Required Practical: Investigating Force & Extension

The mathematical expression for this relationship is $F = ke$, where $F$ is the force in Newtons (N), $k$ is the spring constant in N/m, and $e$ is the extension in meters (m).

On a Force-Extension graph, the linear region passing through the origin indicates direct proportionality, where the gradient of the line is equal to the spring constant $k$.

The area under the linear portion of the Force-Extension graph represents the Elastic Potential Energy stored in the spring, calculated as $E_e = \frac{1}{2}Fe$ or $E_e = \frac{1}{2}ke^2$.

If the spring is stretched beyond its elastic limit, it undergoes plastic deformation, meaning it will not return to its original length when the force is removed.

Setup: Secure a clamp stand to the bench and attach two clamps; use the top clamp to hold the spring and the bottom clamp to hold a ruler vertically.

Initial Measurement: Record the position of the bottom of the unstretched spring against the ruler using a horizontal pointer (fiducial marker) to ensure accuracy.

Incremental Loading: Add a known mass (e.g., 100g) to the spring, which exerts a force of approximately 1 Newton ($W = mg$), and record the new position of the pointer.

Data Collection: Repeat the process by adding further masses one at a time, recording the total mass and the new length for each step, ensuring the spring does not oscillate before reading.

Calculation: For each load, calculate the extension by subtracting the original length from the current length, then plot a graph of Force (y-axis) against Extension (x-axis).

It is vital to distinguish between total length and extension; extension is the change in length, while total length includes the original length of the spring.

Mass vs. Force: In the lab, we add masses (kg), but the formula requires Force (N). Convert mass to weight using $W = m \times g$ (where $g \approx 9.8$ N/kg).

Parallax Error: Always state that the ruler must be read at eye level to avoid parallax error, which occurs when the measurement is viewed from an angle.

Fiducial Marker: Mention the use of a pointer or 'fiducial marker' attached to the bottom of the spring to make the readings against the ruler more precise and consistent.

Unit Consistency: Ensure all measurements are converted to SI units (meters for extension, Newtons for force) before calculating the spring constant $k$.

Graph Interpretation: If the graph is Extension vs. Force (axes swapped), the gradient is $\frac{1}{k}$ rather than $k$. Always check the axis labels carefully.

Zeroing: If the ruler cannot be positioned so the zero mark is at the top of the spring, simply subtract the initial reading from all subsequent readings.

Measuring from the top: Students often forget that extension is the change in length; measuring the total length from the clamp to the bottom of the weight is not the extension.

Exceeding the limit: Adding too much weight can permanently damage the spring, making the data for the spring constant invalid as the relationship becomes non-linear.

Weight of the hanger: The mass hanger itself has mass; the initial 'zero' reading should ideally be taken with the hanger attached if it is used for all subsequent measurements.