A 0.05 kg toy is made up of a spring of constant 466 N/m . When you place the toy on the...

Question:

A {eq}0.05\, kg {/eq} toy is made up of a spring of constant {eq}466\, N/m {/eq}. When you place the toy on the floor, cock the spring {eq}5\, cm {/eq} and release it, the toy jumps upwards.

What is the spring potential energy in joules stored in the toy when sitting on the floor with a cocked spring? Use {eq}g = 10\, m/s^2 {/eq}.

Spring Potential Energy:

When spring is deformed then due to the external work done in deforming it, spring potential energy is generated. This spring potential energy is equal to the work done on it. The spring potential energy is proportional to the square of the deformed length.

Answer and Explanation: 1

Given:

The mass of the toy, {eq}m = 0.05\ kg {/eq}

The spring constant is, {eq}k = 466\ N/m {/eq}

The deformation is, {eq}x = 0.05\ m {/eq}

The spring potential energy is,

$$\begin{align} SPE &= m\ g\ x + 0.5\ k\ x^2\\ SPE &= 0.05\times 10\times 0.05 + 0.5\times 466\times 0.05^2\\ SPE &= 0.6075\ J\\ \end{align} $$


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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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