3. In a recent bicycle race through a mountainous region in Spain the world champion, Annemiek van Vleuten, asked her team for an unpainted bike. In the hope of making the climbs easier to ride, her request was based on a total mass saving of about 100 grams. Suppose her bike has a section of carbon tubing as in Figure 2(a) below. The inner and outer diameter of this tube is 4.76 cm and 5.07 cm respectively. Both ends are cut at 45° with the cuts centred on == 20 cm. For convenience we may take the cuts to be in the direction. Figure 3: (a) The full length of tube and (b) the top end showing the 45° cut. Construct and evaluate a triple integral in cylindrical coordinates to (i) find the mass of the carbon fibre tube, taking its density as 7 = 1.7 g/cm³. (ii) find the mass of removed paint, taking its thickness to be 8, = 0.01 cm and density 7 = 1.4 g/cm³.

3. In a recent bicycle race through a mountainous region in Spain the world champion, Annemiek van Vleuten, asked her team for an unpainted bike. In the hope of making the climbs easier to ride, her request was based on a total mass saving of about 100 grams. Suppose her bike has a section of carbon tubing as in Figure 2(a) below. The inner and outer diameter of this tube is 4.76 cm and 5.07 cm respectively. Both ends are cut at 45° with the cuts centred on == 20 cm. For convenience we may take the cuts to be in the direction. Figure 3: (a) The full length of tube and (b) the top end showing the 45° cut. Construct and evaluate a triple integral in cylindrical coordinates to (i) find the mass of the carbon fibre tube, taking its density as 7 = 1.7 g/cm³. (ii) find the mass of removed paint, taking its thickness to be 8, = 0.01 cm and density 7 = 1.4 g/cm³.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 50A

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