chp. 9.1-9.5 #8 Please answer part B. (3.16 is NOT the correct answer) An object
ID: 1415356 • Letter: C
Question
chp. 9.1-9.5 #8
Please answer part B. (3.16 is NOT the correct answer)
An object of mass M = 5.00 kg is attached to a spring with spring constant k = 55.0 N/m whose unstretched length is L = 0.180 m, and whose far end is fixed to a shaft that is rotating with an angular speed of omega = 1.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 1.00 radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2) Given the angular speed of omega = 1.00 radians/s, find the radius R(omega) at which the mass rotates without moving toward or away from the origin. Express your answer in meters. R(omega) = 0.198 m Assume that, at a certain angular speed omega_2, the radius R becomes twice L. Find omega_2. Express your answer in radians per second. Omega_2 =Explanation / Answer
Balance of forces:
m²R = ma = F = (R - L)k
(k - m²)R = Lk
Answer:
R = L k/(k - m²)
R becomes 2*0.180=0.360
0.360=0.180*55/(55-5²)
=2.3452 rad/s
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