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A steel spring is hung vertically. Using a ruler, the lower end of the spring was measured to be...

Question:

A steel spring is hung vertically. Using a ruler, the lower end of the spring was measured to be 25.0cm from its upper end. However, when an object of mass 0.500kg it attached to the lower end of the spring the spring stretches to a new length of 45.0cm. With the aid of a diagram and with a detailed explanation of your reasoning determine:

(a) The stiffness constant k of the spring.

(b) The additional weight needed to extend the spring to 50.0cm

(c) The force needed to extend the spring by 50.0mm from its natural length.

Hooke's Law:

When the length of the spring is changed either by stretching or compressing it, a restoring force is developed in it which tries to bring spring back to its normal state. According to the Hooke's law, the restoring force developed in the spring is directly proportional to the change in the length of the spring and is oppositely directed. Mathematically:

{eq}F_{restoring} \propto -x\\ or\\ F _{restoring} = -kx {/eq}

here:

  • k is the spring constant
  • x is the change in the length of the spring

Answer and Explanation: 1

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Given data:

  • {eq}l_0 = 25\ cm {/eq} is the natural length of the spring
  • {eq}m = 0.500\ kg {/eq} is the mass of the object attached to the spring
  • {eq...

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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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