Question

Chapter 09, Problem 49 Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 1.39 rad/s. The mass m of each object and its perpendicular distance r from the Z axis are as follows: (1) m = 7.30 kg and r - 2.80 m, (2) m2 = 9.60 kg and 2 = 3.50 m, (3) m3 = 5.20 kg and 3 = 4.00 m. Find the tangential speed of (a) object 1, (b) object 2, and (c) object 3. (d) Determine the total kinetic energy of this system using the expression KE= 1012 2032 + 33(e) Find the rotational kinetic energy of the system using the relationIw to verify that the answer is the same as that in (d). (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units Click If you would like to Show Work for this question: Open Show Work LINK TO TEXT

Please make sure the answer is clear and stated with units. thanks!

Answer 1

Given, angular Speed of each object. W = 1.39 radle mi = 7.3kg m₂ = 9.6kg m₂ = 5.2kg N = 2.8m N2 = 3.5m 3 = 4.om of an object Tangential speed = r.w (a). V, - ri.w b) No - V2.60 = 2.8.(1.39) Vo = 3.892 m/s - 3.5(1.39) V2 = 4.865 m/s . . (C) 2 = r₂. W = 4.(1.39) 13:5.56 mis (d). Total kinetic energy of the system KE = 2 movint ma vart / mg v gr : = { (73)(3-542)* {(9.6)(4:865)+_(52)(5.5" KE = 249.27 lg mys" (ov) KE=249.27 Joules 10). rotational kinetic energy (KE) Not = 1/2 Iw' I= morit maret margt

I- 7.3 (2.8)+(9:6) (3.5)*+ (5.2) (4) I= 258.032 kg mo A. (KE) Not = 1 / 2 I wr = 4(258-032)(1139) (KE) not = 249.27 Joules - V Therefore, the kinetic energy of System of particles is same as the rotational kinetic energy of given objects.