An object of mass M = 2.00 kg is attached to a spring with spring constant k = 5

Question

An object of mass M = 2.00 kg is attached to a spring with spring constant k = 550 N/m whose unstretched length is L = 0.140 m , and whose far end is fixed to a shaft that is rotating with an angular speed of = 5.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

Part A

Given the angular speed of = 5.00 radians/s , find the radius R() at which the mass rotates without moving toward or away from the origin.

Express your answer in meters.

Thanks!

Explanation / Answer

we use centripetal force = spring force
m²R = k(R - 0.140m)
2 * (5.00)² * R = 550 * (R - 0.140)
50 R = 550R -77
77= 550R +50R

600R= 77

R= 77/600

R = 0.128 m

so radius= 0.128 m

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