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1 LABORATORY MANUAL for PHYSICS 21 by Physics Instructors PHYSICS 21 GUIDE FOR THE STUDENTS I. Laboratory procedure and policies. Before going to the laboratory to perform an experiment, you should familiarize yourself with that particular experiment. To this end, you should read the experiment carefully and consult at least one reference which covers the theory involved in the experiment. You should have clearly in mind what you are going to do and how you are going to do it. Although you are expected to study these references carefully and conscientiously you are not expected to understand them completely after only one reading. Therefore, listen well to the instructor's explanations and please ASK QUESTIONS on things you don't fully understand. Remember, "He who ask a question is a fool for five minutes, He who never asks a question is a fool forever," - A Chinese ProverbEach group is jointly responsible for the instruments loaned to them during the laboratory period. The group should submit an itemized receipt duly signed by every member of the group present to the laboratory assistant in charge of the stockroom or to the instructor. After receiving a set of instruments, examine them for damage and report any to the instructor before beginning the experiment, otherwise your group will be held accountable for this damage. Note particularly whether any of the pointers on the instruments are bent. During the process of an experiment the experimental set-up should be constructed neatly and should never take on a cluttered appearance. In taking experimental data you should always strive for accuracy and reproductivity of results. Always record experimental data in some orderly manner, such as in a data table. The data should be recorded permanently at the time they are taken. You should not take data on scratch paper or in any other careless manner. Before leaving the laboratory, replace all plugs in resistance boxes, close cases of ammeters and voltmeters, and pile connecting wires neatly in one bundle. Do not twist or tie the wires together. Return all instruments in the stockroom and have your receipt cancelled. II. Use and care of the instruments. Since electrical apparatus are, in general, so much more fragile and expensive than apparatus used for mechanics and heat experiments, special care must be taken in order to avoid breakage or damage of any sort. Use these instruments with "tender love and care", for the sake of the other students who will also need them in the coming semesters. (You might be one of them, too!!!) The most frequent damaging of electrical apparatus is due to three causes: 1. Incorrect arrangement in the circuit. Have the instructor inspect and approve your wiring arrangement before the connection is made to the battery or power line. Leave at least one terminal of the battery or power line disconnected until the instructor has approved the wiring. It is not enough to leave the switch open-something may be wrongly connected elsewhere. Trace the path of the positive conventional current, which comes out of the positive terminal of a battery. When facing the trademark of a battery, the terminal to the right is the positive terminal. The positive conventional current must enter the positive terminal of a voltmeter, ammeter, galvanometer, etc. 2 2. Overheating and other injuries due to excessive current. This can be minimized by making a rough preliminary calculation of the current through each part of the circuit. It is also a good technique to insert a protective resistor after a terminal of the battery to reduce the total current flowing through the external circuit. At the start of the experiment, always use the highest range of a multi-range meter to avoid possible overloading. If, after the circuit is turned on, it is found that a lower range can be safely used, then you may use that lower range for greater accuracy. Introduce a switch after a terminal of the battery. Tap the switch lightly at the very start of the experiment to see if any meter is overloaded. Thereafter, switches should be kept closed only long enough to take the necessary readings. This will avoid both the excessive heating of apparatus and deterioration of cells. 3. Mechanical injuries due to dropping, etc. Obviously, DO NOT DROP the instruments. Keep delicate apparatus from being wet by corrosive chemicals. After the experiments, wipe and clean wet apparatus after use. III. Technique for achieving reliable and accurate results. Make a detailed record of the instruments used. For example, there are several ammeters in the stockroom; record the property number of the particular ammeter used by your group, and if it is a multi-range ammeter also record the range used. In general, meters should be read only when they are in their normal positions. Zero the meter by turning an adjustable screw located opposite the armature. If this can not be done, take the zero reading and subtract this from all other readings to be made using the same meter in the same range setting. The desired accuracy in most experiments may be realized by reading instruments to fractions of the smallest scale division. The most common source of errors in electrical measurements is faulty connections. Never twist wires together in making an electrical contact. Use binding posts to do this, tightening them moderately. 3 4 SPEED OF SOUND Experiment No. ___1___ OBJECTIVE: 1. To determine the best resonant length of a closed tube for sounds of known frequency. 2. To determine the speed of sound from the wavelengths and frequencies of several sounds. THEORY: Resonance, or sympathetic vibration, occurs when the natural vibration rates of two objects are the same. The air column in a closed glass tube produces its best resonance when it is approximately one-fourth as long as the wavelength of the sound which it reinforces. For example, a tube one meter long produces resonance with a sound wave which is about four meters long. A small correction in wavelength must be made for the internal diameter of tube. The wavelength of the sound may be calculated from the resonant length of the tube by the formula λ = 4(1 + 0.4d), where λ is the wavelength, 1 is the length of the closed tube, and d is the diameter of the tube. In this experiment the best resonant length of a closed tube will be determined. From this length and the diameter of the tube, the wavelength of the sound will be calculated. The speed of sound will then be calculated from the formula v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. APPARATUS: Tuning forks of known frequency, glass tube, 2.5 cm to 4.0 cm in diameter and at least 40 cm long, tall cylinder, thermometer, meter stick, tuning fork hammer, large rubber stopper. PROCEDURE: Hold the tube vertically in a cylinder nearly full of water, as shown in the figure. Make a tuning fork vibrate by holding it by the shank and striking it with the tuning fork hammer or striking it with a large rubber stopper. Do not strike the tuning fork on the table top or other hard surface. As you hold the vibrating tuning fork over the end of the tube, move the glass tube slowly up or down in the water of the graduate cylinder to locate the position of the loudest sound called the resonance. Then hold the glass tube firmly while another student measures the length of the tube from its top to the water surface inside the tube. This length should be recorded to the nearest thousandth of a meter. Carefully measure the internal diameter of the tube to the nearest thousandths of a meter also. Use the thermometer to determine the temperature of the air inside the tube in degrees Celsius. A second and third trial should be taken using forks of different frequencies. For each fork compute the wavelength of the sound produced from the resonant length of the tube. Also calculate the wavelength from the mark frequency of the fork and the speed of sound at the temperature inside the tube. Find the differences between these values. Compute the accepted value for the speed of sound using the to relation V = 331.45 m/s + toC (.61) m/s/oC. Data: Trial Length Diameter Waveof the of tube length tube (m) (m) (m) Frequency (sec-1) TemSpeed of Sound perature ExperiAccep(oC) mental ted (m/sec) (m/sec) % error QUESTIONS: 1. Through what fraction of a vibration has the prong of a tuning fork moved while the sound wave traveled down to the water surface and was reflected back up to the fork again? 2. If a longer glass tube were available, would it be possible to find another position where resonance is produced? Explain. 3. How could you modify this experiment to determine whether the water vapor inside the tube affects the results? 4. How does the amplitude of vibration affect the data? Verify your answer by experimentation. 5. How could you modify the experiment to find the resonant length of an open pipe? 5 6 ATMOSPHERIC PRESSURE Experiment No. __2___ OBJECTIVE: APPARATUS: To determine atmospheric pressure by the use of Boyle's Law. J-tube, medicine dropper, meterstick, utility clamp, iron stand and mercury. DIAGRAM: IRON STAND UTILITY CLAMP METERSTICK MERCURY J - TUBE Short Arm Long arm FOREWORD: TABLE TOP Atmospheric pressure is the pressure exerted in every direction at a given point by the weight of the atmosphere. It is usually expressed in pounds per square inch, dynes per square centimeter, heights of the column of mercury, bars, millibars or in atmosphere. One atmospheric pressure is equal to 1.013 x 10 6 dynes/square centimeter or 76 centimeters of mercury column at sea level, 45o latitude and at a temperature of 0oC. Boyle's law states that at constant temperature, the volume of a sample of gas is inversely proportional to the pressure applied to it or in other words, at constant temperature, the product of the volume of a sample of gas and its pressure is equal to a constant. In symbols. P : P = V : V (1) PV = PV (2) or where P = pressure of the gas at condition 1, P = pressure of the gas at condition 2, V = volume of the gas at condition 1, V = volume of the gas at condition 2. In the J-tube, the shorter arm is closed and the longer arm is opened to the atmosphere. When the levels of the mercury inside these two arms are of the same height, the pressure of the enclosed air is equal to the atmospheric pressure. If the level of the mercury in the closed arm is higher (lower) than that of the open tube, the pressure of the enclosed air is equal to the atmospheric pressure minus (plus) the pressure exerted by the column of mercury between the two levels. As shown in the diagram, L, L1 and L2 are the readings in centimeters obtained from a standing meterstick indicating the height of the closed arm, the heights of the mercury column of the closed arm and that of the open arm, respectively. So, the pressures at the bottom of these two arms, P 1 and P2, are given by the following equations: For the closed arm, P1 = P + dgL1 in dynes/sq.cm. (3) For the open arm, P2 = Pa + dgL2 in dynes/sq.cm. (4) where P is the pressure of the enclosed air and Pa is atmospheric pressure, d is the mass density of mercury in grams/cu.cm. and g is the acceleration due to gravity, 980 cm./sec.2 7 since P1 = P2 thus P + dgL1 = Pa + dgL2 P = Pa + dg(L2 - L1) The volume of the enclosed air, V in cubic centimeters, can be obtained using the equation, V = A(L - L1) where A is the cross-sectional area of the tube in square centimeters. Similarly, we obtain another set of equations, after adding some more mercury, as follows; P = Pa + d h (L2 - L1) V = A(L - L1) According to Boyle's Law, P/P - V/V Substituting values, Pa + dg(L2 - L1) = A(L2 - L ’1) Pa + dg(L ’2 - L ’1) A(L - L1) or Pa = dg[(L ’2 - L ’1)(L - L ’1) - (L2 - L1)(L - L1)] L ’1 - L1 PROCEDURE: 1. Record the atmospheric pressure, Pa, from the barometer at room temperature. Express this pressure in dynes per square centimeter. Arrange the apparatus as shown in the diagram, measure and record the height of the closed arm, L. 2. Start putting in mercury in the open arm until L2 is at a higher level than L1. A certain quantity of air is then trapped in the closed arm. Measure and record heights, L1 and L2. 3. Without changing the position of the J-tube, add some more mercury into the tube. Measure and record again heights, L1 and L2. COMPUTATION: 1. From the data obtained in steps 2 and 3, calculate the atmospheric pressure by using the equation just derived. Compare this value with the barometric reading obtained at room temperature and compute the percentage error. 2. Using the barometric reading as the atmospheric pressure, compute the pressure of the enclosed air in both cases, these are P and P. 3. Calculate the ratio of the products of the pressure obtained in computation 2 and their corresponding volumes. Compare this value with unity and compute the percentage error. (6) ARCHIMEDES' PRINCIPLE Experiment No. ___3____ 8 OBJECTIVE: To study Archimedes' Principle and to measure the density and specific gravity of solids and liquids by immersion method. APPARATUS: Beam balance, 400 ml. beaker, set of brass masses, metal cylinder, light and heavy hydrometers, hydrometer jars, alcohol and salt solution, and Mohr-Westphal balance. FOREWORD: Density of a specimen is defined as the ratio of its mass to its volume. It is expressed in grams per-cubic centimeter, kilograms per cubic meter and slugs per cubic foot. Weight density of a specimen is defined as the ratio of its weight to its volume. It is expressed in dynes per cubic centimeter, newtons per cubic meter and pounds cubic foot. d = m/V; D = w/V; hence, D = dg. (1) where d is the mass density and D is the weight density of the specimen. The specific gravity of the specimen is the ratio of the density of the specimen to that of water. In symbols, density of the specimen Specific Gravity = ----------------------------density of water (2) Archimede's Principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The volume of the specimen, no matter how irregular it is, is always equal to the volume of the fluid displaced. By knowing the buoyant force exerted by the fluid on the immersed object and the density of the displaced fluid, one can then determine the volume of the submerged object and hence its density. For solids denser than water, the specific gravity is given by the equation: weight in air Sp. Gr. = ---------------------------------apparent loss of weight in water or weight in air Sp. Gr. = ---------------------------------weight in air - weight in water (3) For solids lighter than water, a sinker is used. weight in air Sp. Gr. = --------------------------------------------wt. of specimen in air - wt. of specimen and sinker and sinker in water both in water (4) In getting the specific gravity and density of the liquids, immersion method is applied with the use of a sinker immersed in the liquid to which its specific gravity is to be measured. wt. of sinker in air - wt. of sinker in liquid Sp. Gr. = ---------------------------------------------------apparent loss of weight in water (5) 9 or wt. of sinker in air - wt. of sinker in liquid Sp. Gr. = ---------------------------------------------------wt. of sinker in air - wt. of sinker in water Once the specific gravity of a specimen is obtained, its density can easily be obtained by using the equation that density = specific gravity x density of water Hydrometer is an instrument used for direct measurement of the specific gravity of liquids. It consists of a closed graduated glass tube with a weighted bulb at the lower end. The specific gravity of the liquid in which it floats is read directly on the calibrated scale that lies on the liquid level (lower miniscus). PROCEDURE: 1. Weigh the metal cylinder in air, then in water, in salt solution, and in alcohol. In weighing the cylinder in the liquid specimens, the metal cylinder must be fully immersed but must not touch the beaker. 2. Weigh the paraffin in air. Then attach the metal cylinder to the paraffin by means of a light string and weigh the system with the paraffin in air and the metal cylinder in water. Then weigh them again when both are immersed in water. 3. Study the scales of hydrometer. Then let them float in the liquid specimen in the jars. Observed and record the readings of the scales at the liquid levels. These readings are the densities of the liquids in the metric system. 4. Set up the Mohr-Westphal balance on the table. Adjust its height so that the plummet may be fully immersed in the liquid specimen in the small jar. Hang the plummet at the end of the beam and adjust the screw at the base of the instrument so that the pointers of the beam and the frame are in line. This is done with the plummet in the air. Immerse the plummet now in salt solution and restore the balance condition by placing and adjusting riders on the beam. The riders must be placed on the notches of the beam. If two riders are required to be placed at the same position, hang the smaller rider from the hook of the bigger rider. Record the riders used and their respective positions. Repeat with the plummet immersed in alcohol. TABULATIONS: Table 1. Weight of metal cylinder in air Weight of metal cylinder in water Weight of metal cylinder in salt solution Weight of metal cylinder in alcohol Specific gravity of metal solution Experimental density of a metal cylinder Specific gravity of salt solution Experimental density of salt solution Specific gravity of alcohol Experimental density of alcohol Standard density of metal cylinder Standard density of salt solution Standard density of alcohol Percentage error of metal cylinder Percentage error of salt solution Percentage error of alcohol (6) 10 Table 2. Weight of paraffin in air Weight of paraffin in air and cylinder in water Weight of paraffin and cylinder both in water Specific gravity of paraffin Experimental density of paraffin Standard density of paraffin Percentage error Table 3. Specific gravity of salt solution Specific gravity of alcohol Experimental density of salt solution Experimental density of alcohol Percentage error for salt solution Percentage error for alcohol Table 4. Mohr-Westphal Balance For salt solution For alcohol Riders 1 2 3 1 2 3 Position COMPUTATIONS: 1. From the data of step 1, compute the density and specific gravity of the metal cylinder, salt solution and alcohol. Compare the density of the material with the value in the Physics Handbook. 2. From step 2, compute the density and specific gravity of paraffin and compare it with the value of the hydrometer. 3. Compare the density of salt solution and alcohol obtained in computation 1 with the readings of the hydrometers. 4. From the data obtained in step 4, compute the specific gravity of each liquid and compare the value from those obtained by using the hydrometers. The three riders have relative weights of 1, 0.1, and 0.01. Each kind of rider comes in pairs. The plummet and its components area so constructed that, when it is immersed in water, the state of balance can be restored by hanging the first rider in the hook, same position as the plummet. We can say then, that the buoyant force of water on the plummet is equal to 1. The specific gravity of other liquids can, therefore, be determined by knowing the riders being used and their positions. The first rider takes two positions in the value of specific gravity, namely, the whole number and the first decimal place. The second and the third riders take the second and the third decimal places respectively. For instance, if the first rider is present in the hook and also in the third notch, while the second rider is on the fifth notch and the third rider is on the second notch, then, the specific gravity of the liquid that is being tested is 1.352. MAGNETIC FIELD ABOUT A CONDUCTOR Experiment No. __4___ OBJECTIVE: To study the effect of the magnetic field which is set up in vertical and horizontal conductors by currents in them. APPARATUS: Galvanoscope, with binding posts for a single turn, a few turns, and many turns of wire (Fig. 1); annunciator wire No. 18, for connections; dry cell; d-c ammeter, 0-1 a; rheostat, approximately 25 ohms; knife switch, SPST; 1 large compass; Ampere's law stand; 4 small compasses. (A galvanoscope can be improvised by wrapping a single turn, a few turns, and many turns of insulated wire into a coil large enough to accommodate the large compass). SUGGESTION: For best results, all apparatus should be isolated from local magnetic fields, such as those created by d-c power supplies. For that reason dry cells are recommended. INTRODUCTION: Hans Christian Oersted (1777-1851), a Danish physicist, was the first to show that a current in a conductor produces a magnetic field about the conductor, proving that there is a relation between electricity and magnetism. A magnetic needle placed near a conductor carrying an electric current is deflected. in this experiment we shall study the direction and amount of such deflection. PROCEDURE: 1. Horizontal conductors. Place the large compass inside the galvanoscope coil of many turns. Turn the galvanoscope until the turns of wire lie in the North-and-South plane as indicated by the compass needle. Next turn the compass around until its N-pole is directly above the zero index of the compass card. Connect a dry cell in series with a rheostat, ammeter, and switch to the binding posts serving the coil of many turns in such a manner that electron flow will be from south to north through the loop segments above the needle. With all the resistance of the rheostat in the circuit, close the switch and adjust the current to a magnitude which just produces the maximum deflection of the compass needle. Record the current, the direction in which the N-pole of the compass needle is deflected, and the number of degrees of deflection. By rheostat adjustments, maintain this same magnitude of current for all galvanoscope tests in Part I. Reverse the direction of the electron flow and adjust the rheostat if necessary to supply the same current as before. Note the direction and the amount of the deflection of the needle and record. Keeping the galvanoscope in the same position, move the compass until it is inside the coil of a few turns. Connect the supply circuit to the proper binding posts so the electron flow will be from south to north above the needle. Adjust the rheostat to give the same current previously recorded and observed the direction and amount of deflection. Reverse the direction of electron flow, and again observe and record the readings. Repeat the experiment, using the coil of one turn, with the electrons first flowing from south to north above the needle, and then from north to south. 2. Vertical conductor. Arrange the 4 small compasses on the Ampere's law stand as shown in Figure 2. Connect the terminals to the supply circuit so that the electrons flow upward. Adjust the rheostat to supply the least current that will yield conclusive deflection of the compass needles. Note the position taken by the needles. Reverse the direction of the electron flow. Observe the directions indicated by the N-poles of the compass needles, and make sketches in your report to show them for each case. Do not leave the dry cell connected to the apparatus any longer than is required to make your observations. 11 12 QUESTIONS: 1. State the rule which enables you to predict the direction in which the N-pole of a compass will be deflected if it is placed beneath a conductor through which electrons are flowing. 2. The flow of electrons through a conductor is from south to north. In which direction will the N-pole of a compass needle placed over the conductor be deflected? 3. State the role that enables you to predict the direction in which the magnetic lines of flux circle a vertical conductor through which electrons are flowing. 4. A compass is placed to the east of a vertical conductor. In which direction must electrons flow through the conductor to cause the N-pole of the compass to point south? THE DIRECT CURRENT MOTOR Experiment No. ___5___ PURPOSE: To study the principle of the simple d.c. motor in changing electrical energy to mechanical energy. APPARATUS: St. Louis motor, magnetic compass, battery, connecting wires, switch. PROCEDURE: 1. Examine the motor carefully. Identify its parts and label them in your drawing. 2. Connect the armature binding posts through a switch to the terminals of four dry cells in series and back to the other binding post. Close the switch, if the motor does not function, check a) with another battery of cells in series, b) the firmness of the attachment of the connecting wires, c) the permanent magnets have the N pole of one opposite the S pole of the other and are close as possible to the poles of the armature, d) that the brushes make good contact with opposite commutator, segments and e) by giving the armature a gentle starting push. 3. Remove the permanent magnets and lay them some distance from the motor. Test with a magnetic compass the polarity of one end of the armature. Turn the armature through one revolution. Indicate the polarity of the marked end of the armature for different position by placing a N or S in the small circle as the armature rotates. Compass observation by applying right hand rule for determining polarity of an electro-magnet. Replace the bar magnets and adjust the commutator, brushes and field until the motor runs. If the motor fails to run, do not leave the cells connected but open the switch until the trouble is found. Observe the direction of rotation. Remove the bar magnets, reverse them end for end and replace them. Observe the action of the motor. Reverse the direction of the current by reversing battery connection and observe the effect on the direction of the rotation. As the armature rotated, slowly swing the bar magnets so that the poles move away from the armature. Observe and record the speed of rotation. Restore the bar magnets to their original position. Remove one of the bar magnets. Observe and record the speed of rotation of the armature. Insert tin plate after the third cell and transfer one terminal of connecting wire to it. Observe and record the speed of relation of the armature. Remove the permanent magnets and replace them with the field coil. Connect the field coil in parallel with the armature by connecting each battery wire to an armature binding post, then connect each armature binding post to a separate field coil terminal. The motor is now shunt wound. Connect a switch in the external circuit. Close the switch. Observe and record the direction of armature rotation. Repeat with current reversed by reversing battery connections. Observe and record the direction of armature rotation. Repeat reversing the connection from the armature binding posts to the field coil at the terminals of the field magnets. Observe and record the direction of rotation. Connect the field coil in series with the armature by connecting one battery lead to one of the armature binding posts and the other lead to a field coil binding posts; then connect the remaining two binding posts by a third wire. The motor is now series wound. Close the switch and observe the direction of rotation. Reverse the connection to the armature binding posts; observe and record the direction of rotation. Restore the armature connections. Reverse the connection to the terminals of the battery, and observe and record the direction of the armature rotation. 13 14 DATA AND RESULT: Procedure 3 st 1 Polarity of marked end of armature 2 3rd 4th 5th 6th 7th nd 8th Compass Right Hand Rule Procedure 4 Field poles original Field poles reversed Current reversed Procedure 5 and 6 Magnets farther One magnet removed Two or cells removed Direction of Armature Rotation Rate of Armature Rotation Procedure 7 Shunt wound motor Current reversed Connection from binding post to field coil reversed Direction of Armature Rotation Procedure Series wound motor Connection to the armature binding post reversed Collection to the terminals of battery reversed Direction of Armature Rotation QUESTIONS AND PROBLEMS: 1. What is the purpose of the commutator in a d.c. motor? 2. Would a motor draw more current when it is starting or when it is operating at full speed? Explain on the basis of back off. 3. What are the advantages, disadvantages and application of a) series wound b) shunt wound c) compound wound and d) synchronous motor? 4. A magnet consists of a rectangular 30-turn armature, 4 cm by 8 cm and a horseshoe magnet with a field of 0.15 n/amp. m between each poles. An external power source rotates the armature at 2400 rpm around the center of its 40 cm side a) what is the maximum speed of the wire through the field? b) What is the maximum P.D. induced in a single turn of wire? c) What is the maximum potential difference induced in the entire coil? and d) What is the minimum P.D. induced in the coil? Why? 15 SPECIFIC HEAT Experiment No. 6 PROBLEM : APPARATUS: To determine the specific heat of solid by the method of mixtures. Calorimeter with stirrer; boiler; two thermometers; trip-scale; two objects of different material; watch; Bunsen burner; iron stand. PROCEDURE: Weigh the object and place it in the boiler by sliding it along the hole and holding it in the best position by means of a string. A thermometer introduced in the hole will read the temperature to which the object is heated. Heat the boiler. While the boiler is being heated, weigh the inner vessel of the calorimeter with the stirrer. Fill it about one third full with water (sufficient to cover the object that is being heated), and weigh it again. The difference between the two weighing will give the mass of the water (Mw). The initial temperature of the water (tw) in the inner calorimeter is measured with the second thermometer. When the object has been heated the temperature between 90o and 100o C. (t2), let it slide slowly into the calorimeter, taking care to avoid the splashing of water,. Record the exact time ) when the object falls into the calorimeter. Observe the thermometer carefully and record the time (a) when marks with the highest temperature (t), i.e., the instant at which the temperature begins to fall. Continue taking the temperature every minute during ten consecutive minutes. CORRECTIONS: First - For the heat absorbed by the calorimeter and stirrer, i.e., the water equivalent of the calorimeter and stirrer. This value is found by multiplying separately the weights of the calorimeter and stirrer by the specific heat of the respective materials of which they are made. The sum of these products, k must be added to the mass of the water as indicated in the formula. Second - For the loss of heat by radiation. First, find the rate of full temperature (R) i.e., the decrease of temperature per minute. This is found by finding the mean fall per minute during the ten minutes immediately after the temperature of the mixture has reached its maximum. Multiply this rate of fall by the time (T), in minutes, that elapses from the moment the object is dropped into the calorimeter to the moment in which the mixture attains its highest temperature. This product (RT) will give an approximate value of the heat lost by radiation and must be added to (t) in order to obtain the final corrected temperature (T3). Make a second trial following the same procedure but using a different object. SUMMARY OF THE REQUIRED: Weight of the calorimeter and stirrer (ml) ………………….. Weight of the calorimeter a stirrer and water (m2) …………….. Weight of the water (Mw) = m2 – m1 = ………………………… Weight of the object (Mo) = …………………………………… Initial temperature of the water (t1) = ………………………….. Final temperature of the object (t2) = ………………………….. Highest temperature of the mixture (t) = ………………………. Specific heat of the calorimeter and stirrer …………………….. Water equivalent of the calorimeter and stirrer (K) …………….. Time when object is dropped in water (a) = ……………………. Time when mixture reaches maximum temperature (t) = ………. Duration T (in minutes) = p – a = ……………………………… Mean fall of temperature per minute (R) = …………………….. Correction for radiation (RT) = ………………………………… Specific heat of the sample (c) = ………………………………. Accepted value for c = …………………………………………. % of error = ……………………………………………………. 1st trial __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ 2nd trial ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ 16 QUESTIONS AND PROBLEMS: 1. Why is it necessary to lower the temperature of the cup and water and to raise the temperature of the specimen? Explain. 2. How does the heat conductivity of the metals used in this experiment affect the accuracy of the results? 3. What will be the equilibrium temperature reached when 550 g of brass at 105oC are placed into an 85 g aluminum calorimeter containing 130 g of water at 20oC? 4. Calculate the weight of an aluminum cylinder whose specific heat is 0.217. The aluminum cylinder was dropped into the calorimeter containing 210 g of water at 30oc. The mixture reached a temperature of 35oC after 2 min. The mean fall of the temperature per minute was 0.01o C and the water equivalent of the calorimeter is 9.4. The aluminum cylinder was heated to a temperature of 90oC. COEFFICIENT OF LINEAR EXPANSION Experiment No. __7___ OBJECTIVE: 17 To determine the coefficient of linear expansion of one or more solid rod, METHOD: The temperature of a metal rod is raised and the resulting increase in the length of the rod is measured with a micrometer screw. From the length of the rod the change in length and the rise in temperature, the coefficient of linear expansion is calculated. THEORY: With a few exception solids increase in size as the temperature is raised. It is obvious that the change in length ΔL of a solid depends upon its length L and upon the change in temperature t. It is found experimentally that ΔL is proportional to L and t, or stated algebraically where the constant of proportionality. ΔL = α L Δt (1) α is called the coefficient of linear expansion. From Eq. (1) it follows that ΔL L2 - L1 α = ------- = ----------L Δto L(t2 - t1) (2) Since L, and ΔL are measured in the same units, it follows that ΔL/L is the fractional change in length (a pure number) and that α is the fractional change in length per degree change in temperature. Since the fractional change in length is a pure number, the unit used in expressing the magnitude of α is simply per degree celsius of a certain substance. α = 0.000018 per oC, means it expands eighteen millionths of its length for each celsius degree rise in temperature. Since the length of the rod changes with temperature, the question arises: To what length does the symbol L in Eq. (1) refer? Does it stand for the original length, the final length or the length at some standard temperature? The choice is arbitrary, but actually the value of α given in tables is always based upon the length Lo of the body at 0oC and Eq. (1) should read. ΔL = α Lo Δt (3) This is the equation that is used in very precise work but in most practical situations either the initial or final length may be used for L in Eqs. (1) and (2). This is due to the fact that for most solids α is small and the lengths at the initial temperature, the final temperature and 0oC are all substantially the same. From Eq. (3) it follows that the length L of a body and the temperature toC is given by the equation. L = Lo (1 + αΔt) (4) When a body is heated it expands not only in length but in width and thickness. Its volume is, therefore, increased, and the increase in volume V is given by the equation ΔV = β v Δt (5) where V is volume and β is the coefficient of volume expansion. If the volume at 0oC is Vo, the volume V at a temperature of toC is given by the equation. V = Vo (1 βΔt) If the body is in the form of a cube each dimension of which is L at toC follows that the volume is given (6) 18 by the equation V = L3 = L3αm (1 + αt)3 = L3αm(1 + 3αt + 3α2t2 + α2t2) (7) Since α is small the terms involving α2 and α3 are negligibly small and Eq. (7) may be written V = Vo (1 + 3αt) (8) Comparing Eqs. (6) and (8) it is seen that the coefficient of volume expansion is three times as large as the coefficient of linear expansion. Although the equations above are derived for a cube, it is obvious that since any body may be divided up into a large number of small cubes, these relationships apply to all solids that expand equally in all directions. APPARATUS: Linear expansion apparatus, meter stick, thermometer, battery, buzzer, connecting wires, beaker, busen burner, power supply. PROCEDURE: First pass cold water thru the jacket. Then insert a thermometer thru a cork in the middle of the jacket and note the temperature (t1). Take out the rod from the jacket and measure it with a meter to tenths of a millimeter, after which insert it again. Record this length (L). Connect in series with the apparatus a battery and a buzzer or electric bell, and adjust the micrometer screw at one end of the apparatus until contact is made and the buzzer rings. Press the screw just enough to make the buzzer ring. Note this reading of the micrometer screw when this contact is made. Call this reading (S1). Then loosen the screw from the rod to allow for expansion. Connect boiler steam outlet with a rubber tubing to one of the jacket. Boil the water until steam passes through the jacket. When steam is passing, note the temperature and when it is constant, record it (t2), then adjust the micrometer screw until contact is made and the bell rings. Get the reading of the micrometer screw (S2). From the reading S1 and S2, determine the elongation (e) of the rod, and compute for the coefficient of linear expansion α of the rod from α= e = S2 S1 L( t2 - t1) L( t2 - t1) Repeat the same procedure for another trial. Compute on separate sheets. Another sample rod may be used for the other trial. RECORD OF DATA: Specimen Length of rod Temperature of rod First reading of screw Second reading of screw Therefore, Elongation Final Temperature (computed) (Accepted Value) % of difference Record of Data Trial I (material) (L) (t1) (S1) (S1) (e) (t2) Trial II (Material) QUESTIONS AND PROBLEMS: 1. A metal rod is 75 cm. long at 18oC and 0.072 cm. longer at 98oC. Calculate the coefficient of linear expansion of the metal. 2. A 50-m, steel tape is standard at 0oC. What is the actual length at 28oC? Linear coefficient of expansion is 11 x 10-6/oC 3. When a mercury-in-glass thermometer is plunged into hot water, the thermometer reading at first drops and then rises. Explain why. 4. Beakers should be made of material having a low coefficient of expansions. Explain why. 5. A hole is drilled in a metal plate. When the temperature of the plate is raised does the hole get larger or smaller? Explain. 19 MECHANICAL EQUIVALENT OF HEAT Experiment No. __8___ 20 OBJECTIVE: To study the conversion of mechanical energy into heat energy; in particular, to determine the mechanical equivalent of heat. METHOD: A woven copper band is wound several times around a copper drum acting as a calorimeter in such a manner that each winding of the copper band is in direct frictional contact with the drum. During the experiment, mechanical energy is continually converted into heat energy inside the calorimeter as a result of friction. The heat energy is computed from the mass, specific heat and the rise in temperature of the calorimeter and its contents. The mechanical work is computed form the measured frictional torque and the mechanical equivalent of heat as the ratio of the work done to the heat generated. THEORY: In any familiar processes such as in automobile mechanical brakes, work is done against friction and heat is produced. When a body falls and strikes a solid surface, the kinetic energy is transformed into heat energy. James Prescott Joule (1843) arranged a set of paddles (Fig. 1) that were rotated in water by a pair of falling bodies. the churning of the water produced heat that could be calculated from the rise in temperature of the water and its container. The mechanical work performed in driving the paddles was calculated from the weights of the falling bodies and the distance they descended. Joule found that the ratio of the work done to the heat produced was always the same. The number of units of work W per unit of heat H is called the mechanical equivalent of heat. In symbols W = JH (1) where J is a constant independent of the magnitude of H or h but whose value depends on the units in which W and H are expressed. Experimentally determined values for J are 4.18 joules/cal and 778 ftlb/Btu. The principle of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form into another. The statement of the equivalence of mechanical energy and heat energy is often called the first law of thermodynamics and is stated: a constant ratio exists between mechanical energy and heat energy when either form is converted into the other. It is this constant ratio that is called the mechanical equivalent of heat J. APPARATUS: 1 base plate with two table clamps, handle and reflector, 1 calorimeter drum made of copper, 1 thermometer, with rubber gasket and metal washer to seal the calorimeter, woven copper band with two eyes, about 90 cm long; 1 spiral spring with pin, Cord with spring safety hook and adjusting device. The copper band is wound five times around the drum. On rotating the drum the total friction is so great that the weight of 5 kg counterbalances it. The other end of the copper band need only be held with a weight of very few dynes so that this factor need not be allowed for even when carrying out the most precise experiments. As a result of this mechanical dodge, the friction is to a large extent independent of the speed at which the drum is rotated under the band. The base plate, should be screwed on a left-hand corner of a table. The copper calorimeter is fitted with three pivots, and should be placed on the flange made of insulating material which is connected to the handle, and secured in position, must be kept clean and polished. Should it become dirty it must be cleaned with a metal detergent. The calorimeter is sealed at the front end by the thermometer together with the rubber gasket and metal washer inserted in a locking screw. The reflector can be pivoted underneath the screwed in thermometer thus facilitating the parallax 21 free reading and the approximate reading during rotation. The copper band is narrow after use in both directions, should be wound five times around the calorimeter drum in such a manner that each winding is located alongside the other. The spring safety hook of the cord should be suspended in the end of the band hanging downwards, and the length of the cord should be adjusted so that the weight fastened to it is on the floor when the cord is taut. The other end of the copper band should be connected to the spiral spring which in turn should be fastened by its pin in one of the holes in the base plate and stretched moderately. Be careful to have the calorimeter shaft in the horizontal position, otherwise the turns of the copper band will tend to crowd together at the lower end of the drum. CAUTION: To prevent the hanging mass from falling or the spring being stretched too much, use the handle locking bar when apparatus is not in use. PROCEDURE: A measurement is best taken in the following sequence: 1. Weigh the calorimeter empty and without the thermometer, but with the locking screw. 2. Weigh the copper band. 3. Fill the calorimeter with 50 or 60 g of cold water (about 5o below room temperature) then re-weigh. Insert the thermometer, and then seal by fastening the locking screw. 4. Secure the calorimeter, wind the copper band round it five times, 4 1/4 or 5 1/4. The copper band should be even and not twisted. The hanging end should be approximately 5 cm long. Secure the other end of the copper band to the spring and expand the latter by about 3 cm. Suspend the 5 kg weight, and turn the reflector underneath the thermometer. If there is such a friction that the copper band does not glide over the drum, wind it not more than four times round the drum and lengthen the hanging end correspondingly. A reduction of the friction is also achieve by cleaning the copper band and the drum. 5. Turn the handle until the water in the calorimeter has reached a temperature approximately 3oC below room temperature. 6. Read off the temperature as exactly as possible, and commence the experiment immediately. 200 rotations result in a temperature increase of approximately 5oC. Starting and final temperatures of these levels enable the heat absorption and the omission to counterbalance each other considerably. 7. Read off the final temperature. 8a. In order to determine the mechanical work done during the experiment you must know the Force (weight of mass hanging from copper band and the distance through which it acts (number of revolution of drum x the circumference of the copper drum). 8b. Another method to determine distance is as follows: Measure the height of level h when winding the copper band round the calorimeter drum. The weight should be suspended on the copper band which should be secured by its longitudinal eye to the double slot of the calorimeter holder. The handle should be held in position by the lock on the base plate, and the level of the weight measured. Subsequently turn the handle one or more times measuring the height of level for one rotation. The handle should be locked in position after each rotation. Evaluation of the constant J: W = JH where W = work done H = total heat energy gained by the calorimeter system (1) Now, W = FS = F (πd)(n) (2) 22 H = (mccc Δt) + (mbcb Δt) + (mwcw Δt) + (mTcT Δt) (30 where mb = the mass of that part of the band which is in contact with the drum and the product mTcT can be taken as 0.8 x 10-3 kg cal/oC substituting values of W and H into Eq. (1) F(πd)n = J(mccc + mbcb + mwcw + mTcT) Δt (4) In recording the data for Eg. (4), use MKS system of units. Record the values of specific heat in k cal/kgoC. QUESTIONS: 1. How much is the water warmed at Niagara Falls by falling 50 m? What factors might prevent this rise in temperature? 2. Why was a uniform speed of rotation not necessary in the experiment? What factor must be constant? 3. What are the chief sources of error in the experiment. Cite ways of reducing these errors. 4. Design your method of determining the value of J. Mechanical Equivalent of Heat 1st Mass of calorimeter mc (kg) Mass of copper band mb (kg) Mass of calorimeter and water (kg) Mass of water mw (kg) Initial temperature of water t1 (oC) Final temperature of system t2 (o) Change in temperature (oC) Specific heat of calorimeter oC (kg cal/kgoC) Specific heat of band cb (k cal/kgoC) Diameter of copper drum (m) No. of revolutions n Force F (Newton) Experimental J (by Eq. 4) (joule/kcal) Experimental J (joule/cal) Standard value of J (joule/cal) % error 2nd 23 HEATING EFFECT OF ELECTRIC CURRENT Experiment No. __9___ OBJECTIVE: 1. To study how the heating effect of electric current compares with other effect of electric current. 2. To determine the factors upon which the heating effect of an electric current depends. 3. To measure experimentally Joule's electrical equivalent of heat. APPARATUS: Electric calorimeter, set of masses, voltmeter, ammeter, rheostat, storage battery, switch, thermometer, stop watch distilled water. PROCEDURE: 1. Variation of heating effect with time. Connect the apparatus as in Fig. 1. Leave one terminal of the battery unconnected and the switch open until the instructor has checked the hiring. Never close the switch unless the heating coil is immersed in water. Always turn off the current when no reading are being made, or which no experiment is in progress. R1 + A A + v R1 calorimeter Figure 1 Make a short test run, using the tap water in the calorimeter and a current of about 2 amp. One observer should close the switch and start the time simultaneously, and turn off the switch and stop the watch again at the end of the trial. Another observer, should watch the ammeter and adjust R1 should the current change to bring it back to the original value of the current. For the final run, empty and dry the inner calorimeter cup. Refill it about halfway with distilled water. Turn on the current and kept it at a constant value. Record the temperature at 2-minute intervals. Record your data in the following table: mass of water and cup = mass of cup = mass of water = Time (sec) 30 60 90 120 Initial temp. T1 (oC) Final temp. T2 (oC) switch on 0 24 Heating effect as a function of current, time constant - Empty and dry the inner calorimeter cup. Refill it again about halfway with distilled water. Perform another trial as in (1), except that how you record the temperature after 5 minutes only. Turn off the current and let the water in the calorimeter cup cool for a while. Perform another trial as in (1) again with a higher current, recording the temperature at the start and then after 5 minutes. Repeat the above for a third and still higher current, using the same water in the calorimeter cup. Be careful, however, not to overload the ammeter you are using. Do not heat the water above about 40oC otherwise the effects of radiation might be large. Record your observation in the following table: mass of water and cup = t = 5 minutes mass of cup = mass of water = Temperature T1 _______________ _______________ Temperature T2 _______________ _______________ Current (1) ___________ ___________ Voltage (v) ____________ ____________ Calories (H) ___________ ___________ From the data in step 1 plot temperature rise, T2 - T1 versus time t. Does your graph pass through the origin? Is your graph supposed to pass through the origin? Calculate S from the slope of your graph. From the data in step 2, plot H versus I, plot H versus I2. PROBLEMS: 1. A 2-ton water in a 8 kg container has a temp of 20oC. The heater coil takes in a current of 10 amp and its resistance is 50 ohms. If the specific heat of water and container is 1. and 0.25 respectively, determine the following: a. Power consumed by the heater b. Heat required to reach boiling temperature c. Total times to accomplish the process d. Cost of the operation at P1.20/kw-hr. 2. An electric water heater operates at 110 volts. If the efficiency is 80% and one liter of water can be heated from 20oC to 80oC in 10 min, calculate the cost at 80 centavos/kw-hr. REFLECTION AND MULTIPLE IMAGES Experiment No. __10__ 25 PURPOSE: 1. 2. 3. 4. 5. To compare the angle of incidence with the angle of reflection. To find the characteristics of images formed in plane mirrors. To find how the image compares with the object with respect to size, form and distance from the mirror. To find an experimental relationship between the number of images and the angle between two mirrors. To determine the number of images formed when two mirrors are placed at an angle by geometrical construction. APPARATUS: Plane mirrors, wooden blocks, cardboard box, rubber bands, pencil, ruler, protractor, pins, compass. PROCEDURE: 1. Draw a line across the center of a blank sheet of paper and call this line the mirror line. Set up the mirror vertically so that its back surface is exactly on this line. On a point about 10 cm in front and center, stick a pin vertically. Mark this as point A. Place a ruler a little to the left of this point, such that the ruler points to the image of the pin. To do this accurately, put your face close to the paper and sight in the direction of the image of the pin, adjusting the ruler until it appears to be pointing to the pin image. Press the ruler and draw a line pointing to the image. Remove the ruler and transfer it to the other side of the pin. Again draw a line that points to the image of the pin. Make one more sight line a little farther than the second for checking purposes. Remove the mirror and carefully continue the three sight lines. They should meet at a common point A. This meeting point is the location of the image behind the mirror line. Draw a line perpendicular to the mirror line and also lines at the foot of the pin at A. The lines from A to the mirror line are incident rays and the angles they form with the perpendicular are called angles of incidence. The original line of sight and the perpendicular, form another angle, called the angle of reflection. With the use of protractor measure these two angles in degrees and record it. Make three trials. Connect A to A and measure the angle between this line AA and the mirror line. Measure the distance from A to the Mirror line and the distance of A behind the mirror line. Record all angles and distances measured. Angle of incidence (degrees) Angle of reflection (degrees) Angle between AAN and the mirror line Distance of A from the mirror line Distance of AN from the mirror line 2. On a new sheet of blank paper, draw again a mirror line and place the mirror as before. In front of the mirror, draw an arrow about 6 cm long. Label the head as C and the tail as B. Stick a pin at B and draw three sight line as before. Do the same for C. After removing the mirror, continue the lines to locate the images of B and C which will be labelled B and C. Measure the original length of the arrow BC and also the length of the image BC and record. If time permits make a second trial. Length BC (cm) Length BNCN (cm) 3. Mount two mirrors on blocks and place them at an angle of 90o to one another. Place an object (pencil) between the mirrors but not midway between them. Count the number of images you see in both 26 mirrors. Vary the angle between the mirrors and record your result. 90o 3 Angle Number of images 75o 60o 45o 30o You will find it easier to count the image if, instead of using a pencil you observed the multiple reflections of the rubber bands that hold the mirrors to the wooden blocks. Adjust these rubber bands so that they are straight across the face of each mirror and at the same height on both mirrors. When the mirrors are placed at a 90o angle, the four images of the rubber bands form a pattern like four spokes of a wheel. (You may have trouble seeing the image that lies right next to each of the rubber bands because it may be partial hidden by the rubber band. Therefore, for the rest of the experiment, discount those two images and consider the rubber bands as two of the "spokes" instead). Let n stand for the number of spokes and Θ for the angle between the mirrors. Thus, when Θ = 90o, n = 4. Read just the rubber band, and look toward the image of this rubber band in the other mirror. You should observe that one of the spokes seems to divide into two. Thus, n becomes 5 at 89o, (If you do not see this at 89o, make the angle a little smaller, say 88o or 85o). As Θ is gradually made smaller, note that you still see no more than five spokes at a time (arranged in nonsymmetrical pattern around the axis between the mirrors) until 72o is reached. At 72o, the spokes seem to form a symmetrical pattern. At 71o, the spoke that is just behind the bisector of the angle between the mirrors seems to divide into two and n becomes 6. Use this method of observation to find the maximum number of spokes that can be seen for other angles. Start with the mirrors at 180o angle, and very Θ until the number of spokes changes. For each n, record the smallest angle Θ at which you can still see n spokes. n n 2 3 4 5 6 7 8 9 10 11 From your result form a formula for predicting how many spokes will be seen for any angle between the mirrors. The number of spokes is related to, but is not the same as, the number of images you see when an object such as a pencil is placed between the mirrors. Then convert your formula to one that expressed the number of images, place a pencil between the two mirrors. Note that when the object is in the space between one pair of spokes, all the pencil's images are in space between the other pairs of spokes in the wheel pattern. Let i represent this number of images. Express i in terms of n. Use the relationship between i and n to write a formula from which you can find the smallest angle that will give a certain number of images. 4. You can use a method of geometric construction to locate the position of the images that you observed. From previous exercise, the image of a point object always appears to lie on the extension of the perpendicular line from the object to the mirror. The image appears to be as far behind the mirror as the object is the front of it. We shall call this as the equal distance rule. This rule is used to locate graphically all the images of an object placed between two mirrors when the mirrors are at one of the angles that you have recorded in the previous table. In constructing your diagram, assume that the eye is kept in line with the bisector of Θ. The graphical procedure that follows is based upon the fact that when you look into either of the mirror you see an image of the other mirror. The successive images of the two mirrors appear to form an angle that is equal to the angle Θ between the two actual mirrors. When Θ is decreased, you can see a second image of a mirror in the mirror's first image, possibly a third image in the second image and so on. In each case, the angle between each of the multiple images of the mirrors will be the same as the angle Θ between the real mirrors. When an object is placed somewhere the real mirrors, its images can also be located according to the equal distance rule. Notice in the following figure that there is an image of the pencil in front of the first image of each mirrors, in which the images of the pencil are reflected. If we think of the images of 27 the pencil as "virtual objects", when the location of their images can be found by the equal distance rule. This process of finding images by locating the virtual mirrors can be repeated until you come to an image of a mirror that is an angle of 180o or more with the line of sight. Since such a mirror is being viewed edge on or from the back (Matched lines), it can not act like a virtual mirror, and therefore the image-locating process must stop. On a sheet of graph paper, draw two mirrors perpendicular to each other. Use the equal-distance rule to locate all the images of an object between these two mirrors. Second image of mirrors (M1 & M2) Second image of pencil Second image of pencil First image mirror M1 First image mirror M2 First image of pencil First image of pencil Mirror M2 Pencil Mirror M1 QUESTIONS AND PROBLEMS: 1. What are some uses of plane mirrors? 2. Why are images formed by plane mirrors sometimes distorted? 3. A plane mirror used as the rear view mirror for a car is to be made in such a way that the driver can see the entire 1.5 m-wide rear window of the car in the mirror. If the mirror is 0.70 m from the driver's eyes and 3.2 m from the rear window, how wide must be mirror be? 4. In a vertical plane mirror 8 cm high you can see the image of a building 30 m high. If the building is 110 m behind you, at what distance from the mirror must you stand in order to see the entire building?