An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1

Question

An object of mass M = 4.00 kg is attached to a spring with spring constant k = 176 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 = 2.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

Part A

Given the angular speed of = 2.00 radians/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

mass m=4 kg

spring constant K=176 N/m

streached length L=0.140 m

this concept belongs to the work energy and power

first we find the velocity

according to the work energy therom

w=1/2mv^2-1/mu^2

1/2KL^2=1/2mv^2

1/2*176*[0.14]^2=1/2 *4*v^2

v=0.8624 m/s

now we find the radius of the block

V=rW

0.8624=r*2

R=0.4312 m

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