Suppose that 5\ \rm{J} of work is needed to stretch a spring from its natural length of 28\...

Question:

Suppose that {eq}5\ \rm{J} {/eq} of work is needed to stretch a spring from its natural length of {eq}28\ \rm{cm} {/eq} to a length of {eq}49\ \rm{cm} {/eq}.

a. How much work is needed to stretch the spring from {eq}36\ \rm{cm} {/eq} to {eq}44\ \rm{cm} {/eq}? (Round your answer to two decimal places.)

b. How far beyond its natural length will a force of {eq}20\ \rm{N} {/eq} keep the spring stretched? (Round your answer one decimal place.)

Hooke's Law

Hooke's law gives the relationship between the restoring force of a spring and the displacement of the spring from its equilibrium position. The direction of the restoring force is opposite to the direction of the displacement of the spring and it is indicated by the negative sign in the equation.

Answer and Explanation:

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Question (a)

Given:

  • {eq}W_1 = 5 \,\rm{J} {/eq}
  • {eq}W_2 = ? {/eq}
  • {eq}x_0 = 0 \,\rm{m} {/eq}
  • {eq}x_1 = 49 - 28 = 21 \,\rm{cm} = 0.21...

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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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