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Suppose you could use wheels of any type in the design of

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 3DQ Chapter 10

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 3DQ

Suppose you could use wheels of any type in the design of a soapbox-derby racer (an unpowered, four-wheel vehicle that coasts from rest down a hill). To conform to the rules on the total weight of the vehicle and rider, should you design with large massive wheels or small light wheels? Should you use solid wheels or wheels with most of the mass at the rim? Explain.

Step-by-Step Solution:

Solution 3DQ Step 1: If a rigid body moving through space,its motion can regard as both the combination of translational motion of center of mass and rotational motion about an axis through center of mass. The objects with smaller moment of inertia will roll down the hill faster.because an object rolling down a hill is essentially converting kinetic energy into potential energy. Since kinetic energy K = 1/2 mv 2 + 1/2I w 2 cm cm Where m mass of object v = velocity of center of mass cm I moment of inertia cm w angular speed of object Step 2: Let the mass of car and wheels be M and mass of each wheel m. The initial total energy at top of incline is Mgh. At the bottom of the incline the total energy is sum of the translational kinetic energy of car and rotational energy of the wheels. K = 1/2 mv cm 2+ 4(1/2I cm) 2 Assuming four wheels by conservation of energy. Mgh = 1/2 mv 2+ 4(1/2I w ) 2 cm cm With no slip w = v/R,where R is radius of wheels. Mgh = 1/2 mv cm 2+ 2I cm /R) Multiply above equation through by 2 and divide through by M,then v + 4I(v /MR ) = 2gh = v (I + 4I/MR ) 2 2 Moment of inertia of wheel I = mR Where = 1/2 for disk-like wheels. = 1for hoop-like wheels. 2 2 v (I + 4m/M) = 2gh = v (M + 4m/M) v = 2gh/(M + 4M/M) 2 v = 2gh(M/M + 4m) Hence maximum speed (M/M + 4m)needs to be as large as possible.

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Chapter 10, Problem 3DQ is Solved
Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

The full step-by-step solution to problem: 3DQ from chapter: 10 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 3DQ from 10 chapter was answered, more than 687 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: wheels, use, vehicle, should, Design. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “Suppose you could use wheels of any type in the design of a soapbox-derby racer (an unpowered, four-wheel vehicle that coasts from rest down a hill). To conform to the rules on the total weight of the vehicle and rider, should you design with large massive wheels or small light wheels? Should you use solid wheels or wheels with most of the mass at the rim? Explain.” is broken down into a number of easy to follow steps, and 67 words. University Physics was written by and is associated to the ISBN: 9780321675460.

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