Hooke's Law Lab

The following lab can be replicated in person by using a metre rule, masses with mass holders and a spring.

Theory

Hooke’s law states that the deformation of an object is directly proportional to the force applied, and is given by the formula $$F=kx$$ where the extension ($x$) is $$x=current\ length-original\ length$$

We can make $x$ the subject of the formula and write it in the form of a straight line equation: $$ \begin{equation}\begin{aligned} x&=\frac{F}{k}\\ \color{limegreen}x&=\color{royalblue}\frac1k\color{red}F\color{black}+0\\ \color{limegreen}y&=\color{royalblue}m\color{red}x\color{black}+c\\ hi&\\ \end{aligned}\end{equation} $$

Thus if we plot a graph of extension ($x$) versus force ($F$), we get a y-intercept of $0$ and a gradient which is the reciprocal of the spring constant($\frac{1}{k}$): $$m=\frac{1}{k}$$

Thus the spring constant $$k=\frac{1}{m}$$ where the units of the gradient $m$ will be $m/N$, meaning the units for $k$ will be $N/m$.

Aim

To find the spring constant of a spring using Hooke’s Law

Materials/Apparatus

• PhET masses and springs simulation

Diagram

View

Diagram showing the setup of the Hooke's Law simulation

Method

1. Run the simulation
2. Choose the ‘Lab’ option
3. Set the damping to ‘Lots’
4. Use the ruler to measure and record the original length of the spring
5. Hang the mass onto the spring and set the mass to 100 grams
6. If the mass is oscillating let it come to rest before taking any measurements
7. Measure and record the new length of the spring
8. Repeat steps 4 to 6 for masses 120 grams to 200 grams at regular intervals of 20 grams

Results

Data Analysis

1. Plot a graph of extension (on the y axis) versus force (on the x axis)
2. Calculate the spring constant using the gradient of the graph