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Spring Constant is the quantity that indicates a spring’s stiffness. It is based on Newton’s Third Law of Motion “For every action, there is an opposite and equal reaction”. Hooke's law describes the relationship between this restoring force and displacement, which says, “Restoring force of the spring is directly proportional to the small displacement”. The constant proportionality is known as Spring Constant. The SI unit of spring constant is N/m (Newton per meter).
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Read More: Mechanical Properties of Solids
Key Takeaways: Spring Constant, Helical Spring, Pointer’s tip, weights
What is Helical Spring?
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Helical Spring is also known as coil spring. It is a mechanical spring that is composed of a wire that is wound into a coil that looks like a screw thread. Helical Springs can be used to push, pull and carry loads. Twisted helical or torsion springs are mostly used in hinges and engine starters.
Helical Spring
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Aim of the Experiment
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Our aim is to find the force constant of the helical spring by plotting a graph between load and extension.
Material Required for the Experiment
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- Spring
- Rigid support
- 6 loads of 20 to 50 g
- 30 or 50 g hanger
- A wooden scale
- A hook
- A fine pointer
Diagram
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Extension of Spring
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Explanation
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If a load F suspended from the free end of a spring hanging from rigid support increases its length by the amount l,
Then
F∞ l
Or
F = Kl
Where K is the constant of proportionality.
It is known as the spring constant of the spring,
If, l = 1, F = k
Therefore, the spring constant is defined as a force required for the spring to produce an extension.
Procedure
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- Suspend the Helical spring vertically from the rigid support and attach a pointer and hook at the free end of the spring.
- Hang a 20g hanger from the hook.
- Keep a vertical wooden scale in such a way that the pointer’s tip comes over the scale without touching it.
- Note down the reading when the position of the pointer’s tip is on the scale and record the loading column against the zero loads.
- Now, gently add the 20g slotted weight to the hanger. The Pointer tip moves down.
- Wait till the pointer tip comes to rest. Repeat step 4.
- Keep repeating steps 5 and 6 till all six slotted weights have been added.
- Now, remove one slotted weight till the pointer tip moves up. Repeat step 6 and record the readings in the unloading column.
- Repeat step 8 till the hanger is free.
- Record your observations as given below in a table
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Observations
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| S. no | Loads of Hanger (W) = Applied Force | Reading of Position of the Pointer Tip | Extension (/cm) | ||
|---|---|---|---|---|---|
| Loading (X cm) | Unloading (Y cm) | Mean z = (x+y)/2 | |||
| 1. 2. 3. 4. 5. 6. 7. | 0 50 100 150 200 250 300 | ||||
Graph
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Now, plot a graph, taking F on X-axis and l on Y-axis. The graph comes to be a straight line as shown in the picture below.
Graph
Through the graph, we can see the change of F from B to C chances to l from B and D. This basically means 250g wt produces a 2.5cm extension.
K = f/l = BC/AC
K = 250 / 2.5 = 100 g wt per cm
Results
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The force constant of the spring is 100g wt per cm.
Precautions
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- Loading and Unloading of the weights should be done very gently.
- Pointer’s tip must be above the scale surface and should not touch it.
- Note the reading only when the pointer’s tip comes to rest.
Read More: Potential Energy of a Spring
Things to Remember
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- The force required for the spring to produce an extension is spring constant.
- In this spring, a scale of length 10 cm will be used for a spring balance weighing 1 kg.
- According to Hooke's law, the strain of any material is proportional to the applied stress, as long as that particular material is within its elastic limit.
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Sample Questions
Ques: What do you mean by Rigid Body? (2 marks)
Ans. When a body does not experience any change in its shape or dimensions, having been subjected to the action of forces, it is said to be rigid.
Ques: What is Stress? (2 marks)
Ans. When a deformed body exerts stress from within by restoring the retracted force per unit area created by its molecules, it is called stress.
Stress = Restoring Force
Effected Area
Ques: What is the SI unit of stress? (2 marks)
Ans. Newton per meter2 (Nm-2) is the SI unit of stress.
Ques. Define Elasticity? (2 marks)
Ans. An elastic body is one that tends to regain its original shape after being deformed by external forces. Such bodies are called Elastic bodies.
Ques. What is Strain? (2 marks)
Ans. When there is a Proportional change in the form of the body is called Strain on the body.
Strain = Change in configuration
Original Configuration
Ques. What is a different way to find out the Force Constant of a spring? (2 marks)
Ans. Another way to find out the Force Constant of a Spring is by Measuring the time period of oscillation of a loaded spring.
T = 2π√m/k
Where,
T = Time Period,
M = Mass Loaded,
K = Force Constant
Ques. Does the Force constant depend upon the loaded weights? (2 marks)
Ans. No, It does not depend upon the loaded weights.
Ques. What is Hooke’s Law as modified by Thomas Young? (2 marks)
Ans. Hooke’s modified Law states, “The stress is proportional to the strain, within elastic limit”.
Strain ∞ Stress
Or
Stress = Modulus of Elasticity × Strain
Ques. Define Modulus of Elasticity? (2 marks)
Ans. When there is a constant ratio of stress and strain is called the Modulus of Elasticity of the material of the body. It is also known as the Coefficient of Elasticity.
Ques. What is Tangential Stress? (2 marks)
Ans. When a deforming force acts along an object's surface (tangentially), e.g., a book that is pressed by a hand with a tangential force, then it is called tangential stress.
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