Problem: An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 5.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s.Given the angular speed of ω = 5.00 radians/s, find the radius R(ω) at which the mass rotates without moving toward or away from the origin.

FREE Expert Solution

Hooke's law:

Centripetal force:

$\overline{){{\mathbf{F}}}_{{\mathbf{c}}}{\mathbf{=}}{\mathbf{m}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{m}}{\mathbf{r}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

The force on the spring is equal to the centripetal force.

k•Δx = mrω2

Problem Details

An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/m whose unstretched length is L = 0.170 m, and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 5.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s.

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