An object of mass M = 1.00 kg is attached to a spring with spring constant k = 9

Question

An object of mass M = 1.00 kg is attached to a spring with spring constant k = 99.0 N/m whose unstretched length is L = 0.200 m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 3.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 3.00 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  ? = 3.00 radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.

Explanation / Answer

Mass = M = 1Kg

Spring constant = K = 99N/m

Length = L = 0.2m

SOlution

In order to find radius we has to analyse the forces acting upon the mass. The forces are

Centripetal force will be provided by the elastic spring force.

MV2 / R = Kx

R = MV2/ Kx

R = MR2 w2 / Kx

R = Kx / Mw2 ..............1

Here x = R-0.2 .................2

Putting equ2 in equa1

R = K(R-0.2) / Mw2

R- KR = -0.2 K / Mw2

R(1-K) = -0.2K / Mw2

R = -0.2(99) / 1(3)2

R = 2.2m

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