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A solid sphere of ice and a solid sphere of plastic are placed at the top of an inclined plane of length L and simultaneously released from rest, as shown in (Figure 1). Each has mass m and radius R. Assume that the coefficient of friction between the ice sphere and the incline is zero and that the plastic sphere rolls down the incline without slipping. Derive expressions for the following quantities in terms of L, 0, m, and R: (a) the total kinetic energy of each sphere at the bottom of the incline; (b) the translational speed of each sphere at the bottom of the incline; (c) the translational kinetic energy of each sphere at the bottom of the incline; (d) the rotational kinetic energy of each sphere at the bottom of the incline. Figure < 1 of 1 Part B Write an expression for the kinetic energy of the ice sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. ▾ View Available Hint(s) Hint 1. Translational kinetic energy Kinetic energy of an object moving without rotation equals its translational kinetic energy. Kice = Submit Part C [ΨΕΙ ΑΣΦ Kplastic = Request Answer Write an expression for the kinetic energy of the plastic sphere in terms of its translational speed v. Express your ans in terms of some or all of the variables R. and v. View Available Hint(s) ΠΫΠΙ ΑΣΦ ? 3 ?

A solid sphere of ice and a solid sphere of plastic are placed at the top of an inclined plane of length L and simultaneously released from rest, as shown in (Figure 1). Each has mass m and radius R. Assume that the coefficient of friction between the ice sphere and the incline is zero and that the plastic sphere rolls down the incline without slipping. Derive expressions for the following quantities in terms of L, 0, m, and R: (a) the total kinetic energy of each sphere at the bottom of the incline; (b) the translational speed of each sphere at the bottom of the incline; (c) the translational kinetic energy of each sphere at the bottom of the incline; (d) the rotational kinetic energy of each sphere at the bottom of the incline. Figure < 1 of 1 Part B Write an expression for the kinetic energy of the ice sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. ▾ View Available Hint(s) Hint 1. Translational kinetic energy Kinetic energy of an object moving without rotation equals its translational kinetic energy. Kice = Submit Part C [ΨΕΙ ΑΣΦ Kplastic = Request Answer Write an expression for the kinetic energy of the plastic sphere in terms of its translational speed v. Express your ans in terms of some or all of the variables R. and v. View Available Hint(s) ΠΫΠΙ ΑΣΦ ? 3 ?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Help with parts B & C would be great, thanks!

A solid sphere of ice and a solid sphere of plastic are placed at the top of an inclined plane of length I and simultaneously released from rest, as shown in (Figure 1). Each has mass m and radius R. Assume that the coefficient of friction between the ice sphere and the incline is zero and that the plastic sphere rolls down the incline without slipping. Derive expressions for the following quantities in terms of L, 0, m, and R: (a) the total kinetic energy of each sphere at the bottom of the incline; (b) the translational speed of each sphere at the bottom of the incline; (c) the translational kinetic energy of each sphere at the bottom of the incline; (d) the rotational kinetic energy of each sphere at the bottom of the incline. Figure 1 of 1 Part B Write an expression for the kinetic energy of the ice sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. View Available Hint(s) Kice Hint 1. Translational kinetic energy Kinetic energy of an object moving without rotation equals its translational kinetic energy. = Submit Part C Kplastic Submit -- ΑΣΦ Write an expression for the kinetic energy of the plastic sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. ► View Available Hint(s) = Request Answer ? VE ΑΣΦ ?
Transcribed Image Text:A solid sphere of ice and a solid sphere of plastic are placed at the top of an inclined plane of length I and simultaneously released from rest, as shown in (Figure 1). Each has mass m and radius R. Assume that the coefficient of friction between the ice sphere and the incline is zero and that the plastic sphere rolls down the incline without slipping. Derive expressions for the following quantities in terms of L, 0, m, and R: (a) the total kinetic energy of each sphere at the bottom of the incline; (b) the translational speed of each sphere at the bottom of the incline; (c) the translational kinetic energy of each sphere at the bottom of the incline; (d) the rotational kinetic energy of each sphere at the bottom of the incline. Figure 1 of 1 Part B Write an expression for the kinetic energy of the ice sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. View Available Hint(s) Kice Hint 1. Translational kinetic energy Kinetic energy of an object moving without rotation equals its translational kinetic energy. = Submit Part C Kplastic Submit -- ΑΣΦ Write an expression for the kinetic energy of the plastic sphere in terms of its translational speed v. Express your answer in terms of some or all of the variables m, R, and v. ► View Available Hint(s) = Request Answer ? VE ΑΣΦ ?
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