Investigating Force & Extension (Cambridge (CIE) IGCSE Physics): Revision Note

Investigating springs

Aim of the experiment

• The aim of this experiment is to investigate the relationship between the load applied to a spring and its extension

Variables

• Independent variable = Load, $L$(The force applied, $F$, to the spring is referred to as the load)

• Dependent variable = Extension, $e$

• Control variables:

  • The same spring throughout (so the spring constant, $k$, does not change)

  • The same reference point on the spring for every reading

Equipment

Equipment list

• Resolution of measuring equipment:

  • Ruler = 1 mm

Method

Equipment for investigating the extension of a spring

1. Align the pointer 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

8. Calculate the difference between the average length at each load and the original length of the spring to get the extension of the spring

Example results table

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

Analysis of results

• The load, $L$, added to the spring is the weight exerted on the mass

• The weight is calculated using the equation:

$W=mg$

• Where:

  • $W$ = weight, measured in newtons (N)

  • $m$ = mass, measured in kilograms (kg)

  • $g$ = 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 load, $L$

• The extension of the spring is calculated using the equation:

$e=l-l_0$

• Where

  • $e$ = extension, measured in metres (m)

  • $l$ = average length of the spring with the load attached, measured in metres (m)

  • $l_0$ = original (unstretched) length of the spring when there were no masses, measured in metres (m)

1. Plot a graph of load $L$ (y-axis) against extension $e$ (x-axis), starting both axes at the origin

2. Draw the best-fit straight line

3. If the graph has a linear region (is a straight line), then the load is proportional to the extension in this region

4. 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

Example load-extension graph

Evaluating the experiment

• Systematic errors:

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

  • Make sure the measurements are taken from the same point on the bottom of the spring every time

  • Check the ruler is vertical with its zero aligned to the pointer's starting position

• Random errors:

  • Wait a few seconds for the mass to become stationary after it is added, before taking the readings for its length

Safety considerations

• Wear goggles during this experiment in case the spring snaps

• Stand up while carrying out the experiment, and make 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 so hard that it breaks or pulls the apparatus over