Elastic Potential Energy

• What is the first equation related to elasticity?

  F = kE
• What does the variable K represent in the elasticity equation?

  K is the spring constant
• What does a lower spring constant indicate about an object?

  It is more elastic and easier to stretch
• What does a higher spring constant indicate about an object?

  It is stiffer and harder to stretch
• What is the second equation related to elastic potential energy?

  Elastic potential energy = $\frac{1}{2} k E^2$
• What does elastic potential energy represent?

  Energy transferred to an object as it stretches
• If 100 joules of energy is used to stretch a spring, what happens to that energy?

  It is transferred to the spring's potential energy
• How do you calculate the extension of a spring if its natural length is 0.6 meters and it stretches to 0.8 meters?

  Extension = 0.8 - 0.6 = 0.2 meters
• How do you find the spring constant using the force and extension?

  Use K = F / E
• What is the spring constant if a force of 14 Newtons causes an extension of 0.2 meters?

  K = 14 / 0.2 = 70 N/m
• What is the elastic potential energy of a spring with K = 70 N/m and E = 0.2 m?

  1.4 joules
• What does the gradient of a force vs. extension graph represent?

  The spring constant
• What does the area under the curve in a force vs. extension graph represent?

  The energy transferred to the spring
• What is the elastic limit in the context of Hooke's law?

  It is when the object stops obeying Hooke's law
• What are the key concepts of elasticity and elastic potential energy?

  • F = kE (Force and extension relationship)
  • K is the spring constant
  • Lower K means more elasticity
  • Higher K means more stiffness
  • Elastic potential energy = $\frac{1}{2} k E^2$
  • Energy transferred as the object stretches
  • Extension calculated as final length - natural length
  • Gradient of force vs. extension graph = spring constant
  • Area under graph = energy transferred
  • Elastic limit is when Hooke's law no longer applies