PHY2053 F23 Quiz 6_V3_solutions (1)

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Mechanical Engineering

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Feb 20, 2024

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PHY2053 QUIZ 6 Please Print Clearly   Follow all instructions, including:    You have 20 minutes to complete this quiz.  Show your work in the space provided for each question.   Writing a correct answer alone will not earn points.  Include correct units in intermediate steps and answers.  Do not use or refer to any additional paper or resources other than what is provided during the quiz by the instructor.  Only work shown in the space provided to answer each question will be graded. The scratch paper will not be graded or evaluated.  Be clear about what your final answer is by drawing a box around your response.  You may use a calculator. You may not use an app or program on a smartphone, tablet, or laptop.  Do not discuss the contents of this quiz or your answers with anyone.   Preserve the integrity of the testing environment:   Remove any hats or hoods, unless this direction interferes with religious customs.   Please keep noises and distractions to a minimum.  Silence and stow your cellphone.  When you are finished or when the time has elapsed, return all provided materials to your instructor.   Submitting your quiz for evaluation signifies your understanding and compliance of the instructions above, and that you completed the quiz according to the standards and intentions defined by the Student Honor Code, including that you neither provided nor received assistance on this quiz.  Name: ___________________ Section Number
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1. A newly fabricated nanotube of radius r m rolls down onto a substrate and decelerates due to the friction (no slip). Suppose the nanotube decelerates at a t m/ s 2 and finally comes to rest after N revolutions and it has a radius of r m. What is the initial angular velocity of the nanotube, in terms of a t , N, r? With a t = αr 0 2 ω i 2 = 2 α ∆ θ N = ∆θ 2 π We have ω i = 2 a t / r × 2 πN = 4 πN a t / r 3 Name: ___________________ UFID: Section Number
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2. You are an alien playing with a CD mounted on a CD player (both the player and the CD are products of your planet but somehow the CD is still in the shape of a disk). Suppose you exert a force of 150 N tangential to the outer edge of the CD, which has a mass of 75 kg, and cause the CD an angular acceleration of 3.2 rad/ s 2 . If the friction between the CD and the player can be neglected, what is the radius of the CD, in meter? With τ = FR τ = I = 1 2 m R 2 We have R = F 1 2 = 150 N 1 2 ( 75 kg )( 3.2 rad s 2 ) = 1.25 m 4