AQA AS Level Physics A

Springs

Aims

In this experiment you will plot a force–extension graph for a spring. This will enable you to measure the limit of proportionality and determine the spring constant of the spring.

Safety

Attach the masses securely to the spring and ensure that, should the masses fall, they will not fall on your feet. You may need to protect the floor.
The clamp stand must be securely attached to the bench with a G-clamp.

Equipment, materials and method

1For this experiment you will need a spring, a clamp stand, a G-clamp, some masses and a mass hanger, some string, a metre ruler, a set squareand a stand with two clamps.

2Secure the first stand to the bench and hang the spring from the clamp. Tie a loop of string through the bottom of the spring. Adjust the ruler and secure it in place as close to the spring as possible, using the second stand and both its clamps. Use the set square to ensure that the ruler is vertical.

3Read the position of the top and the bottom ring of the spring. Use the set square to ensure that the line between the spring and the ruler is horizontal. Subtract these values to calculate the length of the spring. Estimate the precision of each reading.

4Add the mass hanger (whose mass should be the same as the individual masses to be added later) to the loop of string and measure the new length of the spring.

5Continue to add masses and measure the new length of the spring each time until it is clear that the results are no longer linear. At this point caution must be taken.

6For each measurement, calculate the extension of the spring by subtracting the original length of the spring from the new length.

7After the spring has been extended beyond its linear region, repeat the measurements as you unload the spring.

Questions

1What force does each of your masses exert on the spring?

2How can you calculate the extension of the spring from your measurements?

Results

Tabulate your results. For each extension, calculate the force applied and the extension of the spring. Enter these values in your table. Estimate the probable uncertainty in each extension measurement. Plot a graph of force against extension. Differentiate, on your graph, between the measurements taken when loading and when unloading the spring.

Discussion

1Use your graph to find the values for the spring constant and the limit of proportionality of your spring, and estimate the probable uncertainty of this limit.

2When unloading the spring, what do you notice about the gradient (and hence the spring constant) of the new line?

Springs

Aims

To plot a force–extension graph for a spring and use it to determine the spring constant and the limit of proportionality of the spring.

To take suitable precautions to ensure that uncertainty due to experimental technique (for example, parallax) is minimised.

Safety

The clamp stand must be securely attached to the bench with a G-clamp.
The floor may need protection from falling masses.
Ensure that the spring is attached securely to the clamp.
Warn pupils to take care with falling masses.

Teaching notes

3This experiment should take about 25 minutes (although graph plotting may take longer).

4The number of masses added each time in order to ensure a suitable number of measurements for the graph (8–10 minimum) should be determined by assessing how much weight is needed to reach the elastic limit. This depends on the spring used.

5More readings should be taken around the point where the spring reaches the elastic limit.

Answers to questions

1Weight of mass in newton = number of kg×9.81Nkg−1

2Extension = length of extended spring−original length

Columns for both of these values should be added to the table of results.

Discussion

3The spring constant is found by finding the gradient of the straight part of the graph. Encourage students to extrapolate this line in order to draw a larger triangle to calculate the gradient. This minimises error.

The limit of proportionality is the point at which the graph ceases to be a straight line. Encourage students to draw a line of best fit for this region. Take account of the probable uncertainty in each measurement to estimate the probable uncertainty in the gradient and in the limit of proportionality.

4As the spring is unloaded it will not return to its original length, thus a new line is formed on the graph. However, the gradient (and hence the spring constant) should be approximately the same for this second line.

Practical assessment opportunities

5ISA preparation:
practical task – practice in recording measurements, estimating errors and plotting a graph
written task Section A and B – opportunities to draw conclusions and to evaluate the strength of the conclusion

Springs

Equipment and materials required

Each student or pair of students will require the following equipment:

a stand and clamp

a spring (for which 1N gives an extension of 2–3cm)

a 15cm length of string

some masses and mass hanger(s)

a second stand with two clamps

a metre ruler

a set square

a G-clamp

graph paper

The number of masses and mass hangers depends on the spring used. The spring needs to extend beyond its elastic limit.

Safety

The clamp stand must be securely attached to the bench with a G-clamp.
The floor may need protection from falling masses.
Ensure that the spring is attached securely to the clamp.