A spring has a force constant of 500.0 N / m. Show that the potential energy stored in the sprin

step 1 question as sparing have a spilling constant k is given and we have to calculate the potential e

A spring has a force constant of 500.0 N / m. Show that the...

A spring has a force constant of $500.0 \mathrm{N} / \mathrm{m}$. Show that the potential energy stored in the spring is as follows: a. $0.400 \mathrm{J}$ when the spring is stretched $4.00 \mathrm{cm}$ from equilibrium b. 0.225 J when the spring is compressed $3.00 \mathrm{cm}^{-}$ from equilibrium c. zero when the spring is unstretched (See Sample Problem $5 \mathrm{D}$.)

A spring has a force constant of $500.0 \mathrm{N} / \mathrm{m}$. Show that the potential energy stored in the spring is as follows:
a. $0.400 \mathrm{J}$ when the spring is stretched $4.00 \mathrm{cm}$ from equilibrium
b. 0.225 J when the spring is compressed $3.00 \mathrm{cm}^{-}$ from equilibrium
c. zero when the spring is unstretched (See Sample Problem $5 \mathrm{D}$.)

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Key Concepts

Unit Conversion

Unit conversion is crucial when using physical formulas to ensure consistency in measurements. Converting units, such as changing centimeters to meters in the displacement term x in the formula for elastic potential energy, is necessary to obtain accurate and meaningful results in calculations.

Hooke's Law

Hooke's Law establishes a linear relationship between the force exerted by a spring and its displacement from equilibrium, expressed as F = -kx. This principle is essential for understanding spring dynamics and how the restoring force and stored energy are derived in elastic systems.

Elastic Potential Energy

Elastic potential energy is the energy stored in deformable objects when they are displaced from their equilibrium position. In the context of springs, this energy is calculated using the formula U = 1/2 k x², where k is the spring constant and x is the displacement. This concept is fundamental in analyzing energy conservation in systems involving elastic deformations.

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