Four different ideal springs lie side by side on a horizontal

PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids

Problem

Four different ideal springs lie side by side on a horizontal, frictionless surface. Their properties are listed below. Spring W:

k = 400\,\text{N}\!\cdot\!\text{m}^{-1}

, extension

\Delta x = 3.0\,\text{cm}

Spring X:

k = 200\,\text{N}\!\cdot\!\text{m}^{-1}

, compression

\Delta x = 6.0\,\text{cm}

Spring Y:

k = 300\,\text{N}\!\cdot\!\text{m}^{-1}

, extension

\Delta x = 4.0\,\text{cm}

Spring Z:

k = 500\,\text{N}\!\cdot\!\text{m}^{-1}

, compression

\Delta x = 2.0\,\text{cm}

Treat each extension or compression as positive when computing

\Delta x^2

. (a) Calculate the elastic potential energy stored in each spring. Show all work, keep at least three significant figures throughout, and express each answer in joules. (b) Rank the springs from greatest to least stored elastic potential energy. If any energies are equal within rounding, state that explicitly. (c) Identify the single factor (spring constant or displacement) that had the larger influence on your ranking, and explain, using numerical evidence from part (a), why that factor dominated in this specific data set.

Related theory

Browse the problem library