Investigating Force & Extension

• Aim of the Experiment

  •  The aim of this experiment is to investigate the relationship between force and extension for a spring
• Variables:

  • Independent variable = Force, F
  • Dependent variable = Extension, x
  • Control variables:
  • Spring constant, k
• Equipment List:

  
• • Resolution of measuring equipment:
  • Ruler = 1 mm
• Investigating Hooke's law apparatus:

  
• Method: (part 1)

  1. Set up the apparatus as shown in the diagram, initially without any masses hanging from the spring
  2. Align the marker to a value on the ruler, record the initial length of the spring
  3. Add the 100 g mass hanger onto the spring
  4. Record the mass (in kg) and position (in cm) from the ruler now that the spring has extended
• Method: (part 2)

  1. Add another 100 g to the mass hanger
  2. Record the new mass and position from the ruler now that the spring has extended further
  3. Repeat this process until all masses have been added
  4. The masses are then removed and the entire process is repeated again until it has been carried out a total of three times, and an average length is calculated
• Analysis of Results:

  • The force, F added to the spring is the weight of the mass
  • The weight is calculated using the equation:

  W = mg
• • Where:
  • W = weight in newtons (N)
  • m = mass in kilograms (kg)
  • g = gravitational field strength on Earth in newtons per kg (N/kg)
• • Therefore, multiply each mass by gravitational field strength, g, to calculate the force, F
  • The force can be calculated by multiplying the mass (in kg) by g = 10 N/kg
  • The extension of the spring is calculated using the equation:

  Final length – Original length
• • The final length is the length of the spring recorded from the ruler when the masses were added
  • The original length is the length of the spring when there were no masses
• 1. Plot a graph of the force against extension
  2. Draw a line of best fit
  3. If the graph has a linear region (is a straight line), then the force is proportional to the extension and the spring obeys Hooke's law for these forces and extension
• Example force-extension graph for a spring that obeys Hooke's law:

  
• Evaluating the Experiment:

  Systematic Errors:

  • Make sure the measurements on the ruler are taken at eye level to avoid parallax error
• Random Errors:

  • The accuracy of such an experiment is improved with the use of a pointer (a fiducial marker)
• Fiducial marker to measure the extension more accurately:

  
• • Wait a few seconds for the spring to fully extend when a mass is added, before taking the reading for its new length
  • Make sure to check whether the spring has not gone past its limit of proportionality otherwise, it has been stretched too far and will stop obeying Hooke's law