Required Practical 6: Investigating Force & Extension
Aim of the Experiment
- The aim of this experiment is to investigate the relationship between force and extension for a spring
- Independent variable = Force, F
- Dependent variable = Extension, e
- Control variables:
- Spring constant, k
Equipment List
- Resolution of measuring equipment:
- Ruler = 1 mm
Method
Investigating Hooke's law apparatus
- Set up the apparatus as shown in the diagram, initially without any masses hanging from the spring
- Align the marker to a value on the ruler, record this initial length of the spring
- Add the 100 mass hanger onto the spring
- Record the mass (in kg) and position (in cm) from the ruler now that the spring has extended
- Add another 100 g to the mass hanger
- Record the new mass and position from the ruler now that the spring has extended further
- Repeat this process until all masses have been added
- The masses are then removed and the entire process repeated again, until it has been carried out a total of three times, and an average length is calculated
- An example table of results might look like this:
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 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
- Plot a graph of the force against extension
- Draw a line of best fit
- 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
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
Examiner Tip
Remember - the extension measures how much the object has stretched by and can be found by subtracting the original length from each of the subsequent lengths.
A common mistake is to calculate the increase in length by each time instead of the total extension – if each of your extensions is roughly the same then you might have made this mistake!