Student Name: MAT-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 Quantity Letter wr wb w d Rider Weight Bike Weight Total Weight Wheel Diameter Value 100 60 160 2.17 Dimensions lbs lbs lbs ft r Gear Ratio 1.5 Table 1: insert here the parameters of the problem, your weight, the bike's weight, the total weight of the rider and bike, the diameter of the wheel, and the gear ratio. 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)=r.t To get the ratio you have to do first gear is 15 divide second gear is 10, so I get the ratio 1.5 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)=r.t.pi.(d/5280).60 2016. Grand Canyon University. All Rights Reserved. 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 f )( t )=g(f ( t ) ) here: ( g f )( t )=g ( f ( t ) )= (1.5)^2 x 19 x pi x (2.17/5280) x 60 = 3.312 What is your speed in MPH with a cadence of 60 RPM? ( g f )( t )=g ( f ( t ) )= (1.5)^2 x 60 x pi x (2.17/5280) x 60 = 10.458 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 w+ 0.0083 v 3) 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 f )( t))=(c g f )(t) is a composition of three functions! What is your expression for (c g f )( t)? ( c g f )( t )=c ( g ( 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.)