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Problem: An object of mass M is attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with angular speed ω. Neglect gravity and assume that the mass rotates with angular speed omega as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2) What is happening to the spring as the angular velocity approaches ωcrit? A. The spring stretches linearly then breaks at ω = ωcrit. B. The value of ωcrit is so large that the spring will behave linearly for any practically attainable ω. C. As ωc approaches ωcrit the spring stops behaving linearly and begins to act more like an unstretchable rod until it eventually breaks.

FREE Expert Solution

In this problem, we are required to explain the behaviour of springs. 

A spring extends linearly until it reaches its elastic limit.

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Problem Details

An object of mass M is attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with angular speed ω. Neglect gravity and assume that the mass rotates with angular speed omega as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2) 

What is happening to the spring as the angular velocity approaches ωcrit

A. The spring stretches linearly then breaks at ω = ωcrit

B. The value of ωcrit is so large that the spring will behave linearly for any practically attainable ω. 

C. As ωc approaches ωcrit the spring stops behaving linearly and begins to act more like an unstretchable rod until it eventually breaks.

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What scientific concept do you need to know in order to solve this problem?

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Based on our data, we think this problem is relevant for Professor Morin, Yacoby, Witkov & Zengel's class at HARVARD.