F23_lab1_worksheet

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Mathematics

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Jun 22, 2024

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G117 Laboratory One Science: Observation and Measurement Name: Course/Section: Objective : Learn how to make observations and measurements and work through the Scientific Method. For this lab, we will use the scientific method to determine which of three objects is the most dense. Density is weight per unit volume. Materials : Pencil, ruler, graduated cylinders, water, scale, and objects to observe and measure. Observations : A. You have three objects. Make at least three observations for each. Fill out the table below. Object 1 Object 2 Object 3 Observation 1 Observation 2 Observation 3 This is a/an … Hypothesis : B. Based on your observations, which do you think will be the densest? That is, which of these do you think is the heaviest for its size? (You don’t have to be correct!) Measurements : C. Length . A meter is the base unit of length in the SI system. Based on the longest part of each object, how many meters long is each? (Note: Measure in centimeters then convert to meters. These will be small numbers!) Fill out the table below. Length (cm) Conversion Factor Length (m) Object 1 Object 2 Object 3 ACTIVITY 1.1 Observations and Measurement
D. Volume . Method 1: A liter is the base unit of volume in the SI system. Volume is the amount of space an object occupies. For our three objects, we can estimate the volume by measuring the length, width, and depth of each object in centimeters then multiply these lengths together go get a volume in cubic centimeters (cm 3 ); a cubic centimeter is the same volume as a milliliter. Measure all three sides of the object: the longest side, the second longest side, and the third longest side. None of your objects are perfect cubes, so just make your best estimation of the longest, second longest, and third longest side. Fill out the table below. Length 1 (cm) Length 2 (cm) Length 3 (cm) Estimated Volume (cm 3 ) Object 1 Object 2 Object 3 E. Volume . Method 2: An easier way to do this is the use a graduated cylinder to measure the volume of water each object displaces. To do this follow these instructions. (1) Based on your understanding of accuracy, precision, and detection limit, choose a graduated cylinder that you think would best measure the volume of your object. (2) Fill the graduated cylinder at least half way with water. Record this volume by looking at the point nearest the bottom of the meniscus, the curved surface of the water. A meniscus forms in a graduated cylinder because water sticks to the sides of the tube. (See figure to the right.) (3) Drop your object into the graduated cylinder. Record the new volume. (4) Subtract the new volume from the original volume to calculate the volume of your object. (5) Repeat for all objects and fill out the table below. Original Volume (mL) Volume with Object (mL) Volume of Object (mL) Volume of Object (cm 3 ) Object 1 Object 2 Object 3
F. Weight or Mass . We need to measure the mass or heaviness of the objects. We can do this by using a scale. Make sure that the scale is “zeroed” and set to grams before you attempt to weigh your objects. Note that the scales are pretty finicky, so you will want to measure each object at least three times and obtain an average mass. Fill out the table below. Mass 1 (g) Mass 2 (g) Mass 3 (g) Average Mass (g) Object 1 (1) Object 2 Object 3 G. Density . Finally, we can calculate the density of our objects. Density is the mass per unit volume. While volume is normally measured in milliliters (mL), when reporting density, it is shown as a mass per cubic centimeter or g/cm 3 . Fill out the table below. Average Mass (g) Volume (cm 3 ) Density (g/cm 3 ) Object 1 Object 2 Object 3 Summary and Conclusion : Given your observations and measurements, would you accept or reject your hypothesis? (Circle one.) ACCEPT REJECT Which object is the most dense? (Circle one.) Object 1 Object 2 Object 3
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Name: Course/Section: Objective : Learn how to make observations and measurements and work through the Scientific Method. Understand how scientists account for natural variability within a population. Understand why scientific knowledge is probabilistic. For this lab, we will use the scientific method to determine the relationship between foot size and height . Materials : Student workbook file (on Canvas) Observations : A. We will start by making observations about a list of celebrities from the data in the given Excel file. 1) Open the excel file on your Canvas page titled “G117_lab1_student_workbook”. 2) When you open the file, there will be a sheet called “data_table”. 3) Listed in the “data_table” are 25 celebrity names, their height in feet & inches as well as just inches, and their shoe size. 4) Browse the list and make some observations about a few of the celebrities listed. In your groups or as a class, discuss the following: Do you observe any general patterns? If so, what are they? Are there any obvious outliers? How do you think this will affect the data? ACTIVITY 1.2 Observations and Measurement
Hypothesis : B. Based on your observations, do you think there is a relationship between a person’s height and shoe size? If so, what do you think that relationship is? Write your hypothesis below. Experiment : C. General Design . Our experiment will seek to test if there is a relationship between height and shoe size and then to determine what that relationship is. 1) Convert Height Measurements: Height and shoe size are given for each celebrity in the excel file. Therefore, measurements have already been “taken”. In your group, convert each celebrity’s height (in) to height (cm) using the conversion factor given. The conversion factor is 1 inch = 2.54 cm . In excel, it will look like the following: 2) Convert Shoe Measurements: Within the same excel file, there is a sheet called “Size_to_flength”. This sheet contains 3 images showing US Women’s, US Men’s, and US Kids’ shoe sizes and its corresponding foot length in cm. Using those images, convert each celebrity’s US shoe size to foot length (cm). There is no exact conversion for this. In excel, it will look like the following: 3) Data Table : At this point, all columns in your “data_table” sheet should be filled and the average for both
Height (cm) and Foot Length (cm) should be automatically calculated at the bottom of your data table for you. Double check with your group and/or the TA. 4) Graph the Results : In the same excel file, there is another sheet called “Height_vs_flength_graph”. This is where your graph results will show up. You will graph Height (cm) vs Foot Length (cm), which are the two data columns that you calculated. Click on the sheet titled “Height_vs_flength_graph”. Right click on the blank graph, and within the options given, click on “Select Data”. The following box will appear: This is where you will add your data. Click “Add” on the left-hand side of the box. A new box should appear as follows: In the “Series name:” box, type a title. For example, it can be as simple as “Height (cm) vs Foot Length (cm) of 25 Celebrities”. In the “Series X values:” box, click on the up arrow, and then, click on the “data_table” sheet. Highlight the values in the “Height (cm)” column and press Enter. In the “Series Y values:” box, click on the up arrow and make sure you are still in the “data_table” sheet. Highlight the values in the “Foot Length (cm)” column and press
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Enter. Go back to your graph, and your data should appear. 5) Alter graph appearance: In order for us to analyze the data, we need to alter graph features. Add Axis Titles : At the top of your excel file, go to “Chart Design”, “Add Chart Element”, and then “Axis Titles”. Two options appear: “Primary Horizontal” and “Primary Vertical”. When you click on one of the options, a text box will appear on the corresponding axis where you will type in the titles. (X = Height (cm); Y = Foot Length (cm)) Alter Axis Lengths : You will notice that the data is clustered and small. We want to expand it to fill the whole graph. Start by clicking on the X-axis. From the options given, select “Format Axis”. Change the Minimum to “150” and the Maximum to “200”. Repeat for the Y-axis, but change the Minimum to “20” . Add Trendline: At the top of your excel file, go to “Chart Design”, “Add Chart Element”, and then “Trendline” and “Linear”. In reality, graphing or statistical programs can test for normal distributions and graph your data, which can be shown through a trendline. The trend line is a calculated interpretation of the data, showing the correlation (relationship) between the two data sets (height and foot/shoe length) based on a regression analysis. Add Regression Analysis Equation: Click and then right click on your trendline. From the list of options given, select “Format Trendline”. Towards the bottom on the “Format Trendline Panel”, click on the box next to “Display Equation on chart”. Describe any trends you see in the data. Are the data related? When you see the data plotted with a trend line in MS Excel, does it look like height is related to foot/shoe length? Circle one: Yes No
Regression analysis is a powerful tool because it can give you a slope or equation to the trend line. You can use this trend line to predict what shoe size someone would have based on his/her height. Using the equation, estimate what shoe size someone who is 7 feet 10 inches tall would have. Show your work: Do you think this trend line could predict what an eight or ten foot tall person’s shoe/foot size would be? Why or why not? Summary and Conclusion : Given your observations and measurements, would you accept or reject your hypothesis? (Circle one.) ACCEPT REJECT Is height positively related, negatively related, or neither to shoe size? (Circle one.) Positively Negatively Neither