5.3.4 Work Done on a Spring

• What happens when a force is applied to a spring?

  Work is done on the spring, causing it to stretch or compress.
• What is stored in a spring when work is done on it?

  Elastic potential energy is stored in the spring.
• How is the work done on a spring calculated?

  The work done is equal to the elastic potential energy stored in the spring.
• What is the formula for calculating work done on a spring according to Hooke's Law?


  W = \frac{1}{2} k x^2
• What does the variable 'W' represent in the formula W = \frac{1}{2} k x^2?

  'W' represents the work done in Joules (J).
• What does the variable 'k' represent in the formula W = \frac{1}{2} k x^2?

  'k' is the spring constant measured in Newtons per meter (N/m).
• What does the variable 'x' represent in the formula W = \frac{1}{2} k x^2?

  'x' is the extension or compression from the natural length of the spring in meters (m).
• What does Hooke's Law state about the force needed to stretch or compress a spring?

  The force needed is proportional to the extension of the spring.
• How is work done calculated when stretching or compressing a spring?

  Work done is calculated by integrating the force over the distance stretched or compressed.
• What is the result of integrating Hooke's Law to find work done on a spring?


  The result is W = \frac{1}{2} k x^2.
• What is elastic potential energy in relation to a spring?

  It is the work done on the spring stored as energy when deformed.
• What does a higher spring constant (k) indicate about a spring?

  A higher spring constant indicates a stiffer spring that requires more force for the same extension.
• What is the definition of extension in the context of springs?

  Extension is the amount the spring is stretched or compressed from its natural length.
• What are some practical examples of work done on springs?

  • Springs in Toys: Energy is stored when a spring is pulled or compressed.
  • Shock Absorbers: Springs absorb and store energy from road bumps.
  • Mechanical Scales: Springs measure weight based on extension proportional to force applied.
• What does a force-extension graph for a spring indicate in the linear region?

  The graph is a straight line, indicating that Hooke’s Law is followed.
• What does the area under the force-extension graph represent?

  The area under the graph represents the elastic potential energy.
• How does the area under a linear force-extension graph relate to the formula for work done on a spring?


  The area forms a triangle with base x and height F, matching \frac{1}{2} k x^2.
• What is the summary of work done on a spring?

  • Work Done: Energy transferred when a spring is stretched or compressed.
  • Formula: W = \frac{1}{2} k x^2.
  • Elastic Potential Energy: Stored energy in the spring when deformed.
  • Spring Constant (k): Measure of the stiffness of the spring.
  • Extension (x): Amount by which the spring is stretched or compressed.