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This Document Contains Experiments 5 to 11 Name____________________________________________________Section________________Date___________ Experiment 5: Centripetal Force Invitation to Inquiry 1. Did you ever try to figure out which is a cooked egg and which is a raw one withoutbreaking the shell? One way to accomplish this is by spinning the eggs on a plate, and the wellcooked one will continue to spin while the uncooked egg will rock back and forth. The yolk is heavier than the white, but why would an uncooked egg spin more slowly? Use your understanding of centripetal force to develop some ideas about why eggs should behave this way, then design a demonstration or experiment to test your idea. 2. Experiment with some things that rotate, such as rolling cylinders. Roll large, small, solid,hollow, and various combinations of large and solid cylinders, small and solid cylinders down an incline. Predict ahead of time which will reach the bottom of the incline first. Then test your predictions. 3. A hollow and solid cylinder of the same size do not have the same weight. If you roll thetwo cylinders down an incline slope together, side by side, which cylinder should win? If you attach strings of equal lengths to make pendulums from the same hollow and solid cylinders, will they swing together, side by side? Experiment to find out, then be prepared to explain your findings. 4. Explore relationships between mass distance from an axis and how hard it is to set anobject into rotational motion. Consider using a baton with some kind of movable masses that can be fixed to the baton different distances from the axis of rotation. A large wooden dowel rod and lumps of clay might be a good experimental alternative to a baton. Background This experiment is concerned with the force necessary to keep an object moving in a constant circular path. According to Newton’s first law of motion there must be forces acting on an object moving in a circular path since it does not move off in a straight line. The second law of motion (F = ma) also indicates forces since an unbalanced force is required to change the motion of an object. An object moving in a circular path is continuously being accelerated since it is continuously changing direction. This means that there is a continuous unbalanced force acting on the object that pulls it out of a straight-line path. The force that pulls an object out of a straight-line path and into a circular path is called a centripetal force. The magnitude of the centripetal force required to keep an object in a circular path depends on the inertia (or mass) and the acceleration of the object, as you know from the second law (F = ma). The acceleration of an object moving in uniform circular motion is a = v2/r, so the magnitude of the centripetal force of an object with a mass (m) that is moving with a velocity (v) in a circular orbit of radius (r) can be found from mv2 F = r . The distance (circumference) around a circle is 2πr. The velocity of an object moving in a circular path can be found from v = d/t, or v = 2πr/T where 2πr is the distance around one complete circle and T is the period (time) required to make one revolution. Substituting for v, F T = r or F = m4π2 2r , r F = 4π2 2r m2 × 1r T m 2πr2 2 F = 4π r m2 . T This is the relationship between the centripetal force (Fc), the mass (m) of the object in circular motion, the radius (r) of the circle, and the time (T) required for one complete revolution. Procedure 1. The equipment setup for this experiment consists of weights (washers) attached to a string, and a rubber stopper that swings in a horizontal circle. You will swing the stopper in a circle and adjust the speed so that the stopper does not have a tendency to move in or out, thus balancing the centripetal force (Fc) on the stopper with the balancing force (Fb), or mg, exerted by the washers on the string. Figure 5.1 2. Place some washers on the string and practice rotating the stopper by placing a finger next to the string, then moving your hand in a circular motion. You are trying to move the stopper with a consistent, balancing motion, just enough so the stopper does not move in or out. Keep the stopper moving in a fairly horizontal circle, without the washers moving up or down. An alligator (or paper) clip placed on the string just below the tube will help you maintain a consistent motion by providing a point of reference as well as helping with length measurements. Be careful of the moving stopper so it does not hit you in the head. 3. After you have learned to move the stopper with a constant motion in a horizontal plane, you are ready to take measurements. The distance from the string at the top of the tube to the center of the stopper is the radius (r) of the circle of rotation. The mass (m) of the stopper is determined with a balance. The balancing force (Fb) of the washers is determined from the mass of the washers times g (Fb = mg). The period (T) is determined by measuring the time of a number of revolutions, then dividing the total time by the number of revolutions to obtain the time for one revolution. For example, 20 revolutions in 10 seconds would mean that 10⁄20, or 0.5 seconds, is required for one revolution. This data is best obtained by one person acting as a counter speaking aloud while another person acts as a timer. 4. Make four or five trials by rotating the stopper with a different number of washers on the string each time, adding or removing two washers (about 20 g) for each trial. For each trial, record in Data Table 5.1 on page 56, the mass of the washers, the radius of the circle, and the average time for a single revolution. Data Table 5.1 Centripetal Force Relationships Trial Mass of Balancing Radius Time Centripetal washers force force (m) (Fb) (r) (t) (Fc) (kg) (N) (m) (s) (N) 1 __________0.02 __________0.20 __________0.10 __________0.6 __________0.22 2 __________0.04 __________0.39 __________0.15 __________0.53 __________0.42 0.06 3 __________ __________0.59 __________0.17 __________0.48 __________0.58 4 __________0.08 __________0.78 __________0.20 __________0.44 __________0.82 5 __________0.10 __________0.98 __________0.25 __________0.46 __________0.93 Mass of stopper _____________0.02 _____kg 5. Calculate and record the balancing force (Fb) for each trial from the mass of washers times g (9.8 m/s2), or Fb = mg. 6. Calculate and record the centripetal force (Fc) for each trial from F = 4π2r m2 . T Considering the balancing force (Fb) as the accepted value, and the calculated centripetal force (Fc) as the experimental value, calculate your percentage error for each trial of this experiment. Analyze the percentage errors and other variables to identify some trends, if any. Trial 1 : × 100 = 10% Trial 2 : × 100 = 7 7. % Trial 3 : × 100 = 1 7. % Trial 4 : × 100 = 5 1. % Trial 5 : × 100 = 5 1. % Results 1. Did the balancing force (Fb) equal the centripetal force (Fc)? Do you consider them equal or not equal? Why or why not? The balancing force and the centripetal force are basically equal. The balancing force creates the tension in the string which keeps the stopper moving in a circle. The data supports this since the error is less than 10%. 2. Analyze the errors that could be made in all the measured quantities. What was probably the greatest source of error and why? Discuss how these errors could be avoided and how the experiment in general could be improved. There are at least two major sources of errors: (a) time measurement, and (b) radius measurement The errors in the time measurement can be reduced by timing a number of revolutions and finding the average. The error in the radius measurement can be reduced by choosing a reasonable radius and marking it on the string. Then you will swing the stopper at such a rate to make the string stay at the mark. This also helps the student keep a constant speed throughout the timing process. 3. Discuss any trends that were noted in your analysis of percentage error for the different trials. Analyze the meaning of any observed trends or discuss the meaning of the lack of any trends. There is more error when the time for a revolution is too long. This is because it is difficult to keep the stopper moving at a constant speed. Thus, as the hanging mass increases, and the time of revolution decreases, there will be less error. For the trial with a small hanging mass, it is best to make the radius small as well. This will reduce the time for a revolution and help keep the error down. 4. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should be reasonable and make sense, showing thoughtful analysis and careful, thorough thinking.) (The student should be able to explain the basics of centripetal acceleration. They should be able to explain how the centripetal acceleration (or centripetal force) changes when the radius changes or when the time of revolution changes. They should also understand that the tension; in the string, or indirectly the hanging weight, supplies the force needed to keep the stopper moving in a circle.) Name____________________________________________________Section________________Date___________ Experiment 6: Work and Power Invitation to Inquiry Tie one end of a string to a book and the other end to a spring scale. Use the spring scale to measure the force needed to pull the book up a smooth board used as a ramp (inclined plane). How much force was required to lift the book straight up (the weight of the book)? How much force was required to pull the book up the ramp? Compare the force needed to lift the book straight up with the force needed to pull the book up the ramp. Is there any relationship of this ratio to the ratio of the length and height of the ramp? Consider how you can reduce friction on a ramp. Experiment with the use of ball bearings, pencils, or oil between two paper sheets on the surface of the ramp. Compare the results of the force ratios of lifting and pulling the book with the length and height ratio when friction is reduced. Background The word work represents a concept that has a special meaning in science that is somewhat different from your everyday concept of the term. In science, the concept of mechanical work is concerned with the application of a force to an object and the distance the object moves as a result of the force. Mechanical work (W) is defined as the magnitude of the applied force (F) multiplied by the distance (d) through which the force acts, W = Fd. Figure 6.1 You are doing work when you walk up a stairway since you are lifting yourself through a distance. You are lifting your weight (the force exerted) the vertical height of the stairs (distance through which the force is exerted). Running up the stairs rather than walking is more tiring because you use up your energy at a greater rate when running. The rate at which energy is transformed or the rate at which work is done is called power. Power (P) is defined as work (W) per unit of time (t), P = W t When the steam engine was first invented there was a need to describe the rate at which the engine could do work. Since people at that time were familiar with using horses to do their work, the steam engines were compared to horses. James Watt, who designed a workable steam engine, defined horsepower (hp) as a power rating of 550 ft·lb/s. In SI units, power is measured in joules per second, called the watt (W). It takes 746 W to equal 1 hp, and 1 kW is equal to about 11⁄3 hp. Procedure 1. Teams of two volunteers will measure the work done, the rate at which work is done, and the horsepower rating as they move up a stairwell. Person A will measure and record the data for person B. Person B will measure and record the data for person A. An ordinary bathroom scale can be used to measure each person’s weight. Record the weight in pounds (lb) in Data Table 6.1 on page 63. This weight is the force (F) needed by each person to lift himself or herself up the stairs. 2. The vertical height of the stairs can be found by measuring the height of one step, then multiplying by the number of steps in the stairs. Record this distance (d) in feet (ft) in Data Table 6.1. 3. Measure and record the time required for each person to walk normally up the flight of stairs. Record the time in seconds (s) in Data Table 6.1. 4. Measure and record the time required for each person to run up the flight of stairs as fast as can be safely accomplished. Record the time in seconds (s) in Data Table 6.1. 5. Calculate the work accomplished, power level developed, and horsepower of each person while walking and while running up the flight of steps. Be sure to include the correct units when recording the results in Data Table 6.1. Results 1. Explain why there is a difference in the horsepower developed in walking and running up the flight of stairs. When running, you are getting the same work done as when walking, but you get it done in a shorter period of time. Horsepower is work per unit time. Thus running up the stairs, which takes less time, develops more horsepower than walking up the same stairs. 2. Is there some limit to the height of the flight of stairs used and the horsepower developed?Explain. Yes, you cannot continue to run up stairs indefinitely at the same rate. Thus,s your horsepower decreases as you get tired. 3. Could the horsepower developed by a slower-moving student ever be greater than the horsepower developed by a faster-moving student? Explain. Horsepower is not only influenced by time, it is also influenced by the amount of work accomplished during the time. So, a slower-moving student could develop more horsepower than the faster-moving student if he/she does more work. How much more, of course, depends on the specific situation. 4. Describe an experiment that you could do to measure the horsepower you could develop for a long period of time rather than for a short burst up a stairwell. (There are many things the student could describe here. One example would be loading firewood into the back of a truck for an extended period of time.) 5. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question shouldshow thoughtful analysis and careful, thorough thinking.) (The student should notice that the work done when walking up the stairs is the same as done when running up the stairs. It is only when you consider the time that it takes to do the work that the difference occurs.) Name____________________________________________________Section________________Date___________ Experiment 7: Thermometer Fixed Points Invitation to Inquiry 1. Wash an aluminum pop can, leaving a small amount of water in the can. Use tongs to holdthe can over a heat source until the water boils, and you can see steam condensing in the air at the opening. Immediately invert the can part way in a container of cool water. Explain what happens in terms of a molecular point of view. 2. Place the ends of a one meter metal rod on two wood blocks and secure one end to itsblock. Place a pin through a tagboard pointer under the free end. The metal rod should be able to move back and forth, turning the pin as it moves. Explain what happens in terms of a molecular point of view to the pointer as the metal rod is heated, then cooled. 3. Boil a small amount of water in a clean 500 mL flask, then apply a round balloon over themouth before the flask cools. Place a rubber band, doubled if necessary, around the balloon on the neck of the flask. Explain what happens to the balloon as the flask is heated or cooled without using the terms “drawn in” or “suck.” Background This experiment is concerned with the fixed reference points on the Fahrenheit (TF) and Celsius (TC) thermometer scales. Two easily reproducible temperatures are used for the fixed reference points and the same points are used to define both scales. The fixed points are the temperature of melting ice and the temperature of boiling water under normal atmospheric pressure. The differences in the two scales are (1) the numbers assigned to the fixed points, and (2) the number of divisions, called degrees, between the two points. On the Fahrenheit scale, the value of 32 is assigned to the lower fixed point and the value of 212 is assigned to the upper fixed point, with 180 divisions between these two points. On the Celsius scale, the value of 0 is assigned to the lower fixed point and the value of 100 is assigned to the upper fixed point, with 100 divisions between these two points. In this laboratory investigation you will compare observed thermometer readings with the actual true fixed points. Variations in atmospheric pressure have a negligible effect on the melting point of ice but have a significant effect on the boiling point of water. Water boils at a higher temperature when the atmospheric pressure is greater than normal, and at a lower temperature when the atmospheric pressure is less than normal. Normal atmospheric pressure, also called standard barometric pressure, is defined as the atmospheric pressure that will support a 760 mm column of mercury. An atmospheric pressure change that increases the height of the column of mercury will increase the boiling point by 0.037˚C (0.067˚F) for each 1.0 mm of additional height. Likewise, an atmospheric pressure change that decreases the height of the column will decrease the boiling point by 0.037˚C (0.067˚F) for each 1.0 mm of decreased height. Thus, you should add 0.037˚C for each l.0 mm of a laboratory barometer reading above 760 mm and subtract 0.037˚C for each 1.0 mm below the normal pressure of 760 mm. This calculation will give you the actual boiling point of water under current atmospheric pressure conditions. Any difference between this value and the observed thermometer reading is an error in the thermometer. Procedure 1. First, verify accuracy of the lower fixed point of the thermometer. Fill a beaker with cracked ice as shown in Figure 7.1. After water begins forming from melting ice, place the bulb end of the thermometer well into the ice, but leave the lower fixed point on the scale uncovered so you can still read it. Gently stir for five minutes and then until you observe no downward movement of the mercury. When you are confident that the mercury has reached its lowest point, carefully read the temperature. The last digit of your reading should be an estimate of the distance between the smallest marked divisions on the scale. Record this observed temperature of the melting point in Data Table 7.1 on page 69. Use 0˚C as the accepted value and calculate and record the measurement error, if any. Beaker Ice Figure 7.1 2. Now verify the accuracy of the upper fixed point of the thermometer. Set up the steam generator as illustrated in Figure 7.2. If you need to insert the thermometer in the stopper, be sure to moisten both with soapy water first. Then hold the stopper with a cloth around your hand and gently move the thermometer with a twisting motion. The water in the steam generator should be adjusted so the water level is about 1 cm below the thermometer bulb. When the water begins to boil vigorously, observe the mercury level until you are confident that it has reached its highest point. Again, the last digit of your reading should be an estimate of the distance between the smallest marked divisions on the thermometer scale. Record this observed temperature of the boiling point in Data Table 7.1. Figure 7.2 3. Determine the accepted value for the boiling point by recording in mm the barometric pressure, then calculating the deviation above or below 100˚C. Record this accepted boiling point in Data Table 7.1, then calculate and record the measurement error here, if any. 4. Repeat the entire procedure for a second trial, recording all data in Data Table 7.1. Results 1. Did the temperature change while the ice was melting? Offer an explanation for this observation. It should not change if all the variables were controlled. Temperature remains constant during a phase change. 2. Describe how changes in the atmospheric pressure affect the boiling point of water. Offer an explanation for this relationship. At sea level, higher atmospheric pressure than normal will result in a boiling point of water greater than 100˚C . If the atmospheric pressure at sea level is less than normal, the boiling point of water is less than 100˚C. For lower atmospheric pressure, it takes less energy to change the water to steam, thus the temperature at which water boils is less than 100˚C. The opposite is true for higher atmospheric pressure. 3. Account for any differences observed in the melting point and boiling point readings. 1. Elevation is different than sea level. 2. Impurities in the water. 3. Thermometer may not be calibrated correctly. 4. How would the differences determined in this investigation influence an experiment concerning temperature if the errors were not considered? The differences in the boiling point due to changes in the atmospheric pressure are actually quite small. The other errors in experiments are larger. For most experiments, ignoring boiling point changes due to atmospheric pressure changes would be acceptable. 5. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should show thoughtful analysis and careful, thorough thinking.) (Students should understand how changes in atmospheric pressure changes the boiling point of water but not the melting point of ice. They should see that all thermometers are not calibrated the same.) Going Further Using data from your best trial, make a graph by plotting the Celsius temperature scale on the x-axis and the Fahrenheit temperature scale on the y-axis. Calculate the slope of the straight line and write it here and on the graph somewhere, then answer the following questions: 1. What is the value of the slope? What is the meaning of the slope? Slope = 1.8 ˚F/˚C. This tell me that there are 1.8 Fahrenheit degrees for every Celsius degree. 2. What is the value of the y-intercept? It is the freezing/melting point of water/ice in ˚F, 32˚ F. 3. The slope-intercept form for the equation of a line is y = mx + b, where y is the variable on the y-axis (in this case, ˚F), x is the variable on the x-axis (in this case, ˚C), m is the slope of the line, and b is the y-intercept. Use this information to write the equation of the Celsius-Fahrenheit temperature graph. What is the meaning of this equation? ˚F = (1.8) ˚C + 32˚ F Use this relationship to convert temperatures in Celsius to temperatures in Fahrenheit. Name____________________________________________________Section________________Date___________ Experiment 8: Specific Heat Invitation to Inquiry 1. Objects that have been in a room with a constant temperature for some time should allhave the same temperature. Touch metal, plastic, and wooden parts of a desk or chair to sense their temperature. Explain your findings. 2. Place about 4 kg of masses on both end of a small-diameter wire. Place the wire over thecenter part of a large block of ice that is supported on both ends. Would different kinds of metal wires change the rate of movement of the wire through the ice? Would different thickness of wire make a difference? 3. Predict what will happen if you heat a brass, glass, and iron ball to 100°C and place themon a sheet of paraffin. Test your prediction, then explain your findings. Background Heating is a result of energy transfer, and a quantity of heat can be measured just as any other quantity of energy. The metric unit for measuring energy or heat is the joule (J). However, the separate historical development of the concepts of motion and energy and the concepts of heat result in separate units. Some of these units are based on temperature differences. The metric unit of heat is called the calorie (cal), a leftover term from the old caloric theory of heat. A calorie is defined as the amount of energy (or heat) needed to increase the temperature of one gram of water one degree Celsius. A kilocalorie (kcal) is the amount of energy (or heat) needed to increase the temperature of one kilogram of water one degree Celsius. The relationship between joules and calories is called the mechanical equivalence of heat, and the relationship is 4.184 J = 1 cal or 4184 J = 1 kcal. There are three variables that influence the energy transfer that takes place during heating: (1) the temperature change, (2) the mass of the substance being heated, and (3) the nature of the material being heated. The relationships among these variables are: 1. The quantity of heat (Q) needed to increase the temperature of a substance from an initial temperature of Ti to a final temperature of Tf is proportional to Tf – Ti, or Q ∝ ∆T. 2. The quantity of heat (Q) absorbed or given off during a certain ∆T is also proportional to the mass (m) of the substance being heated or cooled, or Q ∝ m. 3. Differences in the nature of materials result in different quantities of heat (Q) being required to heat equal masses of different substances through the same temperature range. The specific heat (c) is the amount of energy (or heat) needed to increase the temperature of one gram of a substance one degree Celsius. The property of specific heat describes the amount of heat required to heat a certain mass through a certain temperature change, so the units for specific heat are cal/g˚C or kcal/kg˚C. Note that the k’s in the second set of units cancel, so the numerical value for both is the same—for example, the specific heat of aluminum is 0.217 cal/g˚C, or 0.217 kcal/kg˚C. Some examples of specific heats in these units are: Aluminum 0.217 Iron 0.113 Copper 0.093 Silver 0.056 Lead 0.031 Nickel 0.106 When the units of all three sets of relationships are the same units used to measure Q, then all the relationships can be combined in equation form, Q = mc∆T This relationship can be used for problems of heating or cooling. A negative result means that energy is leaving a material; that is, the material is cooling. When two materials of different temperatures are involved in heat transfer and are perfectly insulated from their surroundings, the heat lost by one will equal the heat gained by the other, Heat lost(by warm substance) = Heat gained(by cool substance) or Qlost = Qgained or (mc∆T)lost = (mc∆T)gained . Calorimetry consists of using the concept of conservation of energy and applying it to a mixture of materials initially at different temperatures that come to a common temperature. In other words, (heat lost by sample) = (heat gained by water). The sample is heated, then placed in water in a calorimeter cup where it loses heat. The water is initially cool, gaining heat when the warmer sample is added. (The role of a Styrofoam calorimeter cup in the heat transfer process can be ignored since two Styrofoam cups have negligible heat gain m cs s∆Ts = m cw w∆Tw [∆T ≈ 0] and very little mass.) In symbols, where ms is the mass of the sample, cs the the specific heat of the sample, and ∆Ts is the temperature change for the sample. The same symbols with a subscript w are used for the mass, specific heat, cs = m cw w∆Tw ms∆Ts and temperature change of the water. Solving for the specific heat of the sample gives Procedure 1. You are going to determine the specific heat of three samples of different metals by using calorimetry. You will run two trials on each sample, making very careful temperature and mass measurements. Do the calculations before you leave the lab. If you have made a mistake you will still have time to repeat the measurements if you know this before you leave. 2. Be sure you have sufficient water to cover at least the bottom two-thirds of a submerged metal boiler cup (see Figure 8.1), but not so much water that it could slosh into the cup when the water heat source) Calorimeter (Two Styrofoam cups) is boiling. Start heating the water to a full boil as you proceed to the next steps. Figure 8.1 3. Measure and record the mass of a dry boiler cup. Pour metal shot into the boiler cup until it is about one-third filled, then measure and record the mass of the cup plus shot. Record the mass of the metal sample (ms) in Data Table 8.1 on page 76. 4. Carefully insert a thermometer into the metal shot, positioning it so the sensing end is in the middle of the shot, not touching the sides of the boiler cup. Carefully lower the boiler cup into the boiling water. Heat the metal shot until it is in the range of 90° to 95°C. Allow the sample to continue heating as you prepare the water and calorimeter cup (steps 5 and 6). 5. Acquire or make a calorimeter cup of two Styrofoam cups, one placed inside the other (see Figure 8.1) to increase the insulating ability of the cup. Measure and record the mass of the two cups. Add just enough water to the cup to cover the metal shot when it is added to the cup. This water should be cooler than room temperature (this is to balance possible heat loss by radiation). Measure and record the initial temperature of the water (Tiw) in Data Table 8.1. 6. Determine the mass of the cup with the water in it, then subtract the mass of the cup to find the mass of the cold water (mw). Record the mass of the cold water in Data Table 8.1. 7. Measure and record the temperature of the metal shot. Record the initial temperature of the sample (Tis) in Data Table 8.1. 8. Pour the metal shot into the the water in the Styrofoam calorimeter cup. Stir and measure the temperature of the mixture until the temperature stabilizes. Record this stabilized temperature and the final temperature for the water (Tfw) and the final temperature for the metal sample (Tfs). Calculate the specific heat (cs) of the metal sample. Note that ∆Tw is obtained from |Tfw – Tiw| and ∆Ts is obtained from |Tfs – Tis|. 9. Repeat the above steps for sample 2, recording all measurement data in Data Table 8.2 on page 77. Repeat the procedure for sample 3, recording all measurement data in Data Table 8.3 on page 78. Run a second trial on all three samples, comparing the results of both trials on each sample. Compare the calculations from the two trials on each sample to decide if a third trial is needed. Results 1. Calculate the specific heat (cs) for each sample. Show all work here and record your result in each data table. 2. Using the accepted value for each sample, calculate the percentage error here and record it in each data table. 3. Discuss and evaluate the magnitude of various sources of error in this experiment. ✓ Temperature measurements. ✓ Transferring water with the sample. 4. What would happen to the calculated specific heat if some boiling water were to slosh into the cup with the metal? The specific heat would be larger than the actual value. 5. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should show thoughtful analysis and careful, thorough thinking.) (The student should get a feel of what specific heat is, and what it means to have a large/small specific heat.) Data Table 8.1 Specific Heat of ___ Lead _____________________ ___ Trial 1 Trial 2 Mass of sample (ms) 500 g _____________ 480 g _____________ Initial temperature of cold water (Tiw) 14.0°C _____________ 13°C _____________ Mass of cold water (mw) 185g _____________ 190 g _____________ Initial temperature of metal sample (T )is 94.0°C _____________ 95.0°C _____________ Final temperature of metal sample (T )fs 20.6°C _____________ 19.3°C _____________ Final temperature of water (Tfw) 206°C _____________ 19.3°C _____________ Calculated specific heat (cs) 0.033 cal/gC° _____________ 0.033 cal/gC° _____________ Accepted value 0.032 cal/gC° _____________ 0.032 cal/gC° _____________ Percent error _____________ 3.1% _____________ Data Table 8.2 Specific Heat of ___ Aluminum _____________________ ___ Trial 1 Trial 2 Mass of sample (ms) 520 g _____________ 550 g _____________ Initial temperature of cold water (Tiw) 17.1°C _____________ 16.9°C _____________ Mass of cold water (mw) 180 g _____________ 190 g _____________ Initial temperature of metal sample (T )is 96.2°C _____________ 97.3°C _____________ Final temperature of metal sample (T )fs 47.5°C _____________ 48.0°C _____________ Final temperature of water (Tfw) 47.5°C _____________ 48.0°C _____________ Calculated specific heat (cs) 0.216 cal/gC° _____________ 0.218 cal/gC° _____________ Accepted value 0.217 cal/gC° _____________ 0.217 cal/gC° _____________ Percent error 0.5% _____________ 0.5% _____________ Data Table 8.3 Specific Heat of ___ Copper _____________________ ___ Trial 1 Trial 2 Mass of sample (ms) 460 g _____________ 480 g _____________ Initial temperature of cold water (Tiw) 15.3°C _____________ 16.1°C _____________ Mass of cold water (mw) 182g _____________ 193 g _____________ Initial temperature of metal sample (T )is 96.7°C _____________ 98.1°C _____________ Final temperature of metal sample (T )fs 31.1°C _____________ 32.0°C _____________ Final temperature of water (Tfw) 31.1°C _____________ 32.0°C _____________ Calculated specific heat (cs) 0.095 cal/gC° _____________ 0.097 cal/gC° _____________ Accepted value 0.093 cal/gC° _____________ 0.093 cal/gC° _____________ Percent error 2.2% _____________ 4.3% _____________ Name____________________________________________________Section________________Date___________ Experiment 9: Speed of Sound in Air Invitation to Inquiry 1. For any sound there is a relationship between v, f, and λ. For any sound produced in a closed air column there is also a relationship between the temperature, λ and the length of the shortest air column at which resonance occurs. Therefore, it should be possible to calibrate a closed air column, making marks on the side of the tube so you can use it as a thermometer. How can you make a sound-resonance thermometer that will show the present temperature? 2. Wash your hands thoroughly with soap and water and dry, paying particular attention tocleaning and drying the forefinger of your writing hand. Dip your clean forefinger in a half-filled, thin walled water glass. Slowly run your forefinger around the top of the rim of the glass. You might need to dry your finger, then start over several times, but eventually if you keep after it a faint, somewhat shrill continuous ringing note will be produced. Your clean, wet finger makes many minute catches on the glass rim as you move it round and round. The ringing note comes from the many tiny catches of your finger. All the tiny forces from your moving finger cause the glass to vibrate, and the vibrating glass produces the continuous note. The pitch of the note will depend on the glass used and the amount of water in the glass. The vibration can be seen clearly on the water surface as they establish circular standing waves. 3. The ringing, rubbed water glass described above can be used to study resonance. First,obtain two similar thin-walled glasses. The two glasses should make the same note when tapped. If they do not make the same pitched notes, add water to one until they do. Place the two wateradjusted glasses side by side, about 3 cm apart. Rub your freshly washed finger slowly around the rim of one of the glasses, being careful not to disturb the other. Observe the second (unrubbed) glass as the humming note is produced from the first glass. The second glass should start to vibrate with the first. Experiment with water levels, different distances between the two glasses, and other variables that might influence the resonance condition. Report your finding of the optimum condition for resonance. Background A vibrating tuning fork sends a series of condensations and rarefactions through the air. When the tuning fork is held over a glass tube that is closed at the bottom, the condensations and rarefactions are reflected from the bottom. At certain lengths of the tube, the reflected condensations and rare factions are in phase with those being sent out by the tuning fork and an increase of amplitude occurs from the resonant condition. Figure 9.1 shows a wave trace representing one wavelength in which the reflected wave is in phase with the incoming wave, forming a standing wave. The antinodes represent places of maximum vibration and increased amplitude. Incoming wave + Reflected wave = Standing wave Node Antinode Node Antinode Node Figure 9.1 Resonance occurs when the length of the tube is such that an antinode (the place of maximum vibration) occurs at the open end. As you can see from the sketch above, there are two situations when this would occur for tube lengths less than one wavelength, 1/4 of the way up and 3/4 of the way up from the bottom. Thus resonance occurs when the length of the tube (L) is equal to 1/4 λ, 3/4 λ, 5/4 λ, and so forth where λ is the wavelength of the sound wave produced by the tuning fork. In this experiment, a vibrating tuning fork is held just above a cylinder that is open at one end. The length to the closed end is adjusted by adding or removing water. The lowest frequency (the fundamental frequency) occurs when the longest wavelength has an antinode at the open end, so the length of the open tube is about 1/4 of the wavelength of the fundamental frequency as shown in Figure 9.2. Since the length of the tube at this fundamental frequency is L = 1/4 λ, then the fundamental wavelength must be λ = 4L. Using the wave equation vT = f λ and substituting the known frequency of the tuning fork for f and the experimentally determined value for the wavelength λ, you can calculate the speed of sound vT in the tube at room temperature by using the relationship vT = v0°C + 0.6°m sC / (Troom) where v0˚C is the speed of sound at 0˚C (331.4 m/s) and Troom is the present room temperature in ˚C. Procedure 1. The water level in the glass tube is adjusted by raising and lowering the supply tank. Adjust thetank so the glass tube is nearly full of water. 2. Strike the tuning fork with a rubber hammer and hold the vibrating tines just above the opening of the tube. 3. Lower the water level slowly while listening for the increase in the intensity of the sound that comes with resonance. Experiment with the entire length of the tube, seeing how many different places of resonance you can identify. 4. Using the information learned in procedure step 3, go to the resonance level immediately below the resonance position of the highest water level as shown in Figure 9.2. (Make sure there is not another resonance point between the highest water level and this second level.) Slightly raise and lower the water level until you are sure that you have found the maximum intensity. Note the relationship between the wavelength and the length of the tube as shown in Figure 9.2. Measure and record in Data Table 9.1 on page 84 the length of this resonating air column to the nearest millimeter. Change the water level and run two more trials, again locating the distance with the maximum sound. Record these two lengths in Data Table 9.1 and average the length for the three trials. Record the frequency of the tuning fork (usually stamped on the handle) and the room temperature. Figure 9.2 5. Repeat procedure steps 1 through 4 for the second resonance point at the highest water level, with an air column about one-third the length of the first as shown in Figure 9.3. (Again, make sure there is not another resonance point between the highest water level and this second level.) Note the relationship between the wavelength and the length of the tube as shown in Figure 9.3. Run three trials at this position and record the data in Data Table 9.2 on page 84 and, as before, average the three trials. Record the frequency of the tuning fork and the room temperature (do not assume that the room temperature remains constant). 6. Repeat the entire procedure using a different tuning fork with a different frequency. Record all data in Data Tables 9.3 and 9.4 on page 85. Figure 9.3 Results 1. Calculate the velocity of sound at room temperature for both tuning forks at both resonance positions and record in data tables at the measured room temperatures. Write the average values for both tuning forks here: frequency 1: vave = 338.5 m/s frequency 2: vave = 342.6 m/s 2. Using the accepted value of sound in dry air at the measured room temperature, calculate the percentage error for both tuning forks [accepted value = 331.4 m/s + (0.6 m/s/˚C)(Troom)]. frequency 1 @ 20˚C: v = 331.4 m/s + (0.6 m/s/˚C)(20˚C) v = 343.3 m/s % error = × 100 = 1.4 % frequency 2 @ 21˚C: v = 331.4 m/s + (0.6 m/s/˚C)(21˚C) v = 344.0 m/s % error = × 100 = 0.4 % 3. Analyze and discuss the possible sources of error in this experiment. ✓ Measuring the length of the air column must measure to the bottom of the meniscus. ✓ Determining when you are actually at resonance. 4. Describe how you could do a similar experiment to find the frequency of a tuning fork with an unknown frequency. Calculate the wavelength the same way you have done it in this lab. Calculate v = 331.4 m/s + (0/6m/s/˚C)(T˚C), then f = v/λ. 5. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should show thoughtful analysis and careful, thorough thinking.) (The student should have an understanding of resonance. It would be helpful if the instructor would explain that sound waves are longitudinal and not transverse as suggested by the illustrations representing nodes and antinodes.) Data Table 9.1 Resonance in an Air Column: Lowest Position - Frequency 1 Trial 1 Trial 2 Trial 3 Average Length of resonating air column (m) 1.160 Room temperature (˚C) 19˚C 20˚C Calculated wavelength (m) ............................................................................ 1.157 Calculated velocity in air (m/s) ...................................................................... 340.3 Tuning fork frequency (Hz)............................................................................ 220 Data Table 9.2 Resonance in an Air Column: Next Higher Position - Frequency 1 Trial 1 Trial 2 Trial 3 Average Length of resonating air column (m) Room temperature (˚C) Calculated wavelength (m) ............................................................................ 1.531 Calculated velocity in air (m/s) ...................................................................... 336.7 Tuning fork frequency (Hz)........................................................................... 220 Name____________________________________________________Section________________Date___________ Experiment 10: Static Electricity Invitation to Inquiry 1. This inquiry experiment works best on a day with low humidity. Tie a string around the lipof a small glass test tube. Try rubbing two tubes with different kinds of cloth, as you then allow the tubes to hang freely near each other and observe any interactions. 2. Try rubbing a hard plastic comb with fur or flannel for several minutes. Bring the combnear a hanging test tube that has been rubbed with cloth and observe any interactions. 3. Try rubbing two combs with fur or flannel for several minutes. Bring one comb near ahanging comb that has been rubbed with fur or flannel and observe any interactions. 4. Extend your investigation to other materials or objects if you wish. Explain the meaning ofwhat you find in your experiments with the test tube, combs, and other materials. Background Charges of static electricity are produced when two dissimilar materials are rubbed together. Often the charges are small or leak away rapidly, especially in humid air, but they can lead to annoying electrical shocks when the air is dry. The charge is produced because electrons are moved by friction and this can result in a material acquiring an excess of electrons and becoming a negatively charged body. The material losing electrons now has a deficiency of electrons and is a positively charged body. All electric static charges result from such gains or losses of electrons. Once charged by friction, objects soon return to the neutral state by the movement of electrons. This happens more quickly in humid air because water vapor assists with the movement of electrons from charged objects. In this experiment you will study the behavior of static electricity, hopefully on a day of low humidity. Procedure Part A: Attraction and Repulsion 1. Rub a glass rod briskly for several minutes with a piece of nylon or silk. Suspend the rod from a thread tied to a wooden meterstick as shown in Figure 10.1. Rub a second glass rod briskly for several minutes with nylon or silk. Bring it near the suspended rod and record your observations in Data Table 10.1 on page 91. (If nothing is observed to happen, repeat the procedure and rub both rods briskly for twice the time.) 2. Repeat the procedure with a hard rubber rod that has been briskly rubbed with wool or fur. Bring a second hard rubber rod that has also been rubbed with wool or fur near the suspended rubber rod. Record your observations as in procedure step 1. Figure 10.1 3. Again rub the hard rubber rod briskly with wool or fur and suspend it. This time briskly rub a glass rod with nylon or silk and bring the glass rod near the suspended rubber rod. Record your observations. 4. Briskly rub a glass rod with nylon or silk and bring it near, but not touching, the terminal of an electroscope (Figure 10.2). Record your observations. Figure 10.2 l 5. Repeat procedure step 4 with a hard rubber rod rubbed with wool or fur, again not touching the electroscope terminal. Record your observations. Part B: Charging by Induction 1. Inflate two rubber balloons and tie the ends. Attach threads to each balloon and hang them next to each other from a support. Rub both balloons with fur or wool and allow them to hang freely. Record your observations in Data Table 10.2 on page 92. 2. Bring a hard rubber rod that has been rubbed with wool or fur near the rubbed balloons. Record your observations. 3. Bring a glass rod that has been rubbed with nylon or silk near the rubbed balloons. Record your observations. 4. Detach one of the balloons by breaking or cutting the thread. Rub the balloon with fur or wool for several minutes. Hold the balloon against a wall and slowly release it. Record your observations. 5. Move the rubbed balloon near an electroscope and record your observations. 6. Move an electroscope near the wall where the balloon was held. Record your observations. Part C: Determining the Sign of a Charge 1. When a rubbed hard rubber rod is brought near the terminal of an electroscope, the leaves will stand apart but fall back together when the rod is removed. 2. When a rubbed hard rubber rod touches the terminal of an electroscope, the leaves stand apart as before. When the rod is removed this time, the leaves remain apart. 3. When the charged rod was brought near the terminal a charge was induced by the reorientation of charges in the terminal and leaves. When the rod was removed, the charges returned to their original orientation and the leaves collapsed because no net charge remained on the electroscope. 4. When the electrode was touched, charge was transferred to (or from) the electroscope and removing the rod had no effect on removing the charge. Touching the terminal with your finger returns the electroscope to a neutral condition. 5. An electroscope may be used to determine the sign of a charged object. First, charge the electroscope by induction as in procedure step 3 above. While the charged rod is near the terminal, touch the opposite side of the terminal with a finger of your free hand. Electrons will be repelled and conducted away through your finger. Remove your finger from the terminal, then move the rubber rod from near the electroscope. The electroscope leaves now have a net positive charge. If a charged object is brought near the electroscope the leaves will spread farther apart if the object has a positive charge. If the charged object has a negative charge, electrons are repelled into the leaves and they will move together as they are neutralized. 6. The process of an object gaining an excess of electrons or losing electrons through friction is complicated and not fully understood theoretically. It is possible experimentally, however, to make a list of materials according to their ability to lose or gain electrons. Gather various materials such as polyethylene film, rubber, wood, cotton, silk, nylon, fur, wool, glass, and plastic. Give an electroscope a positive charge by induction as described in procedure step 5. Rub combinations of the materials together and determine if the charge on each material is positive or negative. Record your findings. Results 1. Describe two different ways that electrical charge can be produced by friction. 1. An object gains an excess of electrons. 2. An object loses electrons. 2. Describe how you can determine the sign of a charged object. What assumption must be made using this procedure? Bring a charged object near a charged electroscope and observe what happens to the leaves. If they close, the object has the opposite charge as the electroscope. If they open further, the object has the same charge as the electroscope. Assumption: that you know the charge on the electroscope. 3. Move a hard rubber rod that has been rubbed with wool or fur near a very thin, steady stream of water from a faucet. Describe, then explain your observations. The stream of water will be attracted toward the rod. This is due to the polar nature of the water molecule. 4. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should be reasonable and make sense, showing thoughtful analysis and careful, thorough thinking.) (Students should have an overall feeling about charge. They should be able to define induction.) Name____________________________________________________Section________________Date___________ Experiment 11: Ohm’s Law Invitation to Inquiry The carbon resistors that are used as standard sources of resistance in electrical circuits are marked with a code of colored bands. Here is the code for the colors: Black = 0 Green = 5 Brown = 1 Blue = 6 Red = 2 Violet = 7 Orange = 3 Gray = 8 Yellow = 4 White = 9 The value of the resistor is AB × 10C ±D where no D band means ±20%, silver means ±10%, and gold means ±5%. The band placement is shown above. As an example, consider bands of red, yellow, red, and silver on a resistor. This means 24 × 102 ±10% ohms, or 2400 ±240 Ω. Obtain 5 or 6 resistors and a meter to measure the experimental resistance of each. Read the code to determine the accepted value, then find the experimental error as described in the Appendix. What could account for experimental errors, if any? Background An electric charge has an electric field surrounding it, and work must be done to move a likecharged particle into this field since like charges repel. The electrical potential energy is changed just as gravitational potential energy is changed by moving a mass in the earth’s gravitational field. A charged particle moved into the field of a like-charged particle has potential energy in the same way that a compressed spring has potential energy. In electrical matters the potential difference that is created by doing work to move a certain charge creates electrical potential. A measure of the electrical potential difference between two points is the volt (V). A volt measure describes the potential difference between two places in an electric circuit. By analogy to pressure on water in a circuit of water pipes the potential difference is sometimes called an “electrical force” (emf). Also by analogy to water in a circuit of water pipes, there is a varying rate of flow at various pressures. An electric current (I) is the quantity of charge moving through a conductor in a unit of time. The unit defined for measuring this rate is the ampere (A), or the amp for short. The rate of water flow in a pipe is directly proportional to the water pressure; e.g., a greater pressure produces a greater flow. In an electric circuit the current is directly proportional to the potential difference (V) between two points. Most materials, however, have a property of opposing or reducing a current, and this property is called electrical resistance (R). If a conductor offers a small resistance, less voltage would be required to push an amp of current through the circuit. On the other hand, a greater resistance requires more voltage to push the same amp of current through the circuit. Resistance (R) is therefore a ratio of the potential difference (V) between two points and the resulting current. This ratio is the unit of resistance and is called an ohm (Ω). Another way to show the relationship between the voltage, current, and resistance is R = V I or V = IR which is known as Ohm’s law. This is one of the three ways to show the relationship; this one (solved for V) happens to be the equation of a straight line with a slope R when V is on the y-axis, I is on the x-axis, and the y-intercept is zero. Procedure Part A: Known Resistance 1. A known resistance will be provided for use in this circuit: power A = ampmeter supply Figure 11.1 2. You will adjust the dc adjustable power supply as instructed by your laboratory instructor, obtaining six values for voltage and current using the supplied resistor. Set up the circuit with the power off and do not proceed until the laboratory instructor has checked the circuit. 3. Record the value of the resistor and the six values for the current and voltage in Data Table 11.1 on page 97. Part B: Unknown Resistance Repeat procedure A with an unknown resistor. Record your data in Data Table 11.2. Results 1. Make a graph of the six data points of Data Table 11.1, placing the current on the x-axis and the voltage on the y-axis. Calculate the slope and write it here and somewhere on the graph. Slope = 60.4 Ω 2. Compare the calculated value of the known resistor with the accepted value as given by your instructor. Calculate the percentage error. Known value = 60.4 Ω 0.7% error 3. Make a second graph, this time of the six data points on Data Table 11.2, again placing the current on the x-axis and the voltage on the y-axis. Calculate the slope and write it here and somewhere on the graph. Slope = 40.0 Ω 4. What is the value of the unknown resistor? 40.0 Ω 5. Explain how the two graphs demonstrate Ohm’s law. Ohm’s law states that there is a direct relationship between the voltage drop across the resistor and the current flowing through that resistor. This is illustrated by the linear graphs. 6. Was the purpose of this lab accomplished? Why or why not? (Your answer to this question should show thoughtful analysis and careful, thorough thinking.) Students should mention that the linearity of the graphs strongly support Ohm’s law. Going Further 1. Check your answer about the value of the unknown resistor by using your calculated value in the equation of a straight line when V = 2 V, 4 V, and 6 V. Verify with the laboratory equipment and calculate the average percentage error. Describe your results here: Measure the current in the circuit for each value of V and compare with the value predicted by Ohm’s law. Average %error should be 5-10%. From Ohm’s law: V = (336 Ω) Thus when V = 2V, I = 0.006A when V = 4V, I = 0.012A when V = 6V, I = 0.018A 2. Use three different resistances (e.g., 16Ω, 30 Ω, and 47 Ω) connected in a series for four different input voltages (2 V, 4 V, 6 V, and 8 V) and connected in a parallel circuit. Plot voltage vs. total current for both the series and parallel circuits and quantitatively show how the total resistance (the slope) differs for series and parallel circuits. Resistance for the parallel circuit is considerably smaller than the resistance of the series circuit. Data Table 11.1 Voltage and Current Relationships with Known Resistance Trial Voltage (V) Current (A) 1 _________________ 0.017 A _________________ 2 _________________ 0.035 A _________________ 3 _________________ 0.035 A _________________ 4 6.0 V _________________ 0.068 A _________________ 5 _________________ 0.132 A _________________ 6 _________________ 0.172 A _________________ 60.0 Resistor ____________________Ω Data Table 11.2 Voltage and Current Relationships With Unknown Resistance Trial Voltage (V) Current (A) 1 _________________1.0 V _________________0.026 2 _________________2.0 V _________________0.048 3 _________________4.0 V _________________0.101 4 _________________6.0 V _________________0.149 5 _________________8.0 V _________________0.203 6 _________________10.0 V _________________0.248 Resistor ____________________Unknown Ω Solution Manual Experiment for Integrated Science Bill W. Tillery, Eldon D. Enger , Frederick C. Ross 9780073512259

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