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 = 0.140 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)

Assume that, at a certain angular speed 2, the radius R becomes twice L. Find 2.

Express your answer in radians per second.

Explanation / Answer

x = stretch in the spring = R - L

spring force = centripetal force

kx = m Rw2

99 (R - 0.14) = 1 (R) (3)2

R = 0.154 m

R = 2 L = 2 x 0.14 = 0.28 m

x = stretch in the spring = R - L = 2L - L = L = 0.14 m

M = mass of object = 1 kg

k = spring constant = 99 N/m

spring force = centripetal force

kx = m Rw22

99 (0.14) = 1 (0.28) w22

w2 = 7.04 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.