AQA GCSE FOUNDATION Physics: Investigating the Relationship Between Force and Extension in a Spring

Investigating the Relationship Between Force and Extension in a Spring

This experiment investigates Hooke's Law, which describes the relationship between the force applied to a spring and its resulting extension. You'll learn how to measure spring extension under different weights, plot a force-extension graph, and determine the spring constant (k).

Materials:

• Spring
• Weights (various masses)
• Ruler or measuring tape
• Stand or clamp to hold the spring
• Weight hanger
• Graph paper or spreadsheet software

Procedure:

1. Set up the Experiment:

   • Securely attach the spring to a stand or clamp.
   • Hang the weight hanger from the spring.
   • Record the initial length of the spring (without any weights) as "L?."

2. Apply Weights and Measure Extension:

   • Start by attaching the smallest weight to the weight hanger.
   • Measure the new length of the spring (L?).
   • Calculate the extension by subtracting the initial length (L?) from the new length (L?).
   • Repeat steps 2-3 for several different weights, recording the weight (W) and the corresponding extension (e) in a table.

3. Calculate Force:

   • For each weight, calculate the force (F) applied to the spring using the formula:
     • F = W * g, where g is the acceleration due to gravity (approximately 9.8 m/s²).

4. Plot a Graph:

   • Plot the force (F) on the y-axis and the extension (e) on the x-axis.
   • Ensure the graph is correctly labeled and uses appropriate scales.

5. Determine the Spring Constant (k):

   • Hooke's Law states that the force applied to a spring is directly proportional to its extension:
     • F = k * e, where k is the spring constant.
   • The spring constant is the slope of the force-extension graph.
   • Choose two points on the linear portion of the graph and calculate the slope using:
     • k = (F? - F?) / (e? - e?)

6. Analyze Results:

   • Observe the shape of the graph. The relationship between force and extension should be linear for a certain range of forces.
   • Determine the spring constant (k) and its units (N/m).
   • Discuss the limits of Hooke's Law. The graph may deviate from linearity beyond a certain extension, indicating the spring has reached its elastic limit.

Understanding Elastic Potential Energy:

• When a spring is stretched or compressed, it stores energy called elastic potential energy.
• This energy is proportional to the square of the extension:
  • Elastic Potential Energy (EPE) = ½ * k * e²

Safety Precautions:

• Always use caution when working with weights and springs.
• Ensure the stand or clamp is secure to avoid the spring falling.

Further Investigations:

• Investigate the effect of using different springs with varying spring constants.
• Explore the relationship between elastic potential energy and the extension of the spring.
• Investigate the elastic limit of the spring and how it relates to Hooke's Law.