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Spinning Mass on a Spring?
An object of mass M = 5.00 kg is attached to a spring with spring constant k = 55.0 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 omega = 1.00 radians/s. Neglect gravity and assume that the mass also rotates with an angular speed of 1.00 radians/s.
Given the angular speed of omega = 1.00 radians/s, find the radius R(omega) at which the mass rotates without moving toward or away from the origin.
Awnser is in meters....
2 Answers
- hallmanjjLv 41 decade agoFavourite answer
This is called cheating. I suggest you obtain conceptual help so as to better understand the material, not to get a number without learning the process.
- AlexanderLv 61 decade ago
ω = 1.00 rad / s
L = 0.200 m
k = 55 N/m
M = 5 kg
Force of tension
F = (R - L)k
Centrifugal force
ma = mω²R
Balance of forces:
mω²R = ma = F = (R - L)k
(k - mω²)R = Lk
Answer:
R = L k/(k - mω²) = 0.2 x 55/(55 - 5x1²) = 0.22 m
