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Force constant of a helical spring by plotting a graph between load and extension.


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Force constant of a helical spring by plotting a graph between load and extension.

Helical spring:

Objective

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

Theory

What is a helical spring?

The helical spring, is the most commonly used mechanical spring in which a wire is wrapped in a coil that resembles a screw thread. It can be designed to carry, pull, or push loads. Twisted helical (torsion) springs are used in engine starters and hinges.

Let’s study how we can use the helical spring to do our experiment.

The helical spring is suspended vertically from a rigid support. The pointer is attached horizontally to the free end of

spring. A metre scale is kept vertically in such a way that the tip of the pointer is over the divisions of the scale; but does not touch the scale.

Helical spring works on the principle of Hooke’s Law. Hooke’s Law states that within the limit of elasticity, stress applied is directly proportional to the strain produced.

When a load ‘F’ is attached to the free end of a spring, then the spring elongates through a distance ‘l’ .Here ‘l’ is known as the extension produced. According to Hooke’s Law, extension is directly proportional to the load.

This can be represented as:

where ‘k’ is constant of proportionality.  It is called the force constant or the spring constant of the spring.

A graph is drawn with load M in kg wt along X axis and extension, l in metre along the Y axis. The graph is a straight line whose slope will give the value of spring constant, k .

Learning Outcomes:

  •     Students understand the principle of  Hooke’s Law.
  •     They learn about the force constant of a spring.
  •     Students understand the relationship between force applied and extension produced in a spring.

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Experiment

LABAPPARA Materials Required

  •     A spring
  •     A rigid support
  •     Weight hanger
  •     50g or 20 g slotted weights
  •     A vertical wooden scale
  •     A fine pointer

 Procedure

  1. The helical spring is suspended vertically from a rigid support.A pointer is attached horizontally at the free end of the spring.
  2. A metre scale is kept vertically in such a way that the tip of the pointer is over the divisions of the scale, but does not touch the scale.
  3. A dead weight, w0 gwt is suspended by the weight hanger to keep the spring vertical. The reading of the pointer on the metre scale is noted.
  4. Now, gently add a suitable load of 50 g slotted weights to the hanger and the reading of the pointer is noted.
  5. The weights are added one by one till the maximum load is reached. In each case, the reading of the pointer is noted.
  6. The weights are then removed one by one and the reading of the pointer is noted in each case of unloading.
  7. The average of the readings for each load during loading and unloading is calculated in each case.    Let z0, z1, z2, z3…etc.., be the average readings of the pointer for the loads w0, (w0+50), (w0+100), (w0+150) etc.
  8. From this, extension, l (in m) for the loads (w0+50), (w0+100), (w0+150)   etc. , are calculated as (z1-z0), (z2-z0), (z3-z0) respectively.
  9. In each case, k =mg/l is calculated. The average value of k gives the spring constant in N/m.
  10. A graph is drawn with load M in kg wt along X axis and extension, l in metre along the Y axis. The graph is a straight line. The reciprocal of the slope of the graph is determined. It gives spring constant in kg wt/m. The spring constant in N/m is obtained by multiplying this with g=9.8 m/s2.

Procedure 

Select the spring for which the spring constant is to be measured, from the 'Select Spring’ drop down list. Select the environment to perform the experiment from the 'Choose Environment' drop down list. Use the ‘Change hanging mass’ slider to change the mass attached at the end of the spring. The spring elongates or compresses according to the addition or removal of mass attached at its end. The elongation or compression of the spring is noted in the scale by using the position of the pointer attached at the end of the spring. Now, calculations are done as per the observation column and the spring constant of the selected spring can be found out. Enable the ‘Show result’ checkbox to view the spring constant of the selected spring. Click on the ‘Reset’ button to redo the experiment.

Observations:

Table for load and extension: 

Serial No of Obs. Load on hanger(W) = applied force (F)(kg wt) Tension= Mg (N)  
Reading of position of pointer tip Extension l= z x 10-2 (m) N/m  
Loading X(cm) Unloading Y(cm) Mean,  (cm)  
  Dead load(W0)              
  (W0+ .05)              
  (W0+.1)              
  (W0+.15)              
  (W0+.2)              
  (W0+.25)              
  (W0+.3)              
Mean k=…………N/m.

Spring constant, k from load extension graph

AB=---------kg wt BC=---------m =  ---------Nm-1

Result

By calculation, the force constant of the given spring = .............N/m. From load-extension graph, the force constant of the given spring =……….N/m