What is Measured?

During the experiment, the following quantities are measured:

• Applied load, $W$
• Compression (deflection), $\delta$

These measurements are used to determine the stiffness and strain energy of the spring.

Why are the Calculations Required?

The experimental observations help determine:

• Spring stiffness (spring constant)
• Elastic behaviour of the spring
• Energy stored during compression
• Verification of Hooke's law

Observation Table

Trial	Applied Load $W$ (N)	Deflection $\delta$ (mm)
1	50	5
2	100	10
3	150	15
4	200	20
5	250	25

Sequential Calculations

1. Spring Stiffness

Using

$$k = \frac{W}{\delta}$$

For Trial 3,

$$k = \frac{150}{15} = 10\ \text{N/mm}$$

2. Strain Energy

Using

$$U = \frac{1}{2}W\delta$$

For Trial 3,

$$U = \frac12 \times 150 \times 15$$

$$U = 1125\ \text{N-mm}$$

Converting to joules,

$$U = 1.125\ \text{J}$$

since

$$1\ \text{J} = 1000\ \text{N-mm}$$

Solved Numerical Example

Given

• Load = $200$ N
• Deflection = $20$ mm

Step 1

Spring stiffness

$$k = \frac{200}{20} = 10\ \text{N/mm}$$

Step 2

Strain energy

$$U = \frac12 \times 200 \times 20$$

$$U = 2000\ \text{N-mm}$$

$$U = 2.0\ \text{J}$$

Interpretation of Results

• A straight-line Load–Deflection graph indicates that the spring obeys Hooke's law.
• The slope of the graph represents the spring stiffness.
• Larger stiffness indicates a stiffer spring requiring greater load for the same deflection.
• The area under the Load–Deflection graph represents the strain energy stored in the spring.

Result

The stiffness (spring constant), spring deflection, and strain energy stored in the compression spring are determined successfully. The Load–Deflection relationship verifies the elastic behaviour of the spring within its working range.