Explanation A marble can be considered as a solid sphere with mass m and radius r Initially, the marble will have a potential energy. As it rolls down, the potential energy is transformed into linear and rotational kinetic energy. Write the equation for potential energy U = m g h (I) Here U is the potential energy, m is the mass of the marble, g is the acceleration due to gravity and h is the height from the bottom. Write the equation for kinetic energy. K E = 1 2 m v 2 + 1 2 I ω 2 (II) Here v is the velocity of the marble, I is the rotational inertia and ω is the angular velocity of the marble. Substitute ω = v r in (II) K E = 1 2 m v 2 + 1 2 I ( v r ) 2 (III) Here r is the radius of the marble. Write the equation for rotational inertia of a solid sphere I = 2 5 m r 2 (IV) Substitute (IV) in (III) K E = 1 2 m v 2 + 1 2 ( 2 5 m r 2 ) ( v r ) 2 = 1 2 m v 2 + 1 5 m v 2 = 7 10 m v 2 (V) Write the energy conservation equation

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Chapter 10, Problem 41E

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Speed of the marble at the bottom.

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Chapter 10, Problem 40E

Chapter 10, Problem 42E

Chapter 10 Solutions

EBK ESSENTIAL UNIVERSITY PHYSICS, VOLUM

Ch. 10.1 - A wheel undergoes constant angular acceleration,...Ch. 10.2 - The forces in Figs. 10.5 and 10.6 all have the...Ch. 10.3 - Would the rotational inertia of the two-mass...Ch. 10.3 - Explain why the rotational inertia of the solid...Ch. 10.3 - The figure shows two identical masses m connected...Ch. 10.4 - A wheel is rotating at 100 rpm. To spin it up to...Ch. 10.5 - The wheels of trains, subway cars, and other rail...Ch. 10 - Do all points on a rigid, rotating object have the...Ch. 10 - A point on the rim of a rotating wheel has nonzero...Ch. 10 - Two forces act on an object, but the net force is...

Ch. 10 - Is it possible to apply a counterclockwise torque...Ch. 10 - A solid sphere and a hollow sphere of the same...Ch. 10 - A solid cylinder and a hollow cylinder of the same...Ch. 10 - A circular saw lakes a long time to stop rotating...Ch. 10 - The lower part of a horses leg contains...Ch. 10 - Given a fixed amount of a material, what shape...Ch. 10 - A ball starts from rest and rolls without slipping...Ch. 10 - Exercises and Problems Exercises Section 10.1...Ch. 10 - Whats the linear speed of a point (a) on Earths...Ch. 10 - Express each of the following in radium per...Ch. 10 - A 25-cm-diameter circular saw blade spins at 3500...Ch. 10 - A compact discs rotation varies from about 200 rpm...Ch. 10 - During startup, a power plants turbine accelerates...Ch. 10 - A merry-go-round starts front rest and accelerates...Ch. 10 - Section 10.2 Torque A 320-N frictional force acts...Ch. 10 - Prob. 19E Ch. 10 - A car tune-up manual calls for tightening the...Ch. 10 - A 55-g mouse runs out to the end of the 17-cm-long...Ch. 10 - You have your bicycle upside down for repairs. The...Ch. 10 - Section 10.3 Rotational Inertia and the Analog of...Ch. 10 - The shaft connecting a power plants turbine and...Ch. 10 - The chamber of a rock-tumbling machine is a hollow...Ch. 10 - A wheels diameter is 92 cm, and its rotational...Ch. 10 - (a) Estimate Earths rotational inertia, assuming...Ch. 10 - A 108-g Frisbee is 24 cm in diameter and has half...Ch. 10 - At the MIT Magnet Laboratory, energy is stored in...Ch. 10 - Section 10.4 Rotational Energy A 25-cm-diameter...Ch. 10 - Humankind uses energy at the rate of about 16 TW....Ch. 10 - A 150-g baseball is pitched at 33 m/s spinning at...Ch. 10 - (a) Find the energy stored in the flywheel of...Ch. 10 - A solid 2.4-kg sphere is rolling at 5.0 m/s. Find...Ch. 10 - What fraction of a solid disks kinetic energy is...Ch. 10 - A rolling ball has total kinetic energy 100 J, 40...Ch. 10 - Prob. 37E Ch. 10 - Example 10.5: The rotational inertia of a thin rod...Ch. 10 - Prob. 39E Ch. 10 - Prob. 40E Ch. 10 - Prob. 41E Ch. 10 - Prob. 42E Ch. 10 - Example 10.12: A 29.5-kg wheel with radius 40.6 cm...Ch. 10 - Prob. 44E Ch. 10 - A wheel turns through 2.0 revolutions while...Ch. 10 - Youre an engineer designing kitchen appliances,...Ch. 10 - You rev your cars engine and watch the tachometer...Ch. 10 - A circular saw spins at 5800 rpm, and its...Ch. 10 - Full-circle rotation is common in mechanical...Ch. 10 - A square frame is made from four thin rods, each...Ch. 10 - A thick ring has inner radius 12R, outer radius R,...Ch. 10 - A uniform rectangular flat plate has mass M and...Ch. 10 - The cellular motor driving the flagellum in E....Ch. 10 - Verify by direct integration Table 10.2s entry for...Ch. 10 - Prob. 55P Ch. 10 - Prob. 56P Ch. 10 - A 2.4-kg block rests on a slope and is attached by...Ch. 10 - Youve got your bicycle upside down for repairs,...Ch. 10 - A potters wheel is a stone disk 90 cm in diameter...Ch. 10 - A ships anchor weighs 5.0kN. Its cable passes over...Ch. 10 - Starting from rest, a hollow ball rolls down a...Ch. 10 - A hollow ball rolls along a horizontal surface at...Ch. 10 - As an automotive engineer, youre charged with...Ch. 10 - A solid ball of mass M and radius R starts at rest...Ch. 10 - A disk of radius R has an initial mass M. Then a...Ch. 10 - A 50-kg mass is tied to a massless rope wrapped...Ch. 10 - Each wheel of a 320-kg motorcycle is 52 cm in...Ch. 10 - A solid marble starts from rest and rolls without...Ch. 10 - A disk of radius R and thickness w has a mass...Ch. 10 - The disk in Fig. 10.29 is rotating freely about a...Ch. 10 - Prob. 71P Ch. 10 - A lighter car requires less power for a given...Ch. 10 - Calculate the rotational inertia of a solid,...Ch. 10 - A thick ring of mass M has inner radius R1 and...Ch. 10 - Prob. 75P Ch. 10 - The local historical society has asked your...Ch. 10 - Youre skeptical about a new hybrid car that stores...Ch. 10 - Figure 10.31 shows an object of mass M with one...Ch. 10 - Figure 10.32 shows an apparatus used to measure...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...Ch. 10 - Centrifuges are widely used in biology and...

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