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An iron block of the mass 1 kg is suspended on a spring of the spring constant 140 N/m and merged...

Question:

An iron block of the mass 1 kg is suspended on a spring of the spring constant 140 N/m and merged into a vessel with 8 liters of water. The mass is displaced by 10 cm from its equilibrium position and released.

(a) How much energy in J has been dissipated by the time the mass comes to rest?

(b) What is the mass of water in the container in kg?

(c) Assuming that the water with the block are thermally isolated from their surroundings, by how much will their temperature increase?

Elastic Potential Energy of a Compressed Spring

Force has to be applied on a spring to compress or stretch it. The magnitude of the force required for stretching or compressing the spring is proportional to the length by which the spring is compressed or elongated. The work done in compressing or stretching the spring is stored as potential energy in the compressed or stretched spring. On releasing the spring from compressed or stretched position, the stored elastic potential energy of the spring will be released.

  • If a block of mass m is attached to a compressed spring is released it will execute simple harmonic motion at the expense of the elastic potential energy stored inn the compressed spring.
  • The elastic potential energy stored in the compressed spring of spring constant k is {eq}U = \dfrac { 1 } { 2 } k x ^2 {/eq}. Here x is the length by which the spring is compressed.

Answer and Explanation:

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Given data

  • Mass of the iron block attached to the spring {eq}m = 1 .0 \ kg {/eq}
  • Spring constant of the spring {eq}k = 140 \ N/m {/eq}
  • Distance...

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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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