A uniform rod of mass m [kg] and length / [m] hangs vertically from a pin through a point 1/3 from its top end. A spherical block of mass M and radius R is rigidly attached to the bottom of the rod. This pendulum is submerged in water, and thus we cannot ignore water resistance, but we will ignore buoyancy. We will model the drag on the pendulum with the damping force F₁=-by CM where b is a constant that depends on the geometry of the pendulum and the СМ viscosity of the water, but just call it b [kg/s], and VCM is the velocity of the center of mass of the pendulum. NOTE: you must model the damping force as acting through the center of mass of the pendulum, and you will have to relate the velocity of the CM to the angular velocity of the pendulum. a) Find the center of mass of the pendulum. b) Draw a complete free-body diagram for the pendulum (when the rod is displaced to the right of equilibrium and moving right) c) Use your free-body diagram to "fill out" Newton's 2nd Law for rotation and show that the motion is that of a damped harmonic oscillator when the maximum angular displacement is small. d) Write an expression for the frequency of the pendulum in [Hz] in terms of the variables given (and maybe g).

A uniform rod of mass m [kg] and length / [m] hangs vertically from a pin through a point 1/3 from its top end. A spherical block of mass M and radius R is rigidly attached to the bottom of the rod. This pendulum is submerged in water, and thus we cannot ignore water resistance, but we will ignore buoyancy. We will model the drag on the pendulum with the damping force F₁=-by CM where b is a constant that depends on the geometry of the pendulum and the СМ viscosity of the water, but just call it b [kg/s], and VCM is the velocity of the center of mass of the pendulum. NOTE: you must model the damping force as acting through the center of mass of the pendulum, and you will have to relate the velocity of the CM to the angular velocity of the pendulum. a) Find the center of mass of the pendulum. b) Draw a complete free-body diagram for the pendulum (when the rod is displaced to the right of equilibrium and moving right) c) Use your free-body diagram to "fill out" Newton's 2nd Law for rotation and show that the motion is that of a damped harmonic oscillator when the maximum angular displacement is small. d) Write an expression for the frequency of the pendulum in [Hz] in terms of the variables given (and maybe g).

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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