An object of mass M = 2.00 k g is attached to a spring with spring constant k =

Question

An object of mass M = 2.00kg is attached to a spring with spring constant k = 550N/m whose unstretched length is L = 0.130m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 5.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

Figure 1: http://session.masteringphysics.com/problemAsset/1011198/17/6172_a.jpg

Figure 2: http://session.masteringphysics.com/problemAsset/1011198/17/6172_b.jpg

Given the angular speed of ? = 5.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin. I got this answer correct: 0.143m

I need help with the second part.

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

Explanation / Answer

speed = v = r*w

w = 5 rad/sec = 286.48 degree/sec

r = 0.143 m..(u founded)

so,

v1= w1r1= 5*0.143 = 0.715 m/s

now,

L = R*m*v

we have,

R2 = 2*L2

==> L2 = 2R2 = R2*mv2

==> v2 = 2/m = 2/2 = 1 m/s

By conservation of momentum

L1 = L2

m*v1*R1 = m*v2*R2

==> R2 = v1*R1/v2

==> R2 = 0.715*0.143/1 = 0.102245 m

so,

w2 = v2/R2

w2 = 1/(0.102245)

w2 = 9.78 rad/sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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