reports for general physics lab 106
GERMAN - JORDANIAN UNIVERSITY SCHOOL OF BASIC SCIENCE AND HUMANITIES REPORTS FOR GENERAL PHYSICS LAB Phys106 MECHANICS Experiment 1: Part B Measurements and Calculation of Errors Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( Partner’s Name: …………... Instructor: …………………. Date: ……………...... ) *Finding Density of a Cylinder Data Table Trial 1 Mass (g) Height (cm) Diameter (cm) Volume (cm3) Density(g/cm3) 2 ∆m = g ∆h= cm ∆D = cm Calculations 1. Calculate the error in the density (∆ρ) for each trial. ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… 2. Find the average value of the calculated densities and compare it with the standard value of stainless steel density ( = 7.7 g/cm3)? [find the percent difference] ……………………………………………………………………………………… ……………………………………………………………………………………… 3. Which quantity contributes more to the error in the density; the mass, the diameter or the height? Why? ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… 3 / 39 Experiment 2: Part A Velocity and Speed Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... * Velocity of a Motorized Cart (Motion Sensor) * DataStudio file: 06 Constant Velocity.ds Data Table Run 1 2 3 Slope Y-intercept Data Sketch in Fig. 2A.1 your graph of Position versus Time (for all the three trials, and label each one). Write the axis title and its units Questions 1. What does the y-intercept of each graph represent? 2. What physical quantity does the slope of each plot represent? 4 / 39 3. What are the units for the slope of each plot? 4. Write an equation for each plot on your graph using the form y = mx + b. Include numbers for the slope and y-intercept. Run 1 2 3 Equation (y = mx + b) 5. Knowing the physical quantities represented by the slope and Y-intercept, what variables could you put in your equation in place of ‘y’, ‘m’, ‘x’, and ‘b’ to make it more specific for the motion of the cart? y:…………….. m:…………….. x:…………….. b:…………….. 6. How long was the motorized cart moving during each data run? Run Time of Motion (s) (Graph) 1 2 3 7. Why is the time of motion different for each data run? 5 / 39 Experiment 2: Part B Linear Motion: Acceleration Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... Part 1: Constant Velocity and Constant Acceleration * DataStudio file: 07 Vel and Acc.ds Data Sketch in Fig. 2B.1 your graph of Position versus Time for the motion of the two carts. Write the axis title and its units. Questions: Cart Motion 1. Which cart was moving with constant velocity? What is the approximate velocity of this cart? 2. Is there a moment when each cart has travelled the same distance at the same time? When? 3. Examine the point on the graph where the two plots cross. Which cart was going faster at that moment? How can you tell? 6 / 39 Select the plot of data for the fan cart’s motion. Click the ‘Fit’ button in the Graph toolbar and select a curve fit that you think will match the plot of data. (If your selection is not a ‘good fit’ for your data, try another curve fit.) 4. Which curve fit is the best for your data? Interpret Graphs EXAMPLE 1: The following graph represents the motion of a cart. Write a description of the motion by answering the questions. 1. What happens during the first 3 seconds of motion? 2. What happens during the time interval between 3 and 5 seconds? 3. What happens after 5 seconds? How is the motion of the car after 5 seconds different from the motion during the first 3 seconds? EXAMPLE 2: 4. Find the speed of the cart at the moments: t=2s, and t=4s. 5. What is the cart doing in EXAMPLE2? 7 / 39 Part 2: Graph Position, Velocity, and Acceleration of a Fan Cart * DataStudio file: 08 Fan Cart.ds Data Sketch in Fig. 2B.2 your graph of Position, Velocity, and Acceleration versus Time for the motion of the fan cart. Write the axis title and its units. Questions 1. Consider the position versus time graph, describe the graph. 2. Consider the velocity versus time graph, describe the graph. How to Find the Acceleration from Position versus Time 1. Highlight a smooth part of the position graph. 2. Click the ‘Fit’ menu and select ‘Quadratic Fit’. The "A" is the coefficient of the squared term in the curve fit formula. Record the coefficient “A”. A = ___________ How to Find the Acceleration from Velocity versus Time 1. Highlight a smooth part of the velocity graph. 2. Click the ‘Fit’ menu and select ‘Linear Fit’. The "m" value is the slope. Record the slope as the acceleration. m = _________ 8 / 39 Compare the Acceleration Values Multiply the value of “A” number by "2" to get the acceleration based on position versus time. Record the value of 2 x "A". 2 x A = _____________ Compare this value to the slope (“m”) of the Linear Fit for the velocity versus time graph. (This is the acceleration based on velocity versus time.) Verification Compute the percent difference of your two values for acceleration. 9 / 39 Experiment 3: Part A Linear Motion with Constant Acceleration (g sinθ) Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... * DataStudio file: 10 g sin theta.ds Data Table Run Angle(degrees) Sin(theta) Acceleration (m/s2) 1 10 2 8 3 6 4 4 5 2 Data Sketch in Fig. 3A.1 your graph of data from the Acceleration Sensor for Acceleration versus sin θ for the cart in each data run and write the axis title and its units. Questions 1. Describe the acceleration versus sinθ plot of the Graph display. 2. Calculate the value of “g” using the acceleration of the cart. 10 / 39 3. What is the percent difference between your measured value for “g” and the accepted value for “g”? 11 / 39 Experiment 3: Part B Linear Motion, Free Falling Bodies Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... Part 1: Acceleration of a Freely Falling Ball * DataStudio file: 11 Falling Ball.ds Data Sketch in Fig. 3B.1 and Fig. 3B.2 your graph for position and velocity versus time, write the axis title and its units. Data Table ‘g’ (slope of velocity versus time) = ___________ Questions 1. How does your value for ‘g’ (slope of velocity versus time) compare to the accepted value of the acceleration of a free falling object (9.8 m/s2)? “Find the percent error” 2. What factors do you think may cause the experimental value to be different from the accepted value? 12 / 39 3. Mark on both Figures 3B.1 and 3B.2, the position versus time and the velocity versus time graphs, the point corresponding to the moment of the first rebound and the moment when the ball was at its maximum height after its first rebound. Part 2: Acceleration of a Freely Falling Picket Fence * DataStudio file: 12 Free Fall Fence.ds Questions 1. Find the slope of the velocity versus time from Fig. 3B.2. How does it compare to the accepted value of the acceleration of a free falling object (g = 9.8 m/s2)? “Find the percent error” 2. What factors do you think may cause the experimental value to be different from the accepted value? 3. Determine whether releasing the Picket Fence from just several centimeters above the Photogate makes any difference in the value of the acceleration. 13 / 39 Experiment 4: Projectile Motion Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... Part 1: Horizontal Launch * DataStudio file: 13A Projectile Motion 1.ds Data Table Range Initial Speed (m/s) Time of Flight (s) Short Middle Long Questions 1. How do the values for the time of flight for the short, middle, and long-range distances compare when the ball was launched horizontally? State your conclusion. 2. Measure the height of the starting point and use it to compute the time of flight. Height of the starting point = m 3. Compare the value you found in the previous question with the values in the table; [find the percentage error] 4. What is the reason behind the small differences in the time of flight values in the table. 14 / 39 Launching with Angle 30° * DataStudio file: 13B Projectile Motion 2.ds 1) Data Table Arrangement Initial Speed (m/s) Measured Time of Flight (s) Calculated Time of Flight (s) Percent Error Short range Mid range 2) Measure the range, the horizontal distance between the launching point and the landing point and record it. Arrangement Initial Speed (m/s) Measured Range (m) Calculated Range (m) Percent Error Short range Mid range Questions 1. Why would time of flight depend on the angle of launch? 2. Compute the time of flight for each range and compare it to the measured time by finding the percent difference. Record your values in the table. Write down, as an example, the calculation for the short range. 3. Why would range depend on the angle of launch? 4. Compute the range for each initial velocity and compare it to the measured range by finding the percent difference. Record your values in the table. Write down, as an example, the calculation for the short range. 15 / 39 5. If you want to change the angle of launch (only) but you want your projectile to land on the same point, what must be the new angle? Why? _______________________________________________________________________ 6. What are the quantities that differ between the cases when the angle was 30° and the new angle in question (5) above? 16 / 39 ** Graph papers are necessary for this experiment. Experiment 5 Newton’s Second Law Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( Partner’s Name: …………... Instructor: …………………. Date: ……………...... ) Part 1: Constant Mass, Changing Force * DataStudio file: 15A Newton’s 2nd Law 1.ds Data Make a sketch in Fig. 5.1 your graph of velocity versus time for the first run of data, Write the axis title and its units. Data Table 1 Masshanger= g Massloaded (on cart) = Total mass of the system (MT) = g g= Massempty cart = 500 g kg atheoritical (m/s2) Percent Difference % Data Table 2 Run m hanger (kg) Fdriving (N) aexperimental (m/s2) #1 #2 #3 17 / 39 1. What does the slope of the sketch above represent? 2. What happens to the value of the acceleration as you increase the value of the driving force but the system's mass remains constant? 3. Plot the Fdriving vs. aexperimental graph, calculate the slope, say what does it represent? and describe the graph. [Use a graph paper] The slope represents: The graph is: Part 2: Constant Force, Changing Mass * DataStudio file: 15B Newton’s 2nd Law 2.ds Data Table 1 mhanger= 45 g = 0.045 kg Fdriving = mhanger × g = 0.045 kg × 9.8 m/s2 = 0.44 N Mloaded → changing (0g, 500g, 1000g) ; MT = (mhanger + mcart) (constant) (constant) (changing) Data Table 2 Run mloaded (kg) Total mass of the cart mcart (kg) MT of the system(kg) aexp. (m/s2) atheor. (m/s2) Percent Diff. (%) 1/aexp. (s2/m) #1 #2 #3 Questions 1. What happens to the acceleration as you increase the mass of the object and keep the driving force constant? 2. Plot mcart vs. 1/aexp. [Use a graph paper] 18 / 39 Extension Problem 3. The motor of the toy cart shown has a thrust of F and a mass of M. Other toys of mass m can be added to the cart and hence its acceleration decreases since the acceleration is inversely proportional to the total mass. The Fig. 5.2 besides shows the relation between the added mass and the inverse of the acceleration of the cart. Use the graph below (m vs 1/a) to find: a) F, the thrust of the cart’s motor. b) M, the mass of the empty cart. 19 / 39 m M Experiment 6: Part A Friction Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... Part 1: Coefficients of Static and Sliding (Kinetic) Friction DataStudio file: 20 Friction Forces.de Data Make a sketch in Fig. 6.1 of one run of the frictional force versus time data 20 / 39 Sketch in Fig. 6.2 the static force and felt. sliding force versus normal for Data Table Record the coefficient of friction (slopes) in the table below Material Felt Coefficient of Static Friction, µs Coefficient of Sliding Friction, µk Cork Questions 1. What happens to the static friction force as the mass is increased when applying a force ? -------------------------------------------------------------------------------------------------2. What happens to the static friction force as the mass is increased ? -------------------------------------------------------------------------------------------------3. Think about your experience with the friction trays. When a car skids to a stop (with wheels “locked”), which friction force is at work? How do you know? -------------------------------------------------------------------------------------------------Prediction : If the mass of the block is increased, will the force of kinetic friction increase? Will the coefficient of kinetic friction increase? Explain. ------------------------------------------------------------------------------------------------21 / 39 Experiment 6: Part B Momentum and Collisions Name: …………………… Reg. No.: ……………… Section: ………… Table no. ( ) Partner’s Name: …………... Instructor: …………………. Date: ……………...... Part 1: Momentum in an Inelastic Collision * DataStudio file: 23A Momentum 1.ds Observations What happens to the carts during the inelastic collision? Calculations Use the mass and the change in velocity of each cart to calculate the momentum of each cart before collision. Find the total momentum before the collision. The momentum after collision is the product of the combined mass and the velocity after collision. Use the total mass and the final velocity to determine the momentum of both carts after collision. Data Table Before Collision Mass Cart (kg) 1 2 Initial Velocity (m/s) Momentum Before (kg m/s) Total Momentum Before After Collision Mass (kg) Final Velocity (m/s) Momentum After Cart1+Cart2 Questions 1. How does the momentum before the collision compare to the momentum after the collision? 22 / 39 2. What factors do you think may cause a difference between the momentum before and the momentum after collision? Part 2: Momentum in an Elastic Collision * DataStudio file: 23B Momentum 2.ds Observations Describe the motion of the carts during the elastic collision. Calculations Use the mass and the change in velocity of each cart to calculate the change in momenta of Cart 1 and Cart 2. Data Table Cart Run#1 Mass (kg) Change in velocity (m/s) Change in momentum (kg m/s) 1 2 Questions 1. How does the change in momentum of Cart 1 compare to the change in momentum of Cart 2? 23 / 39 Experiment 7 Charging and Charge Distribution Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: _____________________ Table #:____________________ Date: _________________________ ___________________________________________________________________ Open the DataStudio file: 64 Charging.ds Part One: Electrostatic Charging Questions: 1. What polarity is the white Charge Producer? What polarity is the blue Charge Producer? Is the change of the charge on the ‘Ice Pail’ permanent or temporary? Sketch in the Fig. 7.1 the resulting graph. White:…………………………………………. Blue: ………………………………………….. Part Two: Electrostatic Charge Distribution on a Conductive Sphere: Graph: Sketch in the Fig. 7.2 your graph of Charge and Location for the sphere: 24 / 39 Questions: 1. What happens to the charge on the Conductive Sphere when it is connected to a source of charge such as the Electrostatic Voltage Source? ……………………………………………………………………………………………….. ……………………………………………………………………………………………….. Part Three: Charging a Conductive Sphere: A. Charging a Conductive Sphere by Conduction: Questions: 1. What is the polarity of the charge on both spheres? Sphere A:…………………………………………….. Sphere B: …………………………………………….. 2. What is the relation between the values of the charge on each sphere? ………………………………………………………………………………………………… ………………………………………………………………………………………….. B. Charging a Conductive Sphere by Induction: Questions: 1. For step 5 in the procedure above, draw schematic diagram for the two spheres and determine the polarity on each sphere? 2. According to step 8 in the procedure above, what is the charge on both sides of sphere B? …………………………………………………………………………………………. 3. According to step 13 in the procedure above. What is the polarity of the charge on the sphere B? ……………………………………………………………………………………… ……………………………………………………………………………………… 25 / 39 4. According to step 13 in the procedure above. Is the charge on the sphere permanent? ……………………………………………………………………………………… ……………………………………………………………………………………… 5. How does the result of charging by contact differ from the result of charging by induction? ……………………………………………………………………………………… ……………………………………………………………………………………… 26 / 39 Experiment 8 Resistors and Resistors Connections Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: ____________________ Table #:____________________ Date: _________________________ __________________________________________________________________ Open the DataStudio file: 67 Ohm’s Law.ds Part (1): Ohm’s Law Graph: Make a sketch in the Fig. 8.1 of the Scope display screen for voltage and current for the given Resistors. Questions & Calculations: 1. From your graphs use the smart tool to calculate the resistance in each case. Resistor (1) = ………………………Ω Resistor (2) = ……………………….Ω 2. Show how did you calculate the resistance of R2? ……………………………………………………….………………………...……………… ……………………………………………………………………............................................ ....................................................................................................................................... 27 / 39 3. Use the DMM to measure the values of R1 and R2 and consider that as the accepted value for each resistor. Resistor (1) = …………………….Ω Resistor (2) = …………………….Ω 4. Calculate the percentage error for both resistors R1 and R2. ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… Part (2): Resistors Connections Graph: Make a sketch in the Fig. 8.2 of the Scope display screen for voltage and current for the series and parallel connections of the given set of resistors. Questions & Calculations: 1. Use the smart tool to calculate the slope of each line in the graphs above. Series connection: ………………………… Parallel connection: ………………………. 2. What does the slope represent in each case? 28 / 39 3. Calculate the theoretical value of the equivalent resistance for the two types of connections below. Series connection: ………………………… Parallel connection: ………………………. 4- Calculate the percentage error for both cases: 5- What factors do you think that may contribute to the errors? 29 / 39 Experiment 9 Kirchhoff's Laws Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: _____________________ Table #:____________________ Date: _________________________ ___________________________________________________________________ Open the DataStudio file: 70 Kirchhoff.ds Data: * Measure the voltage across each resistor, and record the measured values on the diagram 9.1 above. * Measure the current across each branch then fill in the table below. Questions & Calculations: 1. Calculate the sum of the measured voltages around any two loops in the circuit to verify Kirchhoff’s voltage law. ………………………………………………………………………………...……………. ……………………………………………………………………………………………… ………………………………………………………………………………………………. 30 / 39 3. Using your measured values of current and their direction of flow on one of the nods, calculate the sum of currents entering the junction and the sum of currents leaving the junction. ………………………………………………………………………………...……………… ……………………………………………………………………................................. ………………………………………………………………………………...……………… …………………………………………………………………………………………. 4. Using kirchhoff's laws calculate the currents (I1, I2, I3), and insert your calculated values in the table then calculate the % error. ………………………………………………………………………………...……………… ……………………………………………………………………................................. ………………………………………………………………………………...……………… ……………………………………………………………………...………………………… ……………………………………………………...………………………………………… …………………………………………................................................................ ………………………………………………………………………………...……………… ……………………………………………………………………................................. ………………………………………………………………………………...……………… ……………………………………………………………………................................. ………………………………………………………………………………...……………… ……………………………………………………………………................................. ………………………………………………………………………................................. Quantity I1 I2 I3 Measured Values Calculated Values % error 5. What are the main sources of error in this experiment? ………………………………………………………………………………...……………… …………………………………………………………………………………………. 31 / 39 Experiment 10 Capacitors and Capacitors Connections Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: ____________________ Table #:____________________ Date: _________________________ __________________________________________________________________ Open the DataStudio file: 71 RC Circuit.ds Part(1) Capacitance of a single capacitor: From the V-t graph you got, write down the value of (t1/2) for each capacitor you have: (t1/2) for capacitor (1) = __________ s (t1/2) for capacitor (2) = __________ s Questions & Calculations: 1. Use the relation 𝐶= 𝑡1/2 𝑅 × 0.693 to calculate the capacitance of each capacitor: Capacitance for capacitor (1) = ___________ μF Capacitance for capacitor (2) = ___________ μF 2. Calculate the percentage error for each capacitor: 5. What is the maximum theoretical charge (q0) each capacitor can have? ………………………………………………………………………………………………… …………………………………………………………………………………………... 32 / 39 6. From your V-t Graph use the smart tool to determine τ (time needed for the capacitor to charge to 63% of its maximum charge) ………………………………………………………………………………………………… ………………………………………………………………………………………….. 7. Calculate τ theoretically (τ = RC) ………………………………………………………………………………………………… ………………………………………………………………………………………….. 8. Calculate the percentage error for τ: ………………………………………………………………………………………………… ………………………………………………………………………………………….. Part (2) Capacitors connections: (a) Series Connection: (t1/2) for the series connection of the given capacitors = __________ s Questions & Calculations: 7. Using your V-t graph, calculate the equivalent capacitance of the two capacitors connected in series: ………………………………………………………………………………………………… ………………………………………………………………………………………….. 8. Calculate theoretically the equivalent capacitance the two capacitors connected in series: ………………………………………………………………………………………………… ………………………………………………………………………………………….. 9. Calculate the percentage error between the theoretical and the experimental value: ………………………………………………………………………………………………… …………………………………………………………………………………………. (b) Parallel Connection: (t1/2) for the parallel connection of the given capacitors = __________ s 33 / 39 Questions & Calculations: 10. Using your V-t graph, calculate the equivalent capacitance of the two capacitors connected in parallel: ………………………………………………………………………………………………… ………………………………………………………………………………………….. 11. Calculate theoretically the equivalent capacitance the two capacitors connected in parallel: ………………………………………………………………………………………………… ………………………………………………………………………………………….. 12. Calculate the percentage error between the theoretical and the experimental value: ………………………………………………………………………………………………… ………………………………………………………………………………………….. 13. What major factors of error do you think that could account for the percentage error in all the experimental results? ………………………………………………………………………………………………… ………………………………………………………………………………………….. 34 / 39 Experiment 11 Magnetic Field in a Current-Carrying Coil and Magnetic Induction Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: _____________________ Table #:____________________ Date: _________________________ ___________________________________________________________________ Open the DataStudio file: 80 Mag Field Coil.ds Part 1: Magnetic Field of an N turn coil: Data: Number of loops of wire:…………………………………. Radius of coil (m):…………………………………….... Sketch in the Fig. 11.1 your graph of Magnetic Field Strength versus Current. 35 / 39 Calculations: 1. To find the value of the permeability of free space, first convert your slope from gauss to tesla by using the following conversion (1 gauss = 10-4 tesla). Slope (gauss/A):……………………. Slope (tesla/A):……………………... 2. Rearrange the equation (B = µ0NI /2R) to solve for the permeability of free space (μ0). How can you relate the slope of your graph to this equation? ……………………………………………………………………………………….………. ………………………………………………………………………………………………. 3. Substitute your value of slope into your equation and calculate µ0 µ0 = ………………. 4. Compute the percent error between your value and the accepted value (µ0 = 1.26 x 10-6 T m/A). ………………………………………………………………………………………………… ………………………………………………………………………………………….. 5. If we changed the number of loops of the wire or the diameter of the wire. What do you expect about how the value of µ0 will change? ………………………………………………………………………………………………… ………………………………………………………………………………………….. 6. What are the sources of error in this experiment? ………………………………………………………………………………………………… ………………………………………………………………………………………….. 36 / 39 Part 2: Magnetic Induction: Open the DataStudio file: 79 Induction - Magnet.ds 1. Sketch in the Fig. 11.2 the voltage supplied to the primary coil in step 7 of the procedure. 5. Sketch in the Fig. 11.3 the EMF produced in the secondary coil in the same step 7 above. 6. What conclusion can you draw about the relation between the two graphs? ………………………………………………………………………………………………… .………………………………………………………………………………………….. 37 / 39 Experiment 12 Transformer Basics Name: _____________________ Partner’s Name: ________________ Section: ____________________ Instructor: _____________________ Table #:____________________ Date: _________________________ ___________________________________________________________________ Open the Data studio file: 81 Transformer. Data and Calculations: Table (1) Number of Turns Primary Coil Secondary Coil Input Voltage (V) Output Voltage (V) Core None Iron rod U-Shaped Closed Table (2) (Assuming Ideal Transformer) Number of Turns Measured Input Current I1 = Input Output Primary Secondary Voltage Voltage V1 / V 2 N1 / N 2 Coil (N1) Coil (N2) (V1) (V2) 38 / 39 Calculated Output Current I2 Questions & Analysis Part 1: The Effect of the core in the Transformer: 1. Which core configuration gives the maximum transfer of electromagnetic effect to the secondary coil? Explain why? ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………….. Part 2: The effect of the number of turns in the secondary coil: 2. Calculate the ratios V1 / V2 and N1 / N2 Then insert your results in table 1.2. What conclusion do you figure out from your results? ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………... 3. State the major sources of error in this experiment? ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ……………………………………………………………………………….. 39 / 39
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