

Steps to Plot Load vs Extension and Calculate Spring Constant
We know that when a spring is stretched from one end to another, it tries to come back to its original orientation. It happens because there is an interatomic force of attraction between the molecules tightly packed in the solid material like a spring.
Now, when we exert force on these molecules to bring them away from their lattice points, they recover their position and spring regains its shape.
Now, if the same helical spring is extended by a load, we can find the value of spring constant of helical spring by performing the helical spring experiment and this article discusses the same.
What is a Helical Spring?
A helical spring is the most commonly used mechanical spring in which a wire is wounded in a coil that seems like a screw thread. It is designed to carry, pull, or push loads.
We can find the usage of the twisted helical or torsion springs in engine starters and hinges.
Now, let’s study how we can use the helical spring to do a spring constant experiment.
Helical Spring Experiment
Aim of this Experiment:
Our objective is to find the force constant of the helical spring by plotting a graph between load and extension.
Apparatus or Materials Required:
A stiff support
A spring
Six loads of the range 20 to 50 grams
A 30 or 50 g hanger
A movable sharp pointer
A wooden scale
A hook
Desired Diagram of Our Experiment:
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Theory of Spring Constant
If F is the force applied, x is the displacement of the spring, whose magnitude equals the magnitude of the force applied. The equation form is:
F ∝ x
Here,
F = - k x
This means ‘k’ is the force constant and the regaining is specified with a negative sign. A force constant or the spring constant ‘k’ has no unit.
Basically, spring has the formula mentioned in equation (1). Since we are here to find the force constant of helical spring by plotting a graph between load and extension, so instead of using the displacement term, we will use a length by which a helical spring got an extension under the influence of the load.
Here, we have the following equation:
F = kL
L = extension in the length of the helical spring, which is positive by nature.
[Image will be Uploaded Soon]
Procedure of the Experiment:
Suspend the helical spring from a rigid support and attach the pointer vertically and the hook from its lower free end. Hang a 40 g hanger from the hook.
Arrange the vertical wooden scale in such a way that the tip of the pointer comes over the divisions on the scale and can slide over it accordingly without touching it.
Firstly, add a dead weight to the hanger by keeping the spring vertical. Jot down the reading on the scale and record it in the loading column against the zero loads.
The weights of the range 20 g to 50 g are added one by one to the slotted weight to the hanger till the maximum load is reached. In each case, when the tip of the pointer moves down, note the reading of the pointer.
Then, each weight is removed one by one and the reading of the pointer is noted in each case of unloading.
Now, wait for some time till the pointer comes to rest. Repeat step 3.
As the pointer moves up. Repeat step 5 and 6 and record the reading in the unloading column.
Repeat step 7 till the only hanger is free.
Record your observation and perform the helical spring experiment calculations.
Helical Spring Experiment Calculations
The average of the readings for each load/weight during the loading and unloading process is calculated in each case. Let m0, m1,m2, m3…etc.., be the average readings of the pointer for the loads w0, (w0 + 50),
(w0+ 100), (w0+ 45), etc.
From this, extension, ‘L’ (in m) for the loads (w0 + 50), (w0+ 100), (w0+ 150), etc. , are calculated as (m1 - m0), (m2 - m0 ), (m3 - m0), respectively.
In each case, k = mg/l is calculated.
Here, g is the acceleration due to gravity = 9.8 ms-2.The average value of k gives the helical spring constant in N/m.
Now, after making the helical spring experiment calculations, record these in the following table:
Value of Spring Constant of Helical Spring
Graph for the Helical Spring Constant Experiment
After performing all the experimentations, we get the following graph:
[Image will be Uploaded Soon]
OX = ——— kg wt
OY = ——— m
Value of spring constant of helical spring ‘K’ = ——— Nm⁻¹
Result
By calculation, the value of the spring constant of helical spring is = ………….N/m.
From the helical spring load-extension graph, the force constant of the helical spring =……….N/m.
FAQs on How to Find the Force Constant of a Helical Spring Using a Load vs Extension Graph
1. What is the spring constant and how is it defined by Hooke's Law?
The spring constant (k) is a measure of a spring's stiffness. It is defined as the force required to produce a unit extension (or compression) in the spring. According to Hooke's Law, for a spring that is not stretched beyond its elastic limit, the restoring force (F) is directly proportional to the extension (x). The formula is F = -kx, where the negative sign indicates that the restoring force acts in the opposite direction to the displacement. The SI unit for the spring constant is Newtons per meter (N/m).
2. How do you find the force constant of a helical spring using a load vs. extension graph?
To find the force constant from a graph, you first conduct an experiment by applying various loads (masses) to a helical spring and measuring the corresponding extension. Then, you plot a graph with the applied force (F = mass × g) on the y-axis and the extension (x) on the x-axis. The resulting graph should be a straight line passing through the origin. The force constant (k) is determined by calculating the slope of this line, as k = ΔF / Δx.
3. What does the slope of a force-extension graph for a spring represent, and why is it a straight line?
The slope of a force-extension (F vs. x) graph represents the spring constant (k). It tells us how much force is needed to stretch the spring by one unit of length, indicating the spring's stiffness. The graph is a straight line because, within the elastic limit, the spring obeys Hooke's Law, which states a direct and linear proportionality between the applied force and the extension. A constant slope signifies this constant proportionality.
4. What is the correct procedure for performing the helical spring experiment in a lab?
The standard procedure for the helical spring experiment is as follows:
- Suspend the helical spring from a rigid support and attach a pointer and a hanger at its lower end.
- Set up a vertical scale alongside the pointer to measure its position.
- Record the initial reading of the pointer on the scale with no load on the hanger (this is the zero load reading).
- Add a slotted weight (e.g., 50g) to the hanger and record the new position of the pointer. The difference between this reading and the initial reading is the extension.
- Continue adding weights in equal increments and record the extension for each load.
- To check for elastic behavior, remove the weights one by one and record the readings again. The spring should return to its original position.
5. Why is it important that the spring does not exceed its elastic limit during this experiment?
It is crucial not to stretch the spring beyond its elastic limit because doing so causes plastic deformation. This means the spring will not return to its original shape and length after the load is removed. If the elastic limit is exceeded, Hooke's Law (F ∝ x) is no longer valid, the force-extension graph will cease to be a straight line, and the calculated value of the spring constant will be incorrect and meaningless for that deformed state.
6. What are the common sources of error in the spring constant experiment and how can they be minimised?
Common sources of error in this experiment include:
- Parallax Error: Incorrect readings due to viewing the scale from an angle. This can be minimised by keeping the eye level with the pointer.
- Non-Uniform Spring: The spring's wire may not have a uniform thickness, affecting its stretching. Using a high-quality, uniform spring is essential.
- Exceeding Elastic Limit: Overloading the spring can permanently deform it. Ensure the maximum load is well within the spring's limit.
- Rigid Support Oscillation: The support itself may not be perfectly rigid. Use a heavy, stable support stand.
7. How do you calculate the spring constant if the applied force and the resulting extension are known from a single measurement?
You can calculate the spring constant (k) directly using the formula from Hooke's Law: k = F / x. First, ensure all units are in the SI system. For example, if a mass of 2 kg is hung from a spring, the force is F = m × g = 2 kg × 9.8 m/s² = 19.6 N. If this force causes an extension (x) of 0.4 meters, the spring constant would be:
k = 19.6 N / 0.4 m = 49 N/m.

















