An object of mass M = 4.00kg is attached to a spring with spring constant k = 11

Question

An object of mass M = 4.00kg is attached to a spring with spring constant k = 1100N/m whose unstretched length is L = 0.110m , and whose far end is fixed to a shaft that is rotating with an angular speed of omega = 5.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)http://session.masteringphysics.com/problemAsset/1011198/17/6172_a.jpg Part A Given the angular speed of omega = 5.00radians/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) =

Explanation / Answer

ou need to find the radius where the force on the mass gives the centripetal acceleration that is needed to move in a circle without changing the radius. Centripetal accel = r omega^2 Force in spring = k(r-L) whre L is the unstretched length So r omega^2 = k(r-L)/m m r omega^2 = kr - kL (m omega^2 - k)r = -kL r = kL / (k - m omega^2) = 1100 x 0.110 / (1100 - 4x5^2) = 0.121 m

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