Activity 4.1c Mathematical Modeling (Preview), Study notes of Engineering

Download Activity 4.1c Mathematical Modeling (Preview) and more Study notes Engineering in PDF only on Docsity! Introduction In this activity you will collect and analyze data in order to make predictions based on that data. You will use both manual and computer methods to record, manipulate, and analyze the data in order to determine mathematical relationships between quantities. These mathematical relationships can be represented graphically and by equations, also known as mathematical models. You will then use the mathematical models to make predictions related to the quantities. Equipment
Engineering notebook
Pencil
Computer with Excel Procedure 1. Record the number of cubes and weight of each of your puzzle pieces. Activity 4.1c Mathematical Modeling (Preview) Color of Piece Number of Cubes Weight (g) Page 1 of 8Activity 4.1c Mathematical Modeling (Preview) 10/16/2013mk:@MSITStore:C:\Documents%20and%20Settings\waddd\My%20Documents\Dropbo... 2. Graph your data points on the grid below such that the number of cubes in the puzzle piece is represented on the x-axis and the mass of the piece is indicated on the y-axis. Label the axes and indicate units. 3. Consider the data that you have graphed and answer the following. a. Would you expect that this data is linear; that is, if you were to measure the mass of other pieces with more than six cubes or fewer than four cubes, would the points fall on a straight line on the graph? Explain your answer. b. If you were to sketch a line-of-best fit, what would be a reasonable y-intercept. That is, where would the line-of-best fit cross the vertical axis? Explain your answer. c. Based on your data, what would you predict for the mass of a single wooden cube? Explain your answer or show your work. Page 2 of 8Activity 4.1c Mathematical Modeling (Preview) 10/16/2013mk:@MSITStore:C:\Documents%20and%20Settings\waddd\My%20Documents\Dropbo... f. Predict the mass of a puzzle piece that is comprised of 9 wooden cubes. Show your work. g. If a puzzle piece had a mass of 49 grams, how many wooden cubes would it contain? Show your work. 8. Assume that a puzzle cube was rebuilt using 1 in. cubes rather than ¾ in. cubes and the following weights were recorded for the pieces. Complete each of the following. a. Create a scatterplot and find a trendline for the data using Excel. Print a copy of your worksheet that includes
Table of data
Scatterplot with properly formatted axes, axes labels and units, and an appropriate chart title
Trendline and its equation displayed on the scatterplot b. Write the equation relating number of cubes to mass in function notation. Be sure to define your variable. c. What is the slope of the line (include units)? Explain the interpretation of the slope in words. d. How does the slope of this function (relating the number of 1 in. cubes to mass) compare to the slope of the function you found in number 5 (relating the number of ¾ in. cubes to mass)? Explain the difference. Number of cubes Weight (g) 4 39 5 47 6 57 6 58 6 57 Page 5 of 8Activity 4.1c Mathematical Modeling (Preview) 10/16/2013mk:@MSITStore:C:\Documents%20and%20Settings\waddd\My%20Documents\Dropbo... e. Use the function to predict the mass of a puzzle piece (using 1 in. cubes) if the piece includes 8 cubes. Show your work. f. If a puzzle piece 95 grams, how many 1 in. cubes are most likely included in the piece? Show your work. 9. An engineer is redesigning a BMX bike. He is interested in how the weight of the bike affects the height that the bike reaches when the rider “gets air” or jumps the bike off of a ramp. He asked an experienced rider to test bikes of various weights and recorded the following minimum jump heights. Use this data to complete each of the following. a. Create a scatterplot and find a trendline for the data using Excel. Print a copy of your worksheet that includes the following:
Table of data
Scatterplot with properly formatted axes, axes labels and units, and an appropriate chart title
Trendline and its equation displayed on the scatterplot b. Write the equation relating Bike Weight to Minimum Jump Height in function notation. Be sure to define your variable. Bike Weight (lb) Minimum Jump Height (in.) 19 83.5 19.5 82.0 20 79.2 20.5 77.1 21 74.9 22 73.3 22.5 71.0 23 68.1 23.5 65.8 24 64.2 Page 6 of 8Activity 4.1c Mathematical Modeling (Preview) 10/16/2013mk:@MSITStore:C:\Documents%20and%20Settings\waddd\My%20Documents\Dropbo... c. What is the domain of the function? Explain. d. What is the range of the function? e. What is the slope of the line (include units). Is the slope positive or negative? Explain the interpretation of the slope in words. f. If the engineer designed a bike that weighs 18 pounds, predict the minimum jump height. Give your answer in inches (to the nearest hundredth of an inch) and feet and inches (to the nearest inch). Show your work. g. If the engineer designed a bike that weighs1 pound, predict the minimum jump height. Give your answer in inches to the nearest hundredth of an inch and feet and inches to the nearest inch. Show your work. h. Does the predicted height for a one pound bike make sense? Is this function a good predictor for minimum jump heights at all bike weights? Explain. i. If the minimum jump height of 89.7 inches is recorded, predict the estimated weight of the bike. Show your work. 10. Assume that you will build your puzzle cube from 2 cm cubes of solid gold and each cube had a mass of 153 g. Address each of the following. a. Give a mathematical model (in function notation) that would represent the mass of a puzzle piece depending on the number of gold cubes used in the piece. Define your variables. b. What would be the mass of a puzzle piece that is comprised of four gold cubes? Page 7 of 8Activity 4.1c Mathematical Modeling (Preview) 10/16/2013mk:@MSITStore:C:\Documents%20and%20Settings\waddd\My%20Documents\Dropbo...