To study the relationship between load and extension (helical spring) by drawing a graph

 

Abstract

This experiment aims to investigate the relationship between load and extension using a helical spring and to represent the data graphically. By applying known loads to the spring and measuring the resulting extensions, a graph is drawn to analyze the behavior of the spring.

Introduction

The relationship between load and extension of a helical spring is governed by Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension. In this experiment, we aim to verify this relationship by applying known loads to the spring and measuring the resulting extensions. The data obtained is then plotted on a graph to analyze the behavior of the spring.

Procedure

1. Set up a vertical stand with a clamp to hold the helical spring.
2. Attach a load hanger to the bottom end of the spring.
3. Measure the original length of the spring using a ruler.
4. Apply known loads to the load hanger in increments.
5. Measure the extension of the spring for each load using a ruler or vernier caliper.
6. Record the load and corresponding extension values.
7. Repeat the experiment for different loads.

Observations and Calculations

Assume the following observations were made during the experiment:

• Original length of the spring (\( L_0 \)): 10 cm
• Applied loads: 1 N, 2 N, 3 N, 4 N
• Corresponding extensions: 1 cm, 2 cm, 3 cm, 4 cm

The relationship between load (\( F \)) and extension (\( \Delta L \)) can be represented by Hooke's Law:

\( F = k \times \Delta L \)

Where \( k \) is the spring constant.

A graph of load (y-axis) versus extension (x-axis) is drawn to analyze the relationship between them.

Conclusion

The experiment demonstrates the linear relationship between load and extension of a helical spring, as predicted by Hooke's Law. The graph drawn allows for the determination of the spring constant and provides insight into the behavior of the spring under different loads.

Precautions

• Ensure the helical spring is not stretched beyond its elastic limit.
• Handle the loads carefully to avoid accidents or damage.
• Use calibrated instruments for accurate measurements of length and load.
• Repeat the experiment multiple times to ensure the reliability of the results.

Short Questions with Answers

1. What is Hooke's Law?
   Answer: It states that the force exerted by a spring is directly proportional to its extension.
2. What is the purpose of studying the relationship between load and extension?
   Answer: To understand the behavior of a spring and verify Hooke's Law.
3. What is meant by the spring constant?
   Answer: It's the measure of stiffness of the spring, denoted by \( k \).
4. What does the slope of the load-extension graph represent?
   Answer: It represents the spring constant (\( k \)) of the spring.
5. How is the spring constant calculated from the graph?
   Answer: It's calculated as the ratio of load to extension for any point on the graph.
6. What happens to a spring if it is stretched beyond its elastic limit?
   Answer: It undergoes permanent deformation.
7. What is the SI unit of the spring constant?
   Answer: It's Newton per meter (N/m).
8. What factors affect the spring constant?
   Answer: Material properties, diameter, and length of the spring.
9. How does the length of the spring affect its behavior?
   Answer: Longer springs generally have lower spring constants.
10. What is the significance of applying loads in increments?
    Answer: It helps in observing the linear behavior of the spring and ensures accurate data collection.
11. Why is it important to measure the original length of the spring?
    Answer: To calculate the extension accurately.
12. What precautions should be taken during the experiment?
    Answer: Avoid overloading the spring, handle weights carefully, and ensure accurate measurements.
13. How can we verify Hooke's Law experimentally?
    Answer: By plotting a graph of load versus extension and observing a linear relationship.
14. What is the significance of repeating the experiment with different loads?
    Answer: It helps in confirming the consistency of the results and verifying the linear relationship.
15. What does the elastic limit of a spring represent?
    Answer: It's the maximum point beyond which the spring does not return to its original shape.
16. How does temperature affect the behavior of a spring?
    Answer: Higher temperatures may cause changes in material properties, affecting the spring constant.
17. What happens if there is friction between the spring and the support?
    Answer: It may introduce errors in the measurement of extension and affect the accuracy of the results.
18. How can we ensure the spring is in equilibrium before taking measurements?
    Answer: By allowing it to settle without external disturbances and ensuring the load hanger is stationary.
19. What role does the cross-sectional area of the spring wire play?
    Answer: It affects the spring constant, with thicker wires generally resulting in higher spring constants.
20. What factors might cause deviations from Hooke's Law?
    Answer: Non-linear behavior due to large loads, material properties, or temperature changes.

Multiple-Choice Questions (MCQs)

1. What law governs the relationship between load and extension of a spring?
   A) Newton's Law
   B) Pascal's Law
   C) Hooke's Law
   D) Archimedes' Principle
   Correct Answer: C) Hooke's Law
2. What is the purpose of applying loads to the spring in this experiment?
   A) To measure its mass
   B) To determine its volume
   C) To investigate its behavior
   D) To calculate its density
   Correct Answer: C) To investigate its behavior
3. What does the spring constant represent?
   A) The force applied to the spring
   B) The stiffness of the spring
   C) The length of the spring
   D) The weight of the spring
   Correct Answer: B) The stiffness of the spring
4. What happens if the spring is stretched beyond its elastic limit?
   A) It returns to its original shape
   B) It undergoes permanent deformation
   C) Its length decreases
   D) Its stiffness increases
   Correct Answer: B) It undergoes permanent deformation
5. What is the relationship between load and extension according to Hooke's Law?
   A) Inversely proportional
   B) Exponentially proportional
   C) Directly proportional
   D) Unrelated
   Correct Answer: C) Directly proportional