What is Hooke's Law?
Hooke's Law states that the extension (or compression) of an elastic material is directly proportional to the applied force, provided the elastic limit is not exceeded. This is one of the most fundamental principles in physics and engineering.
F = kx
where F = Applied Force (N)
k = Spring Constant (N/m)
x = Extension or Compression (m)
The spring constant 'k' is a measure of the stiffness of the spring. A higher value means a stiffer spring that requires more force to stretch.
Aim of the Experiment
To verify Hooke's Law and determine the spring constant (k) of a given spring by plotting a graph between applied force (F) and extension (x).
Apparatus Required
š¦ Materials You'll Need:
- A helical spring (preferably steel)
- Slotted weights (50g each, total 500g recommended)
- Weight hanger (usually 50g)
- Vertical wooden board or stand with clamp
- Meter scale or ruler
- Pointer attached to the weight hanger
- Graph paper and pencil
Theory Behind the Experiment
When we hang a spring vertically and attach weights to it, the spring extends. According to Hooke's Law, if we plot a graph of Force (y-axis) vs Extension (x-axis), we should get a straight line passing through the origin. The slope of this line gives us the spring constant 'k'.
Slope = k = ĪF / Īx
The steeper the slope, the stiffer the spring!
Step-by-Step Procedure
Part 1: Setup
- Mount the spring: Clamp the upper end of the spring to a rigid horizontal support (like a wooden board or retort stand). Ensure it hangs vertically without any twist.
- Attach the pointer: Fix a light pointer (like a thin wire) horizontally to the weight hanger. This helps you read the extension accurately.
- Set up the scale: Place a meter scale vertically behind the spring, close to but not touching the pointer.
- Note initial reading: With just the weight hanger (no extra weights), note the position of the pointer on the scale. This is your initial reading (Lā).
Part 2: Taking Readings
- Add the first weight: Place a 50g slotted weight on the hanger. Wait for the spring to stop oscillating and come to rest.
- Record new position: Note the new position of the pointer (Lā). Calculate the extension: xā = Lā - Lā
- Repeat for more weights: Keep adding 50g weights one by one (100g, 150g, 200g, etc.) up to 500g. For each weight, record the pointer position and calculate the extension.
- Take at least 8-10 readings for better accuracy and to ensure you're within the elastic limit.
ā ļø Critical Warning:
Do not overload the spring! If you add too much weight, the spring will permanently deform and Hooke's Law will no longer apply. Stop if you notice the spring isn't returning to its original length after removing weights.
Observation Table Format
| S.No. | Load (g) | Force F (N) | Position L (cm) | Extension x (cm) |
|---|---|---|---|---|
| 0 | 50 | 0.49 | 15.0 | 0.0 |
| 1 | 100 | 0.98 | 16.2 | 1.2 |
| 2 | 150 | 1.47 | 17.4 | 2.4 |
| ...continue for all readings | ||||
š” Important Conversion:
Remember to convert mass to force!
Force (N) = Mass (kg) Ć g (9.8 m/sĀ²)
For 50g: F = 0.05 Ć 9.8 = 0.49 N
Graphing Your Results
Plot a graph with:
- X-axis: Extension x (in cm or m)
- Y-axis: Applied Force F (in N)
You should get a straight line. Draw the best-fit line through your points. The slope of this line is your spring constant 'k'.
k = (Fā - Fā) / (xā - xā)
Choose two points far apart on your line for better accuracy
Calculating Spring Constant
Example Calculation:
If from your graph:
Point 1: (xā = 2 cm, Fā = 0.98 N)
Point 2: (xā = 10 cm, Fā = 4.90 N)
k = (4.90 - 0.98) / (0.10 - 0.02) [converting cm to m]
k = 3.92 / 0.08
k = 49 N/m
Precautions
ā Follow These Precautions:
- The spring should be perfectly vertical and not twisted
- Add weights gently to avoid jerking the spring
- Wait for oscillations to stop before taking readings
- Take the reading when your eye is at the level of the pointer (avoid parallax)
- Do not exceed the elastic limit of the spring
- The pointer should be horizontal and perpendicular to the scale
- Use a rigid support that doesn't bend under the weight
- Record all readings in proper units
Sources of Error
- Parallax Error: If you don't read the scale at eye level
- Spring Quality: Old or damaged springs may not follow Hooke's Law perfectly
- Friction: In the spring's coils can affect extension
- Temperature: Very cold or hot conditions can affect spring properties
- Exceeding Elastic Limit: Permanently deforms the spring
Result & Conclusion
Write your result in this format:
"The spring constant of the given helical spring is found to be k = ___ N/m. The graph of Force vs Extension is a straight line passing through the origin, which verifies Hooke's Law within the elastic limit."
Pro Tip for Exams: If your graph doesn't pass exactly through the origin, don't panic! Small deviations are normal due to experimental errors. Just mention this in your sources of error section and you'll still get full marks.