Investigating elasticity

In a nutshell

By applying an increasing force to a spring, the resultant extension of the spring can be measured. This can be used to find spring constant and the work done by the force on the spring.

Equations

Word Equation	Symbol Equation
$force = spring \space constant \times extension$	$F = k \times x$
$force = mass \times gravitational \space field \space strength$	$F = m\times g$
$work \space done = \frac{1}{2} \times spring \space constant \times extension^2$	$W = \frac{1}{2} \times k \times x^2$

Variable definitions

Quantity Name	Symbol	unit name	Unit
$force$	$F$	$newton$	$N$
$spring\space constant$	$k$	$newton \space per \space metre$	$N/m$
$extension$	$x$	$metre$	$m$
$mass$	$m$	$kilogram$	$kg$
$work\space done$	$W$	$joule$	$J$

Equipment list

The following equipment list can be used to conduct the experiment to investigate elasticity.

Equipment	Use
Spring	To measure the extension of.
Masses ( $5 \times 100 \,g$ )	To apply a force to extend the string.
$100\,g$ mass hanger	To hold the masses.
Clamp	To hold the spring and masses.
Clamp stand	To hold the clamp.
Ruler	To measure the extension
Pointer	To read the extension accurately on the ruler.

Experimental variables

The independent variable is the variable you change. The dependent variable is the variable that changes depending on the other variables, and is the one you measure. The control variables are the variables that are kept constant.

Independent Variable	$Force$
Dependent Variable	$Extension$
Control Variables	$Spring\ constant,\ mass\ of\ masses$

Safety precautions

When performing experiments, it is very important to consider safety precautions. This is so that no one gets hurt or injured during the experiment.

Hazard	Risk	Safety Measure
Spring	The spring may snap which could cause injury.	Wear goggles during the experiment.
Clamp and masses	The clamp and masses may fall if not secured to the desk properly.	Use heavy objects (or a G clamp) to ensure the clamp stand doesn't fall over.
Falling masses	Masses may fall off the mass hanger.	Place a mat under the masses and ensure no feet or body parts are directly under the masses.

Method

These are the instructions to complete the experiment. Record all measurements taken as you work through the experiment in a table.

Physics; Physics practicals; KS4 Year 10; Investigating elasticity

1.	Desk
2.	G-clamp
3.	Clamps
4.	Clamp stand
5.	Ruler
6.	Spring
7.	Pointer
8.	Masses
9.	Mass hanger

1.	Set up the apparatus as shown in the diagram.
2.	Measure the initial length of the spring using the ruler when no force is applied by the masses.
3.	Add the mass hanger to the spring and measure the extension. Use the pointer to ensure an accurate measurement is taken each time. Take the measurement at eye level to avoid parallax error. Note: The extension is equal to the difference between the new length and the initial length.
4.	Continue adding masses and recording the extension. Tip: Wait a few seconds for the spring to extend fully after a mass has been added. Then take the measurement!

Analysis

This is how you will use the data recorded to form conclusions.

1.	Plot a graph of force ( $y$ -axis) against extension ( $x$ -axis). Find the force by using the equation $force = mass \times gravitational \space field \space strength \newline \ \newline F = m\times g$ where $g = 10 \,N/kg$ .
2.	Draw a line of best fit for this graph. The gradient of the straight line region should be the spring constant.
3.	Compare this with Hooke's law. Hooke's law states that the extension of the spring is directly proportional to the force applied to the spring, as long as the limit of proportionality has not been reached.
4.	Using the value of the spring constant, calculate the work done each time the spring increases its extension. $work \space done = \frac{1}{2} \times spring \space constant \times extension^2\newline \ \newline W = \frac{1}{2} \times k \times x^2$

Conclusion

Physics; Physics practicals; KS4 Year 10; Investigating elasticity

A.	Force ( $N$ )
B.	Extension ( $x$ )

The graph from the measured values of the experiment should look similar to this. The line curving shows the limit of proportionality which is when the spring no longer obeys Hooke's law and has undergone plastic deformation. The spring constant is equal to the gradient of the straight line region.

Evaluation

Once you have completed your experiment, it is important to consider how it could be improved. You should come up with ways to improve the accuracy of your values. If you got a result that seems unreasonable, think about why this was.