🔗 Hooke's Law Experiment

Verify F = -kx and Calculate Spring Constant

✅ FREE Experiment • 📊 Force-Extension Graph • 🎓 NEB Class 11 Practical

Interactive Spring Simulation

Add masses to see the spring stretch in real-time with accurate physics!

Add Masses

Current State

Total Mass: 0 g

Force (F): 0.00 N

Extension (x): 0.00 cm

Spring Constant (k): --

Calculated Results

Mean Spring Constant (k)
0.00
N/m
Total Readings
0
observations
Standard Deviation
0.00
N/m
Max Extension
0.0
cm

Observation Table

S.No. Mass (m)
grams		 Force (F)
F = mg (N)		 Extension (x)
cm		 x (meters) Spring Constant (k)
k = F/x (N/m)
No readings yet. Add masses and click "Record Reading"

📊 Statistical Analysis

Mean value of k = 0.00 N/m

Standard Deviation = 0.00 N/m

📚 Theory & Concepts

What is Hooke's Law?

Hooke's Law states that within the elastic limit, the force required to extend or compress a spring is directly proportional to the extension or compression. This fundamental principle of elasticity was discovered by Robert Hooke in 1660.

Mathematical Expression

F = -kx

Where:
• F = Restoring force (in Newtons)
• k = Spring constant (in N/m)
• x = Extension or compression (in meters)
• The negative sign indicates the restoring force acts opposite to displacement

Spring Constant (k)

The spring constant is a measure of the stiffness of the spring. A higher value of k means the spring is stiffer and requires more force to stretch. It is calculated as:

k = F/x = (mg)/x

Elastic Limit

Hooke's Law is only valid within the elastic limit of the material. Beyond this point, the material undergoes permanent deformation and does not return to its original shape when the force is removed.

Applications

🔬 Procedure

  1. Observe the spring in its natural unstretched position at the top
  2. Click on a mass button to add weight to the spring
  3. Watch the spring stretch realistically under the applied load
  4. Note the extension (x) and calculated force (F) in the "Current State" panel
  5. Click "Record Reading" to add the observation to the table
  6. Add different masses (50g, 100g, 200g, 500g, 1000g) and record each
  7. Repeat with at least 5 different masses for accurate results
  8. The mean spring constant (k) is calculated automatically from all readings
  9. Verify that F = kx relationship holds for all recorded readings
  10. Calculate the standard deviation to assess measurement precision

💬 Viva Questions & Answers

Q1: State Hooke's Law.
Hooke's Law states that within the elastic limit, the extension produced in a spring is directly proportional to the applied force. Mathematically, F = -kx, where k is the spring constant.
Q2: What is spring constant?
Spring constant (k) is the force required to produce unit extension in the spring. It is a measure of the stiffness of the spring. Its SI unit is N/m (Newton per meter).
Q3: What is meant by elastic limit?
Elastic limit is the maximum stress or force that can be applied to a material such that it still returns to its original shape when the force is removed. Beyond this limit, permanent deformation occurs.
Q4: Why is there a negative sign in F = -kx?
The negative sign indicates that the restoring force exerted by the spring is in the opposite direction to the displacement. When stretched, the spring pulls back; when compressed, it pushes back.
Q5: What does the slope of F-x graph represent?
The slope of the Force-Extension graph represents the spring constant (k). Since F = kx, a graph of F versus x gives a straight line with slope k passing through the origin.
Q6: What happens if we exceed the elastic limit?
If the elastic limit is exceeded, the material undergoes plastic deformation. The spring will not return to its original length when the load is removed, and Hooke's Law will no longer be valid.
Q7: What is the unit of spring constant?
The SI unit of spring constant is Newton per meter (N/m). In CGS system, it is dyne per centimeter (dyne/cm). Dimensionally, it is [M T⁻²].
Q8: Give two applications of Hooke's Law.
Two applications are: (1) Spring balance for measuring weight, and (2) Shock absorbers in vehicles to provide smooth ride by absorbing road bumps.
Q9: What is the relationship between force and extension?
Within elastic limit, force and extension are directly proportional. This means if we double the force, the extension also doubles. The graph of F vs x is a straight line passing through the origin.
Q10: What factors affect the spring constant?
Spring constant depends on: (1) Material of the spring - stronger materials have higher k, (2) Wire diameter - thicker wire gives higher k, (3) Coil diameter - smaller coils give higher k, and (4) Number of turns - more turns give lower k.