13. INVESTIGATIONS

13.1. General lab report structure

 

Nr(#) of investigation: Title of investigation

 

Name: (Sarah Student)

Team : (S.Student, I.Investigator, P.Physicist)

Date(s): (when the investigation was done, not when the report was written)

 

1. AIMS

 

1.1. Identify a focused problem or research question. You may repeat the general aim given by the teacher, but try to express it in your own words, and be more specific.

1.2. Formulate a preferably quantitative hypothesis or prediction, relate it to the problem or research question, and explain what it means.

1.3. Select the relevant variables (usually physical quantities. These are things which affect the result). Some are controlled (kept the same), others varied intentionally.

 

2. METHODS AND TOOLS

 

2.1. What apparatus or other (e.g. software) tools did you select, and why is it appropriate in this investigation?

2.2. How did you control the variables which need to be controlled (make sure they do not vary and thereby distort the results)?

2.3. What did you do to collect sufficient relevant data? (A general explanation of what was done).

 

3. DATA  COLLECTION

 

3.1. What raw data, qualitative or quantitative (including units), were recorded (Often a table of measurement values is suitable here)?  Include and/or discuss the uncertainties that are relevant.

3.2. Present the raw data clearly so that it is easy to interpret (e.g. graph or average of values in 3.1).

 

4. DATA PROCESSING AND PRESENTATION

 

4.1. Process the data (calculations, graphical analyses, other)

4.2. Present the processed data and where relevant, take errors and uncertainties into account.

 

5. CONCLUSION AND EVALUATION

 

5.1. What conclusion(s)  can you draw from the results and reasonable interpretations of them? Compare the result to literature data (if relevant) and any prediction or hypothesis you made.

5.2. Evaluate the procedure(s) (the methods to do things) and results (the collected data or things calculated based on them).

5.3. Identify weaknesses in the procedure(s) and suggest improvements. The improvements should not be too simplistic, or unrealistic.

 

APPENDICES may be added if necessary. Number them and refer to them in the report text with this number.

 

13.2. Model report I

 

Investigation 1: The Density of an Alcohol Solution

 

Name: Sarah Student

Team: S. Student, I.Investigator, P.Physicist

Date: 24.12.2005

 

Note: This is a model report which is not perfect, but should give an idea of what type of work is expected in the IB physics program.

 

 

 

 

1. AIMS

 

1.1. Research question

 

We decided to experimentally determine the density of a given ca 50 % alcohol solution. The density (d) is defined as the relation between its mass (m) and volume (V).

 

1.2 Hypothesis

 

We know from MSDS or PCHB tables (a data booklet) that the density of water is 1000 kgm-3 = 1 gcm-3 and that of alcohol about 800 kgm-3 = 0.8 gcm-3. We therefore make the hypothesis that the density of the given 50% solution will be about 900 kgm-3.

 

1.3. Variables

 

The variables we need to measure are the mass and volume of the given liquid. The temperature could also affect the result since liquids tend to expand in volume when it gets warmer.

 

2. METHODS AND TOOLS

 

2.1. Apparatus

 

To find the volume of the liquid we used five 100 ml graduated measuring cylinders (see picture in appendix 1) and to find the mass we used an electronic scale. We also used a thermometer to check the temperature in the room (see 2.2.) in case comparing our results to values found by other students would be needed.

 

2.2. Control of variables

 

To make sure everything had the same temperature we placed the measuring cylinders and the given flask of liquid in the room where we would do the experiment the day before, and closed the curtains so the sun would not shine on them. We made sure that the cylinders would be totally empty when the experiment was done by cleaning them with acetone the day before (the small amounts of acetone we assumed would evaporate during the night).

 

 

 

 

2.3. The method used

 

We put the empty cylinders on the electronic scale which was then zeroed, and then poured 50 ml of the solution into each of them and weighed them. The results are found in the tables in section 3.1.

 

3. DATA COLLECTION

 

3.1. Measurements and observations

 

Table 3.1.A. Mass measurements

Cylinder nr                           Mass of 50 ml liquid (g)

1                                          44.03

2                                          45.12

3                                          45.20

4                                          44.97

5                                          44.67

 

The average mass was 44.798 g of the residuals, which is the difference between a measurement value and the average of them, are given in table 3.1.B:

 

Table 3.1.B. Residuals

Cylinder nr                           Mass residual (g)

1                                          (-) 0.768

2                                          0.322

3                                          0.402

4                                          0.172

5                                          (-) 0.128

 

The maximum residual, 0.768g for cylinder nr 1 was taken to be the absolute uncertainty in the mass, Dm. The absolute uncertainty in the volume, DV, was estimated to be 1 ml. Using half the limit of reading would have given an uncertainty of 0.5 ml, but the liquid surface was not quite horizontal, so we made this estimation. The temperature in the room was ca 21 oC, with an uncertainty of ± 1oC.

 

3.2. Presentation of the measurement results

 

The volume V = 50 ml ± 1 ml and the mass m = 44.798g ± 0.768g. This value is not approximated here since it will be used for calculating the uncertainty in density in section 4.1.

 

4. DATA PROCESSING AND PRESENTATION

 

4.2. Data processing

 

Some processing of the raw data to find the uncertainties in the key variables was done in section 3.2. above. Using the formula for the density we get

 

d = m / V = 44.798 g/ 50 ml = 0.89596 g/ml = 0.89596 gcm-3.

 

The relative uncertainties are for mass Dm/m = 0.768g /44.798g = 0.0171436 (» 1.7 %) and for volume DV/V = 1 ml/50ml = 0.02 (=2%). The relative uncertainty in the density, Dd/d =  Dm/m + DV/V = 0.0171436 + 0.02  = 0.0371436 ( » 3.7 %). From this follows that

 

Dd =  0.0371436 * 0.89596 gcm-3 = 0.0332791 gcm-3  » 0.03 gcm-3

 

4.3. Presentation of processed data.

 

The result we get is that the density of the given liquid d = 0.86 gcm-3 ±  0.03 gcm-3  which in SI units gives d = 860 kgm-3 ±  30 kgm-3 .

 

5. CONCLUSION AND EVALUATION

 

5.1. Conclusions.

 

There are no given literature values for the density of a 50% solution of alcohol, but the value is, depending on temperature, very close to  1000 kgm-3  for pure water and 790 kgm-3 for pure ethanol. The average of these is 895 kgm-3 which means that the value 860 kgm-3 we reached appears to be a bit too low, if we compare the result we get to our original hypothesis in section 1.3.

 

Note: When dissolving alcohol into water, the volumes will not simply be added;  50 ml water + 50 ml alcohol gives only ca 95 ml solution. This is an example of a complication a student doing an investigation may not be aware of.

 

5.2. Evaluation of the procedures and results.

 

The electronic scale could give mass values with a precision of 0.001 g, but our Dm was much higher than that. It seemed difficult to pour exactly 50 ml of the liquid into the cylinder, and the method for using a precise volume could be improved. The volume of liquid used will also affect the mass measurements.

 

5.3. Suggested improvements.

 

The same investigation could have been done with a cheaper scale with a 0.01g precision without significantly changing the outcome. We could use some volumetric flasks and a pipette to measure up the chosen volume with a smaller uncertainty.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13.3. Model report II

 

Investigation 2 : The relation between mass and time period for a spring

 

Name: Sarah Student

Team: S. Student, I. Investigator, P.Physicist

Date: 1.4.2003

1. AIMS

 

1.1. Research question

 

We decided to experimentally find the relation between the time period T (meaning the time to complete an oscillation, from one extreme to the back and forth) and the mass m attached to a given metal spiral spring.

 

1.2 Hypothesis

 

While planning this lab we had access to the spring and various common lab equipment and we played a little with it. It seemed that the heavier the object on the spring was, the slower it should bounce up and down. We therefore make the hypothesis that T will be proportional to m; or with a formula: T = km. Note that k here is not the spring constant but just a constant we define for now.

 

1.3. Variables

 

The variables we need to measure are the time period T and the mass m attached to the spring. We are not sure if it makes any difference how far we stretch the spring before releasing it.

 

2. METHODS AND TOOLS

 

2.1. Apparatus

 

To find the time period we used a digital stopwatch and to find the mass we used an electronic scale. We used a ruler to measure the initial extension of the spring.

 

2.2. Control of variables

 

In case the initial extension of the spring would make a difference, we used the same extension in all measurements. We were able to take all measurements at one time, but we marked the spring with a small piece of paper with our names taped to it in case we would have had to repeat any measurements since there were many springs that looked the same and we do not know if that means they are all the same. Some may have been used too many times and behave differently from a new spring.

 

2.3. The method used

 

We attached a chosen mass to the spring and secured it with a small piece of tape, stretched it  3 cm and released it. The stopwatch was started when the equilibrium was passed and the time for three full oscillations were taken. Here one full oscillation means the time from start to the upper extreme, down to the lower extreme, and back to a situation where the mass passes the equilibrium position going upwards. We would have liked to taken the time for 5 or 10 oscillations but something (maybe friction or air resistance) damped them very quickly.

 

This was then repeated 5 times for every mass, and 5 different masses were used (one to five 50g metal weights with hooks were placed together on the hook at the end of the spring). The results are given in tables 3.1.A. to 3.1.E in section 3.1. below.

 

3. DATA COLLECTION

 

3.1. Measurements and observations

 

The quick damping of the oscillations is an observation already mentioned in 2.3. The masses used were weighed on an electronic scale with the uncertainty Dm = 0.5 g (half the limit of reading, 1g).

 

Table 3.1.A.: mA = 49g±0.5g

 

Measurement nr                 3T (s)             T(s)                Residual(s)

1                                          0.94               0.313             0.002

2                                          0.92               0.307             (-)0.004

3                                          0.91               0.303             (-)0.008 » 0.01

4                                          0.95               0.317             0.006

5                                          0.94               0.313             0.002

 

Average T = 0.311 s

 

Table 3.1.B.: mB = 100g±0.5g

 

Measurement nr                 3T (s)             T(s)                Residual(s)

6                                          1.33               0.443             (-)0.003

7                                          1.36               0.453             0.007

8                                          1.35               0.450             0.004

9                                          1.71??           -                    -

10                                        1.31               0.437             0.009 » 0.01

 

Average T = 0.446 s

 

Here we note that measurement nr 9 gives an exceptional value, which is excluded from the statistics as a probable outlier.

 

Table 3.1.C.: mC = 152g±0.5g

 

Measurement nr                 3T (s)             T(s)                Residual(s)

11                                        1.63               0.543             (-)0.006

12                                        1.67               0.557             0.008

13                                        1.70               0.567             0.018 » 0.02

14                                        1.61               0.537             0.012            

15                                        1.62               0.540             0.009

 

Average T = 0.549 s

 

 

 

Table 3.1.D.: mD = 199g±0.5g

 

Measurement nr                 3T (s)             T(s)                Residual(s)

16                                        1.88               0.627             (-)0.010

17                                        1.95               0.650             0.013

18                                        1.97               0.657             0.020 = 0.02

19                                        1.86               0.620             (-)0.017

20                                        1.90               0.633             0.006

 

Average T = 0.637 s

 

Table 3.1.E.: mE = 252g±0.5g

 

Measurement nr                 3T (s)             T(s)                Residual(s)

21                                        2.10               0.700             (-)0.009

22                                        2.19               0.730             0.021

23                                        2.00               0.667             (-)0.042 » 0.04

24                                        2.17               0.723             0.014

25                                        2.18               0.727             0.018

 

Average T = 0.709 s

 

The residual, that is the difference between a measurement value and the average of them, are given in table 3.1.F where the largest residual, approximated to one significant digit and estimating the minimum uncertainty under any circumstances to be 0.01s,  for each of the masses mA to mE are used as the absolute uncertainties DmA to DmE . The average times for one oscillation for the five masses are approximated accordingly.

 

Table 3.1.F.

 

m(g)              Tav(s)             Dm(g)            DTav( (s)

49                        0.31               0.5                 0.01

100                0.45               0.5                 0.01

152                0.55               0.5                 0.02

199                0.64               0.5                 0.02

252                0.71               0.5                 0.04

 

3.2. Presentation of the measurement results

 

To present the measurement results, with their uncertainties, we plot Tav as a function of m (including error bars in both dimensions and units on the axes added) in graph 3.2.A below,:

 

 

 

Graph 3.2.A: Average oscillation time in seconds as a function of oscillator mass in grams.

 

4. DATA PROCESSING AND PRESENTATION

 

4.1. Data processing

 

If the graph had been clearly linear, the students could have moved on to find the proportionality constant they called k in section 2.2.. or alternatively just verbally stated that an inspection of the graph shows that it depicts a linear relation, since the research question strictly speaking is just to find the type of the dependency, not to determine a specific value

 

We notice from the graph 3.2.A that the data does not seem to form a straight line but some type of bent curve. Especially a line from the origin to the first data point would not go through the rest of them. We then tried to "linearize" the graph by plotting some function of the variable T on the horizontal axis. To make these graphs linear, we will first calculate the values needed to plot T2 and T½ with their error bars.

 

For the T2 plot, the values of Tav in table 3.2.F are squared and entered into the second column of table 4.2.A below. To find the uncertainty in T2 we use the formula (adapted from the IB data booklet)

 

D(T2)/T2 = DT/T + DT/T = 2DT/T and then D(T2) = 2T2DT/T = 2T*DT

 

Example of one calculation: For the mass mA = 49 g, the absolute error is as before half the limit of the reading or 0.5 g. For the average time of one oscillation we use T = 0.311s±0.01s (see table 3.1.F). This gives T2 = (0.31s)2 = 0.0961 s2. The error in this = D(T2) = 2T*DT = 2*0.31s*0.01s = 0.0062s2 » 0.006 s2. Thus we have T2 = 0.096 s2 ± 0.006 s2 which is the first entry in table 4.2.A. below. The others in that table are calculated in a corresponding way.

 

Table 4.2.A

 

m(g)              Tav2(s2)           Dm(g)            DTav2(s2)

49                  0.096             0.5                 0.006

100                0.203             0.5                 0.009

152                0.30               0.5                 0.02

199                0.41               0.5                 0.03

252                0.50               0.5                 0.06

 

 

 

4.2. Presentation of processed data.

 

The values calculated in section 4.2. are presented in the following graph (error bars in both dimensions and units on the axes added by hand).

 

Graph 4.2.A: The square of the average time for one oscillation as a function of mass.

 

This appears to be a linear graph with the approximate gradient 0.50s2 / 250g = 0.50s2 / 0.25 kg = 2.0 s2kg-1.

 

5. CONCLUSION AND EVALUATION

 

5.1. Conclusions.

 

It seems that the hypothesis of a linear dependency of the form T = km turned out to be wrong. The data would rather suggest a formula of the type T2 = km with k = 2.0 in SI-units. In the literature (reference: ......) we have found that the formula should be:

 

T = 2pÖ(m/k) => T2 = (4p2/k)m

 

where the k represents the spring constant. An investigation of the spring constant of the spring used could give more information about whether or not our k-value is in accordance with this.

 

5.2. Evaluation of the procedures and results.

 

While taking the measurements we found that it was difficult to say exactly when the mass oscillating on the spring was passing its equilibrium - a place where more accurate time values can be obtained than at the points of extreme displacement.

 

5.3. Suggested improvements.

 

To address the problem mentioned in section 5.2. we suggest that the equilibrium level should be indicated by a marker line on a paper directly behind the spring, or possibly with a laser trained at that level, adjusted so that the oscillating mass is hit by the laser spot when it is at the equilibrium.

 

 

 

 

 

13.4. List of investigations

 

Instructions for students    

 

Begin every investigation with a planning and brainstorming session in the group. You may also look for more information about the theoretical background of the investigations in the school library or on the net. If there is time left after completing the tasks given below, try to improve and develop the investigations, possibly into an idea for an Extended Essay!

1. Find the density of a given liquid using the same method as in the given model report. Study the report and discuss what could be improved in it.

2. Let a piece of chalk, a small ball or some other suitable object roll from rest along a somewhat inclined table or other surface. Find its acceleration from measurements of time and displacement Compare this to a value predicted from calculations based on the angle of inclination of the table and the gravity acceleration.

3. Produce a set of time-distance data points which describe a person walking in the corridor. Produce a spreadsheet which presents the measured time values (variable x), the measured distance values (variable yexp), and distance values calculated from the measured time values as ymodel = kx. Use absolute and relative cell references (the teacher or other group members will assist you if necessary). Let the spreadsheet produce a graph of yexp and ymodel as functions of x in the same diagram. Adjust k until the graphs coincide. What quantity does k represent in this model? What assumptions is the model based on?

4. Investigate a given spring using the same method as in the given model report. Study the report and discuss what could be improved.

5. Fill a 500 ml separation funnel with water, let the water flow out of it and investigate the following research questions:

I. How does the flow of water (e.g. in milliliter per second) vary with time?

II. How does the flow of water vary with the depth?

III. What type of motion - uniform, uniformly accelerated or other - is the vertical

       motion of the water surface as the water flows out?

Discuss in the group how to take measurements and how to process them in order to answer these questions.

6. Use the Empirical data-logging equipment (ultra-sound position detector) to study falling motion and find a value for g. The detector signal must be reflected from a flat surface (phone book, manual etc.)

7-I. Investigate a simple (or other) pendulum. This investigation will be assessed on all criteria.

8. To study falling motion where air resistance is significant, make an air-filled balloon (possibly with a very small weight attached to it). Plan an experiment to find out roughly after what falling distance it reaches its terminal velocity.

9. Investigate projectile motion using a rubber band. Produce a graph of range as a function of the angle to the horizon of the initial velocity (which angle gives the maximum range?). Search the literature in the school library for a theoretical analysis of projectile motion and try to produce a corresponding graph based on this. Compare and discuss the graphs.

10-II. Investigate static friction. This investigation will be assessed on all criteria.

11. A. Let a small car roll down a slope and onto the floor until it stops. Plan a and try out a way to find the coefficient of rolling friction specific to this car using measurements of time and distances assuming it follows a formula similar to the one for sliding or static friction. Repeat the experiment several times and for different masses/ and or initial positions for the car.

B. Let a small car roll down a slope and out onto the floor until it stops. Plan a way to determine the rolling friction coefficient. Repeat the experiment several times and for different masses/ and or initial positions for the car using only distance measurements. Combine this information with the result from Investigation 9 and discuss how well the results obtained with the different methods agree, taking into account relevant uncertainties.

12. Put a small object in a horizontal circular motion using a tube and a metal weight which provides the centripetal force. Calculate this force based on the experimentally determined speed of the small object and compare this value to the weight of the metal piece.

13. Find out from where a small metal ball must start to complete a loop in a given metal track (make a sketch of the given equipment) without falling out of it. Compare this to a value based on the radius of the loop.

14. Compare the cooling process of hot water in vessels covered with shiny metal foil and vessels covered with black paper. Replace with: 14. Find the specific heat capacity of ethanol assuming that the specific heat capacity of water is known. If there is time, try to find the specific heat capacity of water without using a "known" value for any substance.

15. Compare the rate of cooling per thickness and surface area for vessels made of different materials (metal, glass or ceramic, plastic, others). Replace with: 15. Find the efficiency of an electric heating plate when heating water in an open steel kettle. Assume that the specific heat capacity of water is known.

16. Heat two identical glass beakers, one filled with water and one with water mixed with potato flour. Measure the temperature as a function of time and suggest a mechanism to explain any differences.

17. Construct a spreadsheet which calculates and graphs a) the rate of cooling as a function of time b) the rate of cooling as a function of temperature given a set of time-temperature data points. Analyse the results of investigation 17 with it.

18. Search the Internet for instructions on how to build a psychrometer to measure relative air humidity. Discuss and test a hypothesis about how the results would differ if a different liquid than water is used (e.g. ethanol).

19. Plan and conduct an experiment to find the efficiency of a microwave oven (the efficiency in converting the energy in the microwaves as reported by the manufacturer to thermal energy in the heated food or drink, not the efficiency in converting electrical energy to energy in the waves)

20. Find the volume expansion coefficient of ethanol and/or water. The relevant formula is not required in the IB program, but given in the Handbook. Search the net or school library for a "known" value for it.

21. Use a laser and a transparent container to experimentally determine the refractive index of water and/or other liquids.

22. Simulate the interference between two "one-dimensional" wave motions in a spreadsheet using the equation for the displacement of an oscillator x(t) = Asin(2pft + phase shift). Investigate the "beat" phenomenon, what formula for the beat frequency is valid, whether and how it depends on the phase shift.

23. Determine the wavelength of a He-Ne-laser light using given diffraction gratings with known numbers of lines per mm or cm indicated on them. Search the Internet for information about the 'correct' value.

24-III. Investigate a DC circuit. This investigation will be assessed on all criteria. (Note: find a research question other than the internal resistance and emf of a battery, which will be done in investigation 25).

25. Determine the internal resistance and emf of one or more batteries graphically by connecting different resistors to them and measuring the current through and potential difference over the external resistor.

26. Construct different series and parallel circuits and investigate with a digital ohmmeter how the total (equivalent) resistance measured compares to a theoretical value. Also observe how the potential difference is distributed in the different circuits and try to express it verbally in a general law.(If time allows: investigate capacitors in the same way).

27. Investigate the qualitative and/or quantitative properties of  the magnetic field outside a current-carrying solenoid using a simple orienteering compass to "measure" the field intensity. Pay attention to which simplifying assumptions are necessary and can be justified.

28. Determine the magnetic field strength B between the poles of a U-shaped magnet using the torque on a current-carrying wire arranged so that the torque can be approximately found with the help of the deflection angle and the mass per unit length of the wire. Pay attention to the necessary simplifications and discuss if a more accurate value would be higher or lower than the one you get with this method.

29. Construct a simple transformer and investigate briefly its function, testing the formulas in the corresponding section in the textbook; then turn it into a metal detector by rotating one of the coils 90°. Investigate what minimum amount of metal it reacts to.

30. Search the available libraries and other sources for information about the history of the atomic model. Which parts of physics were relevant for supplying arguments for the atomic model? How did physics interact with other sciences (e.g. chemistry)? Why did some oppose the atomic model in the 19th century? What arguments for the atomic model would we today present to someone not believing in it?

31. Construct a spreadsheet that simulates a radioactive decay series where the nucleus X with the half-life Tx decays into Y which with the half-life Ty decays into Z, which is stable. Vary the half-lives and the initial amounts of the nuclei (Nx, Ny, Nz) and report any non-trivial phenomena the simulation reveals.

Two of the investigations 32-36 are to be completed.

32. Historical Physics: Choose a given time period (e.g. 1600-1700) and use libraries and the internet to produce a) an outline of the dominant physical theories at the beginning of that period b) a summary of the changes during the period. You may need to focus on some area(s) of physics (e.g. mechanics, electricity).

33. Biomedical Physics (A or B):

A. Determine where the center of gravity in humans is using a bathroom scale and a ca 2-3 m long plank. Put the plank horizontally with one end on the scale and the other on some supporting object (phonebook). The human is placed horizontally on the plank and conditions for mechanical equilibrium applied.

B. Measure the blood pressure with the blood pressure meter first at the heart level, then from the arm or leg keeping it at different levels. Investigate the difference in pressure and compare it to a theoretical value based on the formula for hydrostatic pressure (p = p0 + dgh).

34. Relativity : Find a relativistic version of Newton's II law by using the form F = dp/dt differentiating p = gm0v (the teacher will help you with the differentiation process if necessary). Then use this to construct an Excel spreadsheet to simulate the linear acceleration from rest of an object affected by a constant net force.

35. Astrophysics : Construct a simple quadrant to measure the altitude above the horizon of an astronomical object. Observe and sketch ca 20 stars visible to the naked eye in some area of the sky. Measure the altitude and approximate azimuth of some bright star in the selected 20 to facilitate identification of them with the Sky Map program. Also note the time and place for the observation. Identify the stars with Sky Map, take the visual magnitude value for them from the program and find the maximum magnitude visible. Compare the result for different locations (city, country) and find the limiting brightness value. 

36. Optics : Find experimentally the focal lengths of the given unknown curved lenses.