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A block of mass M hangs from a rubber cord. The block is supported so that the cord is not...

Question:

A block of mass M hangs from a rubber cord. The block is supported so that the cord is not stretched. The unstretched length of the cord is L_0 and its mass is m, much less than M. The "spring constant" for the cord is k. The block is released and stops at the lowest point. (Use L_0 for L0, M, g, and k as necessary.)

(a) Determine the tension in the cord when the block is at this lowest point.

(b) What is the length of the cord in this "stretched" position?

(c) Find the speed of a transverse wave in the cord, if the block is held in this lowest position.

Hooke's Law

According to Hooke's law, when a spring is compressed or stretched by an amount {eq}x {/eq}, the force of restoration exerted by the spring is proportional to the amount of displacement of the spring and is given by: {eq}F \ = \ - \ k \times x \\ {/eq}

Where:

{eq}k {/eq} - is the spring constant

Transverse waves on a string with tension {eq}T {/eq} and mass per unit length {eq}\mu {/eq} travels at a speed given by: {eq}v \ = \ \sqrt{\dfrac{T}{\mu}} {/eq}

Answer and Explanation: 1

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Given:

  • Mass of the block: {eq}M {/eq}
  • Length of unstretched cord: {eq}L_0 {/eq}
  • Mass of the rubber cord: {eq}m {/eq}
  • Spring constant:...

See full answer below.


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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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