Experiment: Determining the Force Constant of a Helical Spring

Force constant of a helical spring: Objective

To determine the force constant (spring constant) of a helical spring by plotting a graph between the applied load and the resulting extension.

Force constant of a helical spring:Materials Required

Helical spring

Stand with a clamp and scale arrangement

Slotted weights (known masses- say 50 g each)

Pointer (attached to the spring)

Hanger (to attach weights)

Force constant of a helical spring- Formula

Force constant of a helical spring- Theory

Hooke’s Law states that the force F applied to a spring is directly proportional to its extension x, provided the elastic limit is not exceeded.

Stronger or stiffer springs will have higher spring constant. For a specific mass added to the spring, springs with higher the spring constant will have more modest(smaller) displacement than that of the springs with lower spring constant value.

Spring constant(k) is the constant of proportionality or the amount of energy delivered proportionality in the Hooke’s law experimental trial.It is the angle of the straight-line part of the chart, force in newton versus extension in meter.

Force constant of a helical spring: Procedure

Experimental setup: 

Suspend the helical spring vertically from a rigid support using a clamp attached to a stand.  

 Attach a hanger to the lower end of the spring.  

 Place a meter scale vertically beside the spring to measure its extension.  

 Attach a pointer or marker to the hanger to accurately read the extension.

Initial Measurement:

Measure the initial length of the spring (without any load) using the meter scale. Let this be Lo.

Apply loads:

Add a known mass (e.g., 50 grams) to the hanger and allow the spring to come to rest.  

Measure the new length of the spring and record it as L1

Calculate the extension  x using the formula:  

                                                      x= L1 –  Lo

Repeat the experiment:

Increase the load step-by-step by adding incremental masses (e.g., 100g, 150g, 200g, etc.) and record the corresponding extensions.Extension data of the given spring  for the addition of various masses of known weight  are noted and tabulated.

The relationship between average change in length and force does produce a straight line passing through the origin which shows the proportionality between force and  extension.

Spring constant is the gradient of the straight-line portion of the graph, force in newton versus extension in meter.

Force constant of a helical spring:Tabular column

Force constant of a helical spring: Plotting the Graph:  

Plot a graph with Load (F) on the y-axis and Extension (x) on the x-axis.  

The graph should be a straight line passing through the origin, as per Hooke’s Law F=kx

Force constant of a helical spring-Calculating the force constant

Spring constant is the gradient of the straight-line portion of the graph, force in newton versus  extension in meter.The slope of the graph represents the force constant.

Force constant of a helical spring-Observations and Results

The graph between load and extension is linear, confirming Hooke’s law.

The slope of the graph gives the force constant k of the spring.

The unit of spring constant is N/m.

Force constant of a helical spring- Precautions

Ensure the spring is not stretched beyond its elastic limit.

Measure the extensions carefully,avoiding parallax error.

Use a uniform and calbrated meter scale.

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