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# To find force constant of helical spring by plotting a graph between load and extension

The graph of a spring or helical spring is a representation of the extension with the load. The graph is a must to indicate the fact that the extension of a spring is completely dependent on the load that is applied. This graph is also referred to as the Extension-load graph. A few things that are going to be observed through this experiment, firstly a perfect lab set up is needed, and then comes the experiment data set and the process where those extension load graph is going to be interpreted.

## Aim

The experiment aims to get out the force constant or spring constant of helical spring simply by plotting it into a graph between the load and extension (Chattopadhyay, 2021). A helical spring, which is used in this experiment, is a spring that has a wire wrapped in a coil. This resembles a screw thread and is common in the field of mechanical experiments.

**Figure 1: The extension of the spring**

## Required material

This experiment requires a few important materials, in absence of one of them; the whole process will be dismissed. A hard support, a helical spring, a hanger of 50 g or 20g, six 20g or 50g slotted weight, a hook, a sharp pointer, and most importantly a vertical wooden scale.

## Theory

In the exact moment when a load, suppose F is suspended from the lower and free end of the helical spring that is hanging from hard support, increases the length of its own about an amount I, then F∝ I or, F=KI, where the K denotes as the constant of proportionality(Chattopadhyay, 2021). It is called the force constant or spring constant of the helical spring.

In the above-mentioned equation, it is clear that if the I=1, then F=K.

Therefore, the force constant or spring constant of a spring can be defined as the force, that is required to produce a unit extension in spring or helical spring.

## Process

For this experiment, some mandatory steps need to be followed.

- The spring must be suspended from a hard support and a pointer should be attached. Then a hook must be attached from the lower free end (golabz, 2022).
- A 50 g hanger should be hanged from the hook.
- A perfect wooden scale is a much-needed, that the tip of the pointer comes over the scale’s division, without touching the scale.
- The reading on the scale should be noted and it should be recorded in the loading column against zero loads.
- An appropriate load of 50g or 20g of slotted weight needs to be added to the hanger. The tip of the pointer should move down.
- Here, the process demands some time, till the pointer comes to rest. Then, once again, the fourth step needs to be repeated, and the reading of the scale should be noted.
- The next two steps too should be repeated respectively till the six slots have been added.
- In the next step, one slotted weight must be removed. Once again, the pointer will move up and the sixth step needs to be repeated.
- 9.The eighth step needs to be repeated till the hanger is left.
- 10.Lastly record all the observations in a table that is given below.

## Observation

The least count of a Vernier scale is 0.1cm.

No. | Load on | Reading of Position of the pointer tip | Extension | ||
---|---|---|---|---|---|

Hanger (W)= Applied Force | Loading (x cm) | Unloading (y cm) | Mean z= [(x+y)/2] | (I cm) | |

0 | |||||

50 | |||||

100 | |||||

150 | |||||

200 | |||||

250 | |||||

300 |

**Table 1: extension and load calculation table**

## Graph

**Figure 2: A graph between Force and extension**

A graph should be plotted in between the F, which meansForce and the I which means the extension, with the F along with the x-axis and I along the y-axis (ncert, 2022). This graph is going to be a straight line as, indicated in Figure 2, above.

From this graph, it is clear that any change of the F from the B to C, can produce a change of the I from the B to D. In simple words, 250 g of weight can produce 2’5cm of extension (learncbse, 2022).

From this data, Force constant or spring constant can be calculated.

As **K= (F/I)= (BC/AC)**

Therefore, **K= (250/2.5) = 100 g wt. per cm**

## The Result

The force constant or spring constant of the helical spring is 100 g wt/cm. It should be remembered, that this spring, that is a spring of balance of range 1kg will have a scale of length 10cm.

## Conclusion

This whole experiment is conducted just to find out how the extension of the length of a helical spring depends on the load that is applied. The above mention graph indicates the results perfectly. The graph forms a straight line up to a point. It means the extension of the length increases equally with the increasing load. Then after a certain limit of applying a load, the graph starts bending. The extension and the load is no more increased in the equal steps.

## FAQ

**Q1. What is a helical spring?**

A helical spring is the most used mechanical spring that has a wrapped coil. It resembles a screw thread. It is used for pull, push, or carry loads.

**Q2. What is the result of the experiment?**

The force constant of the given spring is 100 g wt/cm.

**Q3. What is an Extension-load graph?**

The extension-load graph of a spring is a graph that represents the relation between its extensions with the load. This graph is made to see how the extension of a spring depends on the load, that is applied. It is also referred to as the load-extension graph.

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