5.3.2 Elastic Potential Energy

• What does 'x' represent in the elastic potential energy formula?

  Extension or compression
• Stretching a spring beyond its elastic limit results in the energy being converted to heat.


  True
• Steps involved in storing elastic potential energy in a spring

  1️⃣ Stretch the spring by applying force

  2️⃣ Work is done in stretching the spring

  3️⃣ Energy is stored as elastic potential energy

  4️⃣ Release the spring to convert energy
• A higher spring constant (k) indicates a stiffer spring.
• What unit is used to measure extension in a spring?

  Meters
• What happens if a spring is stretched beyond its elastic limit?

  It loses its elasticity
• What does the spring constant (k) measure in a spring?

  Stiffness of the spring
• What is the relationship between force and extension in a spring according to Hooke's law?

  $F =$$kx$
• The work done in stretching a spring by a distance dx is given by dW = F dx.
• What is the final expression for the total work done in stretching a spring from x = 0 to x = X?

  $W =$$\frac{1}{2} kX^{2}$
• The elastic potential energy (EPE) in a stretched spring is equal to the work done in stretching it.

  True
• The work done in stretching a spring is stored as elastic potential energy.


  True
• The formula for elastic potential energy is \(\frac{1}{2} kx^2\)
• Match the variable with its unit in elastic potential energy:

  Elastic Potential Energy ↔️ Joules (J)

  Spring Constant ↔️ Newtons per meter (N/m)

  Extension ↔️ Meters (m)
• Hooke's law states that the force required to stretch a spring is proportional to its extension and spring constant.


  True
• Hooke's law is expressed as \(F = \)kx
• The extension (x) measures how far the spring is stretched from its original length
• Exceeding the elastic limit of a spring can cause permanent deformation.

  True
• What law is used to derive the formula for elastic potential energy?

  Hooke's Law
• The work done in stretching a spring from 0 to x is equal to \(\frac{1}{2} kx^{2}\)
• Elastic potential energy is measured in joules (J).


  True
• What unit is the spring constant measured in?

  Newtons per meter (N/m)
• The extension of a spring is measured in meters
• Elastic potential energy is stored in an object when it is stretched or compressed
• What does EPE stand for in physics?

  Elastic Potential Energy
• The spring constant measures the stiffness of a spring.


  True
• What is the formula for elastic potential energy?

  EPE = \frac{1}{2} k x^2</latex>
• The spring constant (k) is measured in N/m
• A higher spring constant (k) indicates that more force is needed to stretch or compress the spring.
• The extension (x) of a spring refers to how much it has been stretched beyond its original length.

  True
• Why is elastic potential energy stored in a stretched spring?

  Work done in stretching
• When you stretch a spring, you exert a force over a distance, and this work is stored as elastic potential energy.
• What is the formula for elastic potential energy (EPE) in a stretched spring?

  $EPE =$$\frac{1}{2} k x^{2}$
• Match the variable in the EPE formula with its unit:

  EPE ↔️ Joules (J)

  k ↔️ Newtons per meter (N/m)

  x ↔️ Meters (m)
• Stretching a spring beyond its elastic limit will permanently deform it.


  True
• When a spring is stretched beyond its elastic limit, the stored energy is converted into heat.
• Steps in deriving the formula for elastic potential energy

  1️⃣ Apply Hooke's law: F = kx

  2️⃣ Calculate work done: dW = F dx = kx dx

  3️⃣ Integrate from x = 0 to x = X: W = $\int_{0}^{X} kx \, dx$

  4️⃣ Simplify the integral: W = $\frac{1}{2} kX^{2}$

  5️⃣ Equate work done to elastic potential energy: EPE = $\frac{1}{2} kx^{2}$
• The elastic potential energy (EPE) in a stretched spring is given by EPE = $\frac{1}{2} kx^{2}$.
• The total work done in stretching a spring from its unstretched length to a final stretched length \(X\) is \(\frac{1}{2} kX^2\)
• Steps to derive the formula for elastic potential energy

  1️⃣ Determine the work done to stretch the spring by dx

  2️⃣ Integrate the work done from x = 0 to x = X

  3️⃣ Equate the work done to the elastic potential energy