Investigating Force & Extension (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Extended tier only

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, 
• Dependent variable = Extension,
• Control variables:
  • Spring with spring constant,

Equipment

Equipment list

Equipment	Purpose
Clamp stand, boss and clamp	To apply an upward force on the spring
Ruler	To measure the extension of the spring
Spring	To measure the extension of
6 × 100 g masses	To apply a downward force on the spring
100 g mass hanger	To hold the additional masses
Pointer	To accurately read the extension from the ruler

Resolution of measuring equipment:

• Ruler = 1 mm

Method

Equipment for investigating the extension of a spring

Fixing the ruler to the clamp stand will reduce movement in the ruler and, therefore, reduce errors in measurement

1. Align the marker to a value on the ruler with no mass added to the spring, and record this initial length of the spring
2. Add the 100 g mass hanger onto the spring
3. Record the mass (in kg) and position (in cm) from the ruler now that the spring has extended
4. Add another 100 g to the mass hanger
5. Record the new mass and position from the ruler now that the spring has extended further
6. Repeat this process until all masses have been added
7. 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

Example results table

A suitable table of results must contain space for the calculations of force and extension

Analysis of results

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

• Where:
  • = weight, measured in newtons (N)
  • = mass, measured in kilograms (kg)
  • = gravitational field strength, measured in newtons per kilogram (N/kg)
• Therefore, multiply each mass by gravitational field strength, g = 9.8 N/kg, to calculate the force, F
• The extension of the spring is calculated using the equation:

• 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 in this region

Example force-extension graph

The graph is a straight line that goes through the origin which shows that the extension of the spring is directly proportional to the force applied  (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 precision of the experiment is improved with the use of a pointer at the bottom of the spring
• Wait a few seconds for the mass to become stationary after it is added, before taking the readings for its length
• Check that the spring has not gone past its limit of proportionality otherwise, it has been stretched too far and will no longer obey this relationship
• Make sure the measurements are taken from the same point on the bottom of the spring every time

Safety considerations

• Wear goggles during this experiment in case the spring snaps
• Stand up while carrying out the experiment making sure no feet are directly under the masses
• Place a mat or a soft material below the masses to prevent any damage in case they fall
• Use a G clamp to secure the clamp stand to the desk so that the clamp and masses do not fall over
  • As well as this, place each mass carefully on the hanger and do not pull the spring too hard that it breaks or pulls the apparatus over