An object of mass M = 3.00 kg is attached to a spring with spring constant k = 5

Question

An object of mass M = 3.00 kg is attached to a spring with spring constant k = 528 N/m whose unstretched length is L = 0.120 m, and whose far end is fixed to a shaft that is rotating with an angular speed of omega = 4.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 4.00 radians/s as shown. Assume that, at a certain angular speed omega_2, the radius R becomes twice L. Find omega_2.

Explanation / Answer

By F = mv^2/r = kx =>3 x r x (omega)^2 = kx [by v = r x omega] =>3 x L x 16= 528 x [L-0.12] =>48L = 528L - 63.3 =>576L = 63.3 =>L = 0.1098 m mr?² = kx m = 3.00 kg r = 2L = 2(0.1098m) = 0.219 m k = 528 N/m x = 2L - 0.120m = 0.0997m Solve for ?: ?² = kx / mr ? = v(kx / mr) ? = v[(528N/m)(0.0997m) / (3kg)(0.219m)] ? = 8.9 rad/s

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