An object of mass M = 3.00kg is attached to a spring with spring constant k = 29

Question

An object of mass M = 3.00kg is attached to a spring with spring constant k = 297N/m whose unstretched length is L = 0.150m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 3.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 3.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

Given the angular speed of ? = 3.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.

Express your answer in meters.

Figure 1

Figure 2

An object of mass M = 3.00kg is attached to a spring with spring constant k = 297N/m whose unstretched length is L = 0.150m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 3.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 3.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2) Given the angular speed of ? = 3.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin. Express your answer in meters.

Explanation / Answer

centripetal force = tension force in the spring

centripetal force Fc = m*R*w^2

Tension in spring Ft = k*(R - L )

m*R*w^2  = k*(R - L)

m*Rw^2 = k*R - k*L

k*L = k*R - m*Rw^2

k*L = R (k - m*w^2)

R = k*L / (k - m*w^2)

k = 297 N/m

L = 0.150 m

M = 3 Kg

w = 3 rad/s

R = k*L / (k - m*w^2)

R = 297*0.15 / ( 297 - 3*3^2)

R = 0.165 m

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