Three objects lie in the x, y plane. Each rotates about the z axis with an angul
ID: 1287968 • Letter: T
Question
Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 6.54 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows:
(1) m1 = 6.30 kg and r1 = 2.04 m,
(2) m2 = 3.76 kg and r2 = 13.70 m,
(3) m3 = 2.73 kg and r3 = 2.91 m.
(a) Find the tangential speed of each object. vT1 = Correct: Your answer is correct. m/s vT2 = Correct: Your answer is correct. m/s vT3 = Correct: Your answer is correct. m/s
(b) Determine the total kinetic energy of this system using the expression KE = ½m1v12 + ½m2v22 + ½m3v32. Incorrect: Your answer is incorrect. J
(c) Obtain the moment of inertia of the system. Incorrect: Your answer is incorrect. kg · m2
(d) Find the rotational kinetic energy of the system using the relation KER = ½I2 to verify that the answer is the same as the answer to (b). Incorrect: Your answer is incorrect. J
Explanation / Answer
a) V1 = 2.04*6.54 = 13.3416 m/s
V2= 13.7*6.54 = 89.598 m/s
V3 = 2.91*6.54 = 19.0314 m/s
b) KE = (0.5*6.3*13.3416*13.3416)+(0.5*3.6*89.598*89.598)+(0.5*2.73*19.0314*19.0314) = 15505.1325662994 J
c) I = m1r1^2 + m2r2^2+m3*r2^2
I = (6.3*2.04*2.04)+(3.76*13.7*13.7)+(2.73*2.91*2.91) = 755.050393 kg m^2
d) KEr = 0.5*I*w^2 = 15950.439552125 J
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