Learning Goal Consider The Rigid Body Shown In The Figure Figure 1 An Arbitrary Eth Particle Of The Body Having Mas 1 (72.46 KiB) Viewed 20 times
Learning Goal: Consider the rigid body shown in the figure. (Figure 1) An arbitrary eth particle of the body, having mass dm, is located a distance r from an arbitrary point P in the inertial 2-y reference plane. If, at the instant shown, the particle has a velocity vị, then the particle's kinetic energy is T;= }(dm)? The kinetic energy of the entire body is found by summing similar equations for each particle in the body. As the number of particles increases, by letting the size of each particle go to an infinitesimally small volume, the sum becomes an integral and the kinetic energy of the body is T= 3 Sm dm v When the body is rotating, it is convenient to express the kinetic energy of the body in terms of the velocity of P. Some mathematical manipulation yields: T= zmu} – (up), wym+ (up)wăm + Ipw? where 7 andy are the horizontal and vertical distances, respectively, from P to the mass center of the body, G. In the special case when P coincides with G, the kinetic Figure < 1 of 3 Vi (0) r y VP Р
Part A - Kinetic Energy of a Pulley and Weight System Consider the pulley and weight system shown in the figure. (Figure 2) The pulley has mass 14.0 kg, outer radius R. = 250 mm, inner radius R; = 200 mm, and radius of gyration ko = 220 mm. Cylinder A weighs 67.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when w=47.0 rad/s clockwise, what is the kinetic energy of the system? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) D'HÅ ? T= Value Units
Part B - Kinetic Energy of a Rolling Bicycle Wheel The bicycle wheel shown in the figure rolls without slipping. (Figure 3) The wheel has a weight of 27.0 N, a radius of s=27.0 cm, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v=4.70 m/s. Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) μΑ ? T= Value Units
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