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A 0.250 kg mass is attached to a horizontal spring of spring constant 140 N/m, supported by a...

Question:

A 0.250 kg mass is attached to a horizontal spring of spring constant 140 N/m, supported by a frictionless table. A physics student pulls the mass 0.12 m from equilibrium, and the mass is then let go. Assume no air resistance and that it undergoes simple harmonic motion.

a) Calculate the work done by the student on the mass in pulling it a distance of 0.12 m.

b) Using conservation of energy principles, calculate the maximum speed of the mass.

Horizontal Spring Block System

Every spring has stiffness constant or spring constant and it can be defined as the force required to compress or stretch the spring per unit length. A stretched or compressed spring has certain elastic potential energy stored in it. The elastic potential energy stored in the spring is equal to the work done in compressing or stretching the spring against the stiffness of the spring.

  • According to Hook's law, within the elastic limit, the force F required to stretch a spring of spring constant k by a distance x can be expressed as {eq}F = k x {/eq}
  • The force required to compress the spring varies with the length of compression and the work done in compressing the spring by an extent x can be expressed as {eq}W = U = \dfrac { 1 } { 2 } k x ^2 {/eq}

Answer and Explanation:

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Given data

  • Mass attached to the horizontal spring resting on the table {eq}m = 0.250 \ \rm { kg } {/eq}
  • Spring constant of the spring {eq}k = 140 \...

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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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