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10:51 7 ., LTE O AA nctc.instructure.com ZOOM + LAB: FREE FALL Student’s Name: Objectives 1. Measure your reaction time. 2. Measure the acceleration of gravity (g value). Introduction Free fall is the motion only under the action of gravity. The acceleration is equal to g = 9.8 m/s² (g value)and points downward. The interpretation of this acceleration is that falling objects change their speed by 9.8m/s every second. The value of this acceleration is constant for objects falling close to the surface of the Earth when the air friction can be neglected. Objects for which the air friction can not be neglected will not follow a free fall motion, for example, a feather, an extended sheet of paper, or a parachute. The main difficulty in measuring the acceleration of gravity is the measurements of the falling time. An object falling from a height of 1.5 meters takes about 0.55 seconds to hit the floor. If a stopwatch is used to measure this time just by manually activating and deactivating the stopwatch, the error generated by the student’s reaction time would lead to a large error in the measurement of the falling time. For example, if the student has a reaction time is 0.15s then, it would take a time of 0.3s just to activate and deactivate the stopwatch. In this case, the reaction time is already 55% of the falling time. Therefore, the measurement of time with a manually controlled timer will generate a high error in the measurement of “g”. IMPORTANT: If you don’t have access to the materials in this lab, please used the data already collected by your instructor that is at the end of the handout (no points will be deducted if you use that data). Although, I encourage you to try it and obtain your data. 1 < 10:51 7 ., LTE O AA nctc.instructure.com ZOOM + 1. Measuring your reaction time (30 points) Materials A ruler with a centimeter scale and another person to assist you (we will call this person B). For the following, you will be called person A (the person whose reaction time will be measured). Procedure Follow the following procedure to measure your reaction time. 1. Person B will hold vertically a ruler from the 30cm mark. 2. Person A will place its hand (the dominant one) with his thumb and index finger slightly open just below the lower end of the ruler. See the picture below, Person B Person A 3. Without any advice, person B will drop the rule, and “person A” will try to catch it by only closing its fingers. 2 < 10:51 7 ., LTE O AA nctc.instructure.com ZOOM + dincm 4. In the table1, record the distance (d) in centimeters that the ruler fell. This distance is indicated by the tip of the thumb of person A on the centimeter scale of the ruler. 5. Calculate the reaction time of person A by using the following formula t = 2d 980 6. Perform the same procedure above two more times and fill the rest of table 1. Reaction time Distance Trial Distance t = 2d 980 d [s] [cm] ܝܙ ܚ 3 Table 1 3 < > 10:51 7 LTE O AA nctc.instructure.com ZOOM + Show one calculation: 2. Measuring the acceleration of gravity (40 points) Materials a. PHYPHOX app. Download and install on your phone the application “PHYPHOX” from the app store. No need to pay anything and during installation, just skip any payment option. Watch a short video of the use of this app for this experiment here b. A ruler, a pen, a measuring tape, a small ball, a pen and a book or a metal plate (in this case I have used a book), or anything that makes a clear noise when the ball will hit the floor. Procedure 1. Open the app and choose the option of the acoustic stopwatch. Set the setting for threshold and minimum delay with the values as shown below. Anytime you will start to measure time, you will have to press reset and the start button, otherwise the time will not be measure. Now the timer is ready to measure the time between two sounds. 4 < 10:51 7 ., LTE O AA nctc.instructure.com ZOOM + LAB: FREE FALL Student’s Name: Objectives 1. Measure your reaction time. 2. Measure the acceleration of gravity (g value). Introduction Free fall is the motion only under the action of gravity. The acceleration is equal to g = 9.8 m/s² (g value)and points downward. The interpretation of this acceleration is that falling objects change their speed by 9.8m/s every second. The value of this acceleration is constant for objects falling close to the surface of the Earth when the air friction can be neglected. Objects for which the air friction can not be neglected will not follow a free fall motion, for example, a feather, an extended sheet of paper, or a parachute. The main difficulty in measuring the acceleration of gravity is the measurements of the falling time. An object falling from a height of 1.5 meters takes about 0.55 seconds to hit the floor. If a stopwatch is used to measure this time just by manually activating and deactivating the stopwatch, the error generated by the student’s reaction time would lead to a large error in the measurement of the falling time. For example, if the student has a reaction time is 0.15s then, it would take a time of 0.3s just to activate and deactivate the stopwatch. In this case, the reaction time is already 55% of the falling time. Therefore, the measurement of time with a manually controlled timer will generate a high error in the measurement of “g”. IMPORTANT: If you don’t have access to the materials in this lab, please used the data already collected by your instructor that is at the end of the handout (no points will be deducted if you use that data). Although, I encourage you to try it and obtain your data. 1 < 10:51 7 ., LTE O AA nctc.instructure.com ZOOM + 1. Measuring your reaction time (30 points) Materials A ruler with a centimeter scale and another person to assist you (we will call this person B). For the following, you will be called person A (the person whose reaction time will be measured). Procedure Follow the following procedure to measure your reaction time. 1. Person B will hold vertically a ruler from the 30cm mark. 2. Person A will place its hand (the dominant one) with his thumb and index finger slightly open just below the lower end of the ruler. See the picture below, Person B Person A 3. Without any advice, person B will drop the rule, and “person A” will try to catch it by only closing its fingers. 2 < 10:51 7 ., LTE O AA nctc.instructure.com ZOOM + dincm 4. In the table1, record the distance (d) in centimeters that the ruler fell. This distance is indicated by the tip of the thumb of person A on the centimeter scale of the ruler. 5. Calculate the reaction time of person A by using the following formula t = 2d 980 6. Perform the same procedure above two more times and fill the rest of table 1. Reaction time Distance Trial Distance t = 2d 980 d [s] [cm] ܝܙ ܚ 3 Table 1 3 < > 10:51 7 LTE O AA nctc.instructure.com ZOOM + Show one calculation: 2. Measuring the acceleration of gravity (40 points) Materials a. PHYPHOX app. Download and install on your phone the application “PHYPHOX” from the app store. No need to pay anything and during installation, just skip any payment option. Watch a short video of the use of this app for this experiment here b. A ruler, a pen, a measuring tape, a small ball, a pen and a book or a metal plate (in this case I have used a book), or anything that makes a clear noise when the ball will hit the floor. Procedure 1. Open the app and choose the option of the acoustic stopwatch. Set the setting for threshold and minimum delay with the values as shown below. Anytime you will start to measure time, you will have to press reset and the start button, otherwise the time will not be measure. Now the timer is ready to measure the time between two sounds. 4 < 10:51 7 LTE O AA nctc.instructure.com ZOOM + 5. Repeat the above procedure three more times and record your values in the next table. of Acceleration Gravity 2h Trial g = 72 Timet [s] Heighth [m] [m/s2) 1 2 3 4 Table 2. Now, calculate the average value of g by taking the average of acceleration of gravity g values in the last column of table 2 and write it below. Note that to find the average, you will have to add all values of the last column in table 2 and divide it by 4. Fill the blank below: Average value of g = gave. = (with two decimals) Let’s compare this value with the accepted value of the acceleration of gravity which is 9.81m/s2. Use the average value of gave obtained above as the experimental value to find the error in the measurement of the acceleration of gravity. Fill the blank below: Error = 9ave. – 9.81 9.81 | x 100 = ………………………… % Note that the error is always positive because of the absolute value symbols in the definition (the two vertical bars). Errors below 5% are expected in experiments, but different factors can affect measurements 6 < 10:51 7 LTE O AA nctc.instructure.com ZOOM + 5. Repeat the above procedure three more times and record your values in the next table. of Acceleration Gravity 2h Trial g = 72 Timet [s] Heighth [m] [m/s2) 1 2 3 4 Table 2. Now, calculate the average value of g by taking the average of acceleration of gravity g values in the last column of table 2 and write it below. Note that to find the average, you will have to add all values of the last column in table 2 and divide it by 4. Fill the blank below: Average value of g = gave. = (with two decimals) Let’s compare this value with the accepted value of the acceleration of gravity which is 9.81m/s2. Use the average value of gave obtained above as the experimental value to find the error in the measurement of the acceleration of gravity. Fill the blank below: Error = 9ave. – 9.81 9.81 | x 100 = ………………………… % Note that the error is always positive because of the absolute value symbols in the definition (the two vertical bars). Errors below 5% are expected in experiments, but different factors can affect measurements 6 < 10:51 7 LTE O AA nctc.instructure.com ZOOM + 5. Repeat the above procedure three more times and record your values in the next table. of Acceleration Gravity 2h Trial g = 72 Timet [s] Heighth [m] [m/s2) 1 2 3 4 Table 2. Now, calculate the average value of g by taking the average of acceleration of gravity g values in the last column of table 2 and write it below. Note that to find the average, you will have to add all values of the last column in table 2 and divide it by 4. Fill the blank below: Average value of g = gave. = (with two decimals) Let’s compare this value with the accepted value of the acceleration of gravity which is 9.81m/s2. Use the average value of gave obtained above as the experimental value to find the error in the measurement of the acceleration of gravity. Fill the blank below: Error = 9ave. – 9.81 9.81 | x 100 = ………………………… % Note that the error is always positive because of the absolute value symbols in the definition (the two vertical bars). Errors below 5% are expected in experiments, but different factors can affect measurements 6 < 10:527 LTE O AA nctc.instructure.com ZOOM + and the error can be larger. I do not expect you to get an error below five percent, but if you decide to make the experiment it is recommended to repeat the experiment if you get a large error. 4. Graph of the Distance versus Time (20 points) At the graph paper below, plot the height (h) versus the average of the times (t). Make sure your graph does not look too small and use most of the graph paper. Do not forget to join the points, label the axis, and put a title to the plot. (15 points). After getting the plot, circle from the options below the type of curves obtained in your graph (5 points). v Ļ Ut 7 < 10:527 LTE O AA nctc.instructure.com ZOOM + 3. Questions (10 points) 1. In this lab, you have measured two quantities, height and time. Which of these quantities do you think contributes more to the error and why? You can also look at the video to have some intuition. 2. If you could use a marble (which is lighter), instead of a steel ball, would the new value of g change. In other words, does a heavier object fall faster than a lighter one? Data collected by your instructor that can be use to complete this lab. If you don’t do the experiment you can use the following data to fill the tables in sections 1 and 2 and then complete the required calculations in those sections. Reaction time Trial d Distance Distance [cm] 2d 980 [s] 9 < 10:527 LTE O AA nctc.instructure.com ZOOM + 1 10 2 12 3 7 Table 1 Acceleration of Trial Gravity 2h g= 72 Height h [m] Time t[s] 1 0.43 0.300 2 0.74 0.410 3 0.94 0.470 4 1.41 0.555 Table 2 References [1] Jerry D. Wilson, Cecilia A. Hernandez-Hall. Physics Laboratory Experiments. Cengage, 8th edition, 2015. 10 <

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