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Question: mat154 topic 2 project assignment the purpose of this project...

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MAT-154 Topic 2 Project Assignment

The purpose of this project is to explore the use of function composition to connect different quantities. We will use the intuitive idea that the harder we workout, the more calories we burn. In particular, we will use a cycling example to relate the physical properties of a bike and its rider with the calories burned at different speeds/cadences.The purpose of this project is to explore the use of function composition to connect different quantities. We will use the intuitive idea that the harder we workout, the more calories we burn. In particular, we will use a cycling example to relate the physical properties of a bike and its rider with the calories burned at different speeds/cadences. We want to connect effort and calories while biking. To do so, we need to understand the relationship between pedal and wheel movement. Pushing on the bikes pedal moves the chairn that in turn moves the wheel. Does a full pedal turn imply a full wheel turn? That depends on the current gear of the bike. The gear of the bike is determined by the front and rear sprockets (aka gears) that are moving the chain (see figure) Each sprocket has a certain number of teeth and the ratio between the number of teeth in the front sprocket and the number of teeth in the back sprocket (called the gear ratio-r) determines how many times the wheel will turn with each pedal turn. If the gear ratio is two (r-2), it means that for each pedal stroke, the wheels of the bike turn 2 times The large front sprocket here has 56 teeth Find a bike (real or from an internet search). If the bike has more than one gear, then pick a front and rear gear and count the number of teeth on each. Also measure the radius of the wheel (in feet) The large rear sprocket has 28 teeth The gear ratio for the large front sprocket to large back sprocket is 56/28-2.0 tron,-# of teeth on the front sprocket trear # of teeth on rear sprocket d - diameter of wheel in feet Now the gear ratio is defined as r - tfront/trear. Notice that a large front gear and a small rear gear result in a higher ratio or high gear, whereas a small front gear and a bigger rear gear results in a lower ratio or low gear. Let t be the number of turns the front pedal makes and let f(t)be the corresponding number of turns the rear wheel makes given the gear ratio r, and we are ready to start! First respond to Topic 2 DQ 1 using the above information. Then complete Topic 2 Project Worksheet. You may write your expressions using the Equation Tools tab in Word, or handwrite the expression and then scan or take a picture of the worksheet to submit to your instructor for gradingMAT-154 Topic 2 Project Worksheet Respond to the following questions. Refer to Topic 2 Project Assignment resource for complete instructions. Fill the following table with the parameters of your study Project 2 Parameters Quanti Letter Value Dimensions 170 26 196 Rider Weight Jbs Bike Weight Total Weight Jbs ft Wheel Diameter Gear Ratio Table 1: insert here the parameters of the problem, your weight, the bikes weight, the total weight of the rider and bike, the diameter of the wheel, and the gear ratio. 4 to 1 The following two questions you previously answered in Topic 2 DQ 1. Copy your answers here and then complete the rest of the worksheet. Let t be the number of turns the front pedal makes and let f(t) be the corresponding number of turns the wheel makes given the gear ratio r. Input your expression for f (t) here using the value of r from Table 1: f(t) = 4 Let g (t) be the speed in miles/hour (use the conversion 1 mile-5280 ft) that the bike is moving if the wheel is turning at t turns per minute Give your expression for g (t)here g(t)-The cadence is the number of turns of the pedal per minute made by the rider measured in revolutions per minute (RPM). In practice, a cadence of 19rpm means that the rider does 19 pedal strokes in one minute 1. The composition of g with f gives the speed of the bike in miles per hour (MPH) Input your expression for (g o f) (t)- g (f (t)) here: What is your speed in MPH with a cadence of 60 RPM? HINT: you can use the Cadence Excel Worksheet to check your work, just make sure to have the correct parameters in formulas inside the worksheet. 2. One formula for calories burned while riding is Calories burned/hour 7.2 (0.0053 v w0.0083 v3) where v - average velocity in MPH and w is the combined weight of the rider, bike, and accessories in pounds. View this as a function of c(v) with the parameter w fixed. Find the function for calories/hour burned while biking as a function of cadence. You will have to use your own mass and guess the mass of the bike (or look it up on google) Calories burned as a function of cadence is c(v)- c((g o f)(t)) - (c o g o f)(t)is a composition of three functions! What is your expression for (c o g o f) (t)? How many calories do you burn per hour at a cadence of 60 RPM? HINT: you can use the Cadence Excel Worksheet to check your work, just make sure to have the correct parameters in formulas inside the worksheet. 3. If you wished to burn 500 calories/hour what cadence would you need to maintain? (You do not need to find an exact answer (although you can...), just a good approximation and how you found such approximation) 4. Use the provided Excel worksheet to plot the relationship between calories burned per hour and cadence, where cadence ranges from 50 RPM to 120 RPM (Do not cut and paste chart here, submit together with this completed worksheet.)Student Name Project 2 Parameters Value Quantit Rider Weight Letter Dimensions wh Total Weight Wheel Diamet Gear Ratio Calories/hour vs. Cadence 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Cadence Speed mplh 40 70 90 00 110 120 130

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