the experiment with ease in the laboratory. 4. Starting experiments: All laboratory equipment must be checked prior to students commencing their experiments. DO NOT switch ON equipment until it is checked by your teacher!! 5. Laboratory report submission: All laboratory reports must be submitted to the class teacher ONLY on the date it is due. If your laboratory report submission date falls on a public holiday, then the report must be submitted on the next available school day. Laboratory reports must be submitted with the appropriate cover sheet (with all the details completed) and a signed anti-plagiarism sheet. Students will given until the following day, of performing the experiment, at 10:30am (break time) to submit their lab reports. At this time the student would sign the teachers’ lab record book as evidence the lab was submitted. 6. Absenteeism: Students absent from any experiment must provide a medical/excuse to administration. 7. Students who are absent on the day of the lab practical activity would be scheduled with the lab technician to perform the lab within a one week period from the date of iii

the missed lab. They are to sign the lab technician’s rcord book with the date the lab was performed. This report would be due the following day at 10:30am. 8. Students who fail to submit their lab reports at the deadline would be marked as no work submitted. Special allowances would be given to studetns with a valid excuse, for example a death in the family or physical injury. This excuse must be confirmed via a note and phone call from the parents or medical where applicable, on the day the report is due. 9. Laboratory requirements: For each laboratory session students are required to bring their laboratory manual, writing paper, graph pages, a scientific calculator and other stationery items inclusive of pen/pencils, erasers, rulers and geometrical instruments (if needed for the laboratory experiment). 10. Laboratory attire: Students are required to wear a laboratory coat and closed shoes while present in the laboratory. 11. Work stations: Students must remain at their assigned work station for the duration of the laboratory session. If a student needs to leave the work station, permission must be sought and granted from the class teacher. 12. Difficulties with an experiment: Students experiencing difficulties with experiments should seek assistance from their class teacher. 13. At the end of each laboratory session: At the end of each experiment, students are required to take all their results to their teacher for review and correction. These results pages must be signed by the teacher and must be included in the laboratory report. The signed results pages must not be altered after the teacher has fixed his/her signature. Students must seek the permission of the teacher prior to the exiting of the laboratory at the end of each session. Additionally, before students leave their work station they must ensure that they have removed all their personal belongings and replaced all equipment to the designated area. A check of equipment assigned to each student will be made by the technicians at the end of each laboratory exercise. Students should not leave the laboratory until this check is made. Students will have to pay a compensation fee for missing or broken equipment. 14. Copying and plagiarism in the lab scripts are strictly forbidden. Plagiarized work will not be marked. 15. General rules: Students are not permitted to eat, drink or smoke in the laboratory. The use of the internet is strictly permitted for laboratory research only. 16. Mobile phones: The use of mobile phones is not permitted for the duration of the laboratory session unless approval is given. iv

Policy Principles Practical work and lab reports are an important part of the student’s understanding of the subject area. They provide an avenue where theory taught in the classroom can be tested, applied and/or proved. Practical work engages students, helps them to develop important skills, to understand the process of scientific investigation and develop their understanding of concepts. Lab Reports form 20% of the student’s Caribbean Advanced Proficiency Examinations (CAPE) Physics grade. Timely submission of work ensures students can receive timely feedback from their teachers. Also scripts written up during the practical activity ensures that the students recall information clearly about the experimental procedure (e.g. the method, sources of error, teacher’s guidelines).

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Format for Written Reports 0. Cover Sheet Title of Experiment, your name, date that experiment was performed, partners’ names. (First and last names. Get the spelling right!)

1. Title Titles should be straightforward, informative, and less than ten words (i.e. Not "Lab #4" but "Lab #4: Sample Analysis using the Debye-Sherrer Method").

2. Aim/Objective(s) 3. Theory/ Introduction 1-2 paragraphs. Summarize the basic physics of your experiment. Include equations and other principle things the reader would need to know in order to understand the experiment. Keep it short! If there are standard or accepted values known these should be included in this section.

4. Apparatus This can usually be a simple list, but make sure it is accurate and complete.

5. Diagram These should be clearly labelled with a title.

6. Method/ Procedure/ Experimental Details This section describes the process in chronological order. Using clear paragraph structure (or step by step format), explain all steps in the order they actually happened, not as they vi

were supposed to happen. If you’ve done it right, another researcher should be able to duplicate your experiment. It is always written in past tense.

7. Precautions & Sources of Error Indicate what steps were taken to reduce/eliminate random and systematic errors. Note: Mistakes are not classified as errors.

8. Results The original raw data that you take in the lab. This should be easy to follow, in tabular form. Poor data recording skills lead to poor writeups. If your raw data is illegible, the grade will suffer. The table should have a title and include the uncertainty of the measurement as well as the unit in the heading (e.g. Variable ± uncertainty in the measurement/ unit).

9. Sample Calculations Include a few of your calculations in this section, e.g. one of each type. Do not show each and every calculation.

10. General Analysis The computed results are shown in a clear and concise manner utilizing properly labelled tables and graphs. “Table/Graph showing results” is not an appropriate title. Each column of the table must have a heading and units, if applicable. Tables must be bordered by 4 lines and neatly constructed. If a graph is to be drawn, it must include the following: title, appropriate scales, accurate plotting of points, drawing best straight line (smooth lines through experimental data points) and labeling of axes. Slope calculations should be included after the graph. Each graph should convey a complete message and be fully understandable without referring to any other section in the report.

11. Error Analysis This section must include the pertinent computed uncertainties (error estimates). It is important here that the rule governing significant figures be used in computing and displaying these values. vii

12. Discussion This is the most important part of your report, because here, you show that you understand the experiment beyond the simple level of completing it. Explain. Analyse. Interpret. Some people like to think of this as the "subjective" part of the report. By that, they mean this is what is not readily observable. This part of the lab focuses on a question of understanding "What is the significance or meaning of the results?" To answer this question, use both aspects of discussion: Analysis: What do the results indicate clearly? What have you found? Explain what you know with certainty based on your results and draw conclusions. Interpretation: What is the significance of the results? What ambiguities exist? What questions might we raise? Find logical explanations for problems in the data. The experimental results should be compared with predicted values. If known values exist, the results should be compared with these and a reference given (see below). Discrepancies should be considered in the light of the experimental error obtained and other random and systematic errors not evaluated numerically in ‘Results’. If no known value is available, it is still important to consider all the possible errors. Then discuss the experiment in general, its advantages and failings, procedural difficulties, ways of improving it etc. If any questions are asked in the lab manual, they should be answered in this section of the report.

13. Final Results with Errors and Conclusion This should indicate how well the experiments have fulfilled the aims stated at the beginning. Simply state what you know now for sure, as a result of the lab, and justify your statement.

14. References Any source of material used in the report should be listed here.

Note: Labs are always to follow this format except for planning and design labs. Labs are to be communicated in a logical way using correct grammar and spelling.

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Contents Rules and Regulations of the Laboratory

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Policy Principles

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Format for Written Reports

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Lab #1: The Simple Pendulum

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Lab #2 - MM & ORR: Acceleration due to gravity, ’g’

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Lab #3 - MM & ORR: Gravitational Field Strength, ’g’

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Lab #4 - PD: Reaction Time of an Athlete

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Lab #5 - PD: Terminal velocity of steel balls in oil

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Lab #6 - PD: Terminal Velocity with a Parachute

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Lab #7 - MM:Coplanar Forces

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Lab #8 - MM: Paperclip Oscillation

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Lab #9 - MM & ORR: Archimedes’ Principle

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10 Lab #10 - AI: The “Bug-up” Toy

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CONTENTS

Chapter 1 Lab #1: The Simple Pendulum Objective: To investigate the motion of a simple pendulum, and to make an experimental determination of the acceleration due to gravity.

Method: The period of a simple pendulum is measured for each of several lengths, and curves of period versus length and square of period versus length are plotted. From the average value of the ratio of the length to the square of the period, the acceleration due to gravity is computed.

Theory: A simple pendulum is defined, ideally, as a particle suspended by a weightless string. Practically it consists of a small body, usually a sphere, suspended by a string whose mass is negligible in comparison with that of the sphere and whose length is very much greater than the radius of the sphere. Under these conditions, the mass of the system may be considered as concentrated at a point - namely, the center of the sphere - and the problem may be handled by considering the translational motion of the suspended body, commonly called the 1

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CHAPTER 1. LAB #1: THE SIMPLE PENDULUM

“bob,” along a circular arc. A compound pendulum consists of a body of any shape or size vibrating about a horizontal axis under the influence of the force of gravity. Thus a ring hung on a peg, or a bar supported at one point, is a compound pendulum. In this case, the mass may not be considered as concentrated at a point, and the motion is one of rotation rather than translation. The mathematical formulation for the compound pendulum is somewhat more complicated than in the case of the simple pendulum.

Figure 1.1: The Simple Pendulum Consider the diagram of a simple pendulum shown in Figure 1.1. In its equilibrium position the bob is at the point A vertically below the point of support O. In this position the downward pull of gravity ω is counteracted by the upward pull p of the cord. When the bob is displaced, to some point B, the weight ω may be resolved into two components, one n normal to the arc AB which is counteracted by the pull p of the string, and a force f tangent to the arc which tends to restore the pendulum to its equilibrium position. The greater the displacement, the greater is this component f and the less the force p in the string, as can be seen by comparing positions B and C. Thus the bob is subjected to a translational force f which increases with the displacement and always tends to reduce the

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displacement. When the pendulum is released from a given displacement, it moves with increasing velocity toward its equilibrium position, acquiring thereby a momentum which carries it through the neutral position and produces a negative displacement. It should be noted here that the choice of positive and negative directions is purely arbitrary: it is convenient, although not necessary, to call displacements to the right positive and those to the left negative. Neglecting the effect of friction, the maximum negative displacement will be equal exactly to the initial positive displacement. When the point B0 is reached, the restoring force causes a reversal of the motion and the bob returns to B. This to-and -fro motion of a pendulum is called vibratory, or oscillatory, motion. It is interesting to note the energy changes that occur during the oscillation of the pendulum. Potential energy is defined as the energy which a body possesses because of its position, and kinetic energy is that due to its motion. When the bob is displaced (say from A to C) it is lifted against the force of gravity ω = mg through a distance h. The increase in potential energy is equal to the work done mgh. As the body falls from C it loses potential energy and acquires kinetic energy. A body of mass m travelling with a velocity v has a kinetic energy equal to 12 mv2 . The kinetic energy at A is equal to the potential energy at B provided there has been no loss due to friction. Stated differently, at any point in its path the sum of the potential and kinetic energies is constant if the frictional forces are negligibly small. Three fundamental quantities are involved in the motion of the pendulum. 1. The length of the pendulum is measured from the point of suspension to the center of the spherical bob. 2. The period is defined as the time required for the pendulum to execute its complete motion; i.e., the time between successive transits through any point in the same direction. 3. The amplitude of the motion is defined as the maximum displacement from the equlibrium position; it may be described in terms of the anguar displacement θ , or in terms of the linear displacement s along the arc.

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CHAPTER 1. LAB #1: THE SIMPLE PENDULUM

A fundamental characteristic of the pendulum is its tautochronous property; i.e., the period is independent of the amplitude, provided that the amplitude is not too great. This tautochronous property was first observed by Galileo in the sixteenth century. The complete formulation of the mathematical relationships between the length l, the period T , and the amplitude θ , is quite complicated, but when certain limitations are introduced a simple approximation results which is satisfactory in many practical cases. One way of stating the limitation on the amplitude is to require that θ shall be so small that the chord BB0 shall be equal approximately to the arc BAB0 . Under this restriction, it can be shown that, neglecting friction, s T = 2π

l g

(1.1)

It is to be noted that in this equation neither the amplitude θ nor the mass m of the bob appears. Thus the bob may be of any material and of any size subject to the condition that its radius r be small in comparison with l. Moreover, the period is the same for all amplitudes up to the value of θ set by the above approximation. For example, if in Figure 1.1 θ represents the maximum value the time required for the bob to travel from B to B0 and back is the same time required for a very small vibration about the point A. It is this tautochronous property that makes the pendulum useful as a timing device. By making measurements of l and T , the relationship expressed by Equation 1.1 can be used to determine the acceleration g due to gravity.

Apparatus: The essential apparatus employed in this experiment consists of a simple pendulum, which is composed of a metal ball suspended by a light cord from a rigid support. The only auxillary apparaus required consists of a length measuring instrument, usually a meter stick, and a time measuring device which may be a stop watch or merely an ordinary timepiece with a second hand. A vernier caliper for measuring the diameter of the ball is desirable, although not absolutely necessary. A sheet of rectangular coordinate paper is needed for graphing the data.

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Figure 1.2: Simple Pendulum 1

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3

4

5

Length

Time

Period

Square

Ratio

of 50

T

of

l/T 2

Vib.

Period

t

T2

TABLE 1

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CHAPTER 1. LAB #1: THE SIMPLE PENDULUM

Procedure: Experimental: 1. Make a simple pendulum of a ball and string and suspend it from a suitable support as shown in Figure 1.2. The support should be sufficiently rigid that no appreciable movement will be imparted to it by the vibration of the pendulum. Measure the diamter of the bob, using a vernier calliper if one is available; if not, a reasonably good measurement can be made with two blocks and a meter stick. Make the initial length of the pendulum 120 cm, taking into account the radius of the bob. Start the pendulum vibrating through a small arc, not greater than 5 degrees between extreme displacements. Determine the time required for 50 vibrations; in doing so count each passage of the bob, in the same direction, through the midpoint beginning with the count of “zero.” Enter the data in columns 1 and 2 of Table 1. Take a series of six such observations, shortening the length each time by 20 cm. Caution: The angular displacement must be kept within the limit specified; if the linear displacement is held constant the angular displacement will, of course, increase. 2. For some convenient length compare the periods when the arc is less than 5 degrees and when it is over 30 degrees. Analysis: From the data in column 2 compute the corresponding periods and enter in column 3. Square these periods and enter in column 4. Compute the ratios of l to T 2 and enter in column 5. On the same sheet of Cartesian coordinate paper plot two curves: (1) length as abscissa and period as ordinate - column 1 vs. column 3; (2) length as abscissa and square of period as ordinate - column 1 vs. column 4. To calculate g, square Eq. 1.1 which gives T 2 = 4π 2 · Solving for g yields

l g

(1.2)

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g = 4π 2 ·

l T2

(1.3)

Take the average of column 5, substitute in Eq. 1.3 and compute the value of g. Compare with the generally accepted value.

Questions: 1. Compare the shapes of the two curves. 2. Explain how curve 2 confirms the relationship expressed by Eq. 1.1. 3. How is the period influenced by the amplitude for small amplitudes? 4. By what factor is the period of a simple pendulum altered when its length is doubled? 5. Explain how the simple pendulum could be used to compare the values of g in two different localities, e.g. at sea level and on a mountain top. 6. What experimental errors influence the determination of g in this experiment? 7. Discuss the effects of a yielding of the support upon the results of this experiment. 8. A so-called “seconds pendulum” is one that passes through its equilibrium position once a second. (a) What is the period of such a pendulum? (b) By referring to the graph, determine the length of a seconds pendulum. 9. Discuss the energy transformations that occur during one complete vibration of the pendulum.

Chapter 2 Lab #2 - MM & ORR: Acceleration due to gravity, ’g’ Objective: The aim of this experiment is to obtain a value for ’g’, the acceleration due to gravity, to the highest accuracy possible with this simple apparatus.

Procedure: (i) Draw on the given card concentric circles of radii 8, 7, 6, 4 and 3 cm and also mark a diameter AOB. Cut out carefully a circular disc 8 cm in radius. Determine carefully and as accurately as you can the average radius R of the disc. (ii) Place the U-shaped wire on the edge of the desk (at a corner) with the prongs projecting. Place the block of wood on top of the closed end and clamp the assembly to the desk firmly with the G-clamp. (iii) Push the needle normally through the disc at the point of intersection of OA and the 7 cm circle. You must be careful not to bend the card. Hang the disc on the U-shaped wire as shown Fig. 2.1. 8

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Figure 2.1: Setup of Apparatus

Figure 2.2: Circle (iv) Obtain the mean period T of small oscillations of the disc about the needle pivot. Record t1 , t2 , T and T 2 for each observation. Move the needle to the intersection of the 7 cm circle with OB and repeat the procedure to find T and T 2 . Calculate the mean square period, T72 , for these two settings on the 7 cm circle. Measure as accurately as possible the distance 2l shown in Figure 2.2. (v) Repeat your measurements with the needle on the circles of radii 6, 4, and 3 cm. (vi) Tabulate, l, l 2 , T 2 and (l 2 + 0.5R2 )/T 2 . Plot (l 2 + 0.5R2 )/T 2 against l. From your graph, read off the value of (l 2 + 0.5R2 )/T 2 at the point for which l = 5.00 cm.  2 (vii) Substitute these values into the formula: gcalculated = 4πl (l 2 + 0.5R2 )/T 2 to obtain a value of gcalculated . This value must be corrected for the radius r of the needle. Measure r and use the formula gcorrected = gcalculated (1 − r/l) to obtain your final answer.

Chapter 3 Lab #3 - MM & ORR: Gravitational Field Strength, ’g’ Objective: This is a simple experiment for the determination of ’g’, the gravitational field strength, which can give a high degree of accuracy.

Procedure (a) Grip the ’U-shaped’ wire in a clamp about 25 cm above the bench with its plane horizontal. Measure and record ’a’, the length of the plastic drinking straw. Mark the mid-point of the straw. (b) Seal one end of the plastic straw with the smallest convenient piece of Sellotape: pour in dry sand from the opposite end until, after tapping, no more can be added. Seal this end also with Sellotape. (c) Push the needle through the straw at right angles to its axis and at a distance X about 1 cm from the mid-point of the straw. (d) Using the needle as a pivot, support the straw on the U-shaped’ wire so that the straw 10

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can oscillate as a pendulum (Figure 3.1).

Figure 3.1: Setup of Apparatus (e) Determine T , the period of oscillation of small amplitude of the straw. Do this for four values of X between 1 cm and about 2 cm and for three further values of X up to 5 cm. Record your values of X and T . (Note: When withdrawing the needle to alter the value of X, the holes left in the plastic should close up sufficiently to prevent loss of sand. If necessary, this closing can be helped by stroking the plastic at the hole with the side of the needle. In any case, the straw should be carefully checked for loss or settling down of the sand: any loss or vacant space should be made good by ’topping up’.) (f) In your results, state the type of timer you used and the smallest interval of time it is capable of recording.  2  a (g) Tabulate T 2 and 12 + X 2 /X.   4π 2 a2 2 (h) Given that g = T 2 12 + X /X plot a suitable graph and hence calculate g.

Chapter 4 Lab #4 - PD: Reaction Time of an Athlete Figure 4.1 shows how the speed v of an athlete varies witth time t during a 100 m race. The race starts at time t = 0. It takes a short time for the athlete’s speed to increase above zero (the reaction time). You are to design experiments which will enable measurements to be made in order to (a) Determine the reaction time of an athlete. (b) Plot a speed-time graph similar to that of Figure 4.1.

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Figure 4.1: Speed-Time Graph

Chapter 5 Lab #5 - PD: Terminal velocity of steel balls in oil When a ball falls through a fluid, it soon reaches a steady speed called the terminal velocity. It is suggested that this terminal velocity is proportional to the square of the radius of the ball. The diameters of the four smallest balls are given on a card. (a) Design and carry out an investigation to test the validity of the suggestion made above using the materials provided. You should avoid excessive contact between the oil and you skin. (b) Write a brief account of your experimental procedure including any use made of the sticky tapes A and B, the set square C, the plumb-line (thread with a small mass attached) and the magnet. Record your observations, together with any conclusions that you have reached concerning the validity of the suggestion. Plot a suitable graph of your results. (c) Suggest, with a reason, one possible improvement that you would make to the design or execution of your experiment if you had to repeat it, either using existing apparatus, or additional standard laboratory equipment.

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Chapter 6 Lab #6 - PD: Terminal Velocity with a Parachute A parachute falling in air eventually moves with a constant velocity known as the terminal velocity. A toy rocket contains a small parachute which is ejected from the rocket a short time after launching. The designer of the rocket wants to know how the terminal velocity of this parachute is affected by the diameter of the canopy and the load which it carries. Design a laboratory experiment to investigate how the terminal velocity of the parachute depends upon the load which it carries and the diameter of the canopy. In your account you should pay particular attention to the following: (a) the method by which the diameter of the canopy and the terminal velocity to be measured, (b) the control of variables, (c) any important precautions you would take which may improve the accuracy of your experiment..

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CHAPTER 6. LAB #6 - PD: TERMINAL VELOCITY WITH A PARACHUTE

Figure 6.1: Diagram of toy parachute with load

Chapter 7 Lab #7 - MM:Coplanar Forces Method • Students are to connect three spring scales together and alter the angle and forces applied.

• Then line up two projectors together and mark the centre ≈ 9.75 cm.

• Then connect three pieces of thread of the same length and use it as a guide over the centre of the protractor.

• Place your finger over the knot OR ensure that knot is centred over the centre of the protractor.

• Record the values of θ1 ,θ2 , andθ3 . Five sets of readings are sufficient. 17

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CHAPTER 7. LAB #7 - MM:COPLANAR FORCES

Diagram

Figure 7.1: Setup of Apparatus

Table of Results F1 /N 1 2 3 4 5

F2 /N

F3 /N

θ1 /◦

θ2 /◦

θ3 /◦

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Method continued: • Draw the free body diagram for each of the 5 readings with the correct angles. Make sure to keep one of the forces on the ’y’ plane. • Then on the same page as the free body diagram, a scaled diagram with the magnitude and direction of the forces F2 and F3 should be drawn. • Complete the parallelogram. Ensure lines are parallel. Obtain Resultant R. Say, R = 23 cm = 11.5 N for F2 & F3 . R is the resultant of F2 and F3 . • F1 is the equilibriant. Draw in F1 . • Hence, show that R and F1 are in the same straight line. i.e. θ = 180◦ . • Note: In practice this is not obtained. If you are 5◦ off the angle = 5/180 x 100 = 3%. The apparatus has a 3% error. Check to see if your answer is within 10%.

Figure 7.2: Free Body Diagram

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CHAPTER 7. LAB #7 - MM:COPLANAR FORCES

Figure 7.3: Scaled Diagram.

Chapter 8 Lab #8 - MM: Paperclip Oscillation In this experiment you will investigate the oscillations of a chain of paper clips.

Figure 8.1: Setup of Apparatus (ai) Firmly clamp the cork using a clamp, boss and stand. (ii) Attach a chain of n paper clips to the hook as shown in Fig. 8.1 with an initial value of n = 25. 21

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CHAPTER 8. LAB #8 - MM: PAPERCLIP OSCILLATION

(iii) Displace the chain from its equilibrium position by moving the bottom clips sideways, and briefly describe how the chain behaves until it reaches a state where it oscillates smoothly and reproducibly. (iv) When the chain is oscillating smoothly, measure and record the time t for twenty oscillations. (v) Estimate the uncertainty in your value of t and suggest one way in which this uncertainty could be reduced. (b) Change the value of n (25 ≥ n ≥ 5) and repeat (a) (iv) until you have six sets of readings of t and n. Include values of the period T for each value of n in your table of results. (c) For this oscillator it is suggested that the quantities T and n are related by a simple power law of the form T = pnq

(8.1)

where p and q are constants. Plot a suitable graph, and assuming that the proposed mathematical model is an acceptable one, use your graph to calculate values for p and q.

Chapter 9 Lab #9 - MM & ORR: Archimedes’ Principle Aim To determine the upthrust on an object totally immersed in water. The balance you will use, illustrated in Figure 9.1, consists of a metre trule suspended by a thread from a retort stand and clamp.

Figure 9.1: Setup of Apparatus 23

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CHAPTER 9. LAB #9 - MM & ORR: ARCHIMEDES’ PRINCIPLE

Method • First, adjust the position of the thread on the rule so that it balances horizontally on its own with no other masses suspended. Record the position of the thread. • Take the RUBBER stopper provided and suspend it by a thread close to one end of the metre rule. Now balance the rule by suspending a 100g mass by a thread on the other side of the rule. The rule should be horizontal when balanced. Record the point of suspension of the 100g mass. • When the rule is balanced, the principle of moments states that the sum of the moments of forces about the point of suspension in the clockwise direction is equal to the sum of the moments in the anticlockwise direction. • Draw a diagram indicating forces acting on the rule. Write an equation for the balance of the moments of the forces. Hence, determine the mass of the stopper. Q1 Why balance the metre rule with nothing suspended at the start? • Leaving the stopper suspendded from the same point, place a beaker of water below the stopper and arrange it so that the stopper is completely immersed in water. Now find a new position for suspension of the 100g mass so that the rule is again balanced. Be careful to see that the stopper does not touch the edge or bottom of the beaker. All the results should be carefully tabulated. • From the above readings calculate the “apparent weight” of the stopper while it was immersed in water. The loss of weight is due to the upthrust of the water or “buoyancy force”. Archimedes Principle shows that: upthrust = weight in air - apparent weight in water (assuming air gives negligble upthrust). Thus, find the upthrust on the stopper. Q2 Does it matter how far below the surface of the water you immerse the stopper, providing you do not touch the bottom? Why? A. Determination of upthrust on an object floating in water.

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• Place the CORK stopper provided in a beaker of water. Note that since the cork is floating it is only partially immersed. Q3 What must the relation be between the upthrust on the stopper and its weight? What is this upthrust in your case? You may use the commercial balance to determine the mass of the cork. B. Determination of the weight of water displaced by the rubber and cork stoppers. • For these measurements a displacement measuring vessel (d.m.v.) is used. Place the d.m.v. on the shelf over the sink. Fill it with water until water runs out of the spout into the sink. Wait a minute or so until the water has stopped draining from the spout then place an empty beaker under the spout and carefully lower the rubber stopper into the displacement measuring vessel (d.m.v.). Find the weight of the displaced water collected in the beaker. Again, wait until the water has completely stopped draining from the spout. Repeat the above procedure with the cork and find the weight of water displaced by the floating cork in the beaker. • Compare the weights of displaced water with the upthrust found in the corresponding cases in A and B above.

Chapter 10 Lab #10 - AI: The “Bug-up” Toy The diagram shows, approximately life-sized, a jumping toy called a “Bug-up”. A spring joins the hollow plastic top of the toy at P to the base of Q. Whe n the top is pushed down and the spring is fully compressed, the rubber sucker sticks to the plastic base. A few seconds after being let go, the entire Bug-up jumps into the air when the rubber sucker separates from the base. With a hollow plastic top the centre of gravity of the Bug-up rises about 60 cm.

Figure 10.1: The Bug-Up Toy 26

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(a) A student proposes to investigate the height h to which the Bug-up jumps when a mass m of Plasticine is stuck inside the hollow plastic top. By considering the physical principles associated with the mechanics of the toy, derive a relationship which predicts how h will vary for different values of m. Take the mass of the Bug-up itself to be mo and assume that the spring is fully compressed before each jump. (b) The table shows the results of a series of experiments measuring m and h. Unfortunately the student forgot to record the mass mo of the Bug-up itself. m/g

h/m

0

0.57

2.5

0.44

5.6

0.33

8.2

0.28

12.0

0.23

15.8

0.19

TABLE 1

(i) Explain how you would use these results to test the prediction you made in (a). (ii) Draw up a suitable table of values and plot a graph which would enable you to deduce mo , the mass of the Bug-up. (iii) Determine mo .

(c) The student decided to investigate the energy stored in the spring before each jump by finding its spring constant k, which, he assumed to be the same for compression and extension. When supporting a mass M, the period of oscillation T of a mass-spring system is given by T = 2π

p M/k

(10.1)

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CHAPTER 10. LAB #10 - AI: THE “BUG-UP” TOY

(i) Assuming that the spring has been detached from the Bug-up, describe briefly how you would obtain a set of values of T . State any precautions which would take to reduce uncertainties in your measurements. (ii) The graph shows T 2 plotted against M for the student’s results.

Figure 10.2: Graph of Student’s Results Use the graph to find k, the spring constant. (iii) The student’s measurements of M were only found to the nearest 1g. Explain whether the possible errors in the values of M are more significant for large or for small oscillating masses.