What is Spring Extension & Elasticity?
When you stretch a helical steel spring with an external force, it gets longer. The extra length added to the original spring is called Extension ($e$).
Key Formula: Extension
Original Length ($L_0$): The spring's natural length when no weights or forces are hanging on it.
Stretched Length ($L$): The total measure of the spring from top hook to bottom hook while under load.
What makes a material Elastic?
An object is elastic if it automatically snaps back to its original shape and initial length ($L_0$) as soon as the stretching force is completely removed.
Try Pulling the Spring!
Virtual Spring Extension Experiment
Add weights in increments of 1 Newton (N). Observe how the length increases live and record the data into the table!
Experimental Spring Rig
Load: 0 NRecorded Data Table
| Force (N) | Length (cm) | Extension $e$ (cm) | Behavior Region |
|---|---|---|---|
| 0 N | 10.0 cm | 0.0 cm | Unloaded Baseline |
Every 1 N of additional force adds exactly 2 cm of extension during the initial stage! This direct relationship is called Hooke's Law.
Hooke's Law & Limits of Elasticity
Hooke's Law states that the Extension ($e$) of a spring is directly proportional to the Force ($F$) applied, provided the limit of proportionality is not exceeded ($F = k \cdot e$).
Linear vs Non-Linear Curve
The exact point on the graph where the linear straight line stops and begins to curve.
Beyond this threshold, the spring suffers permanent plastic deformation and won't bounce back!
Elastic vs Plastic Deformation
Spring fully recovers its original shape ($L_0$) once force is removed. Bonds stretch safely without slipping.
Spring stays permanently stretched or bent. Internal atomic layers slide past each other permanently.
Real-World Physics Devices
Force Meter
Uses linear spring extension to measure forces accurately in Newtons.
Pogo Stick
Heavy stiff spring operating in Hooke's elastic zone to absorb jump impact.
Bungee Cord
Elastic latex rubber that provides non-linear smooth deceleration for jumpers.
Mastery Check & Calculations
Answer these 3 interactive questions to test your comprehension of spring extension, calculations, and graphs!
A spring extends by 2 cm when a force of 10 N is applied. Assuming Hooke's Law holds, what force is needed to produce an extension of 5 cm?
10 N produces 2 cm extension $\rightarrow$ Stiffness constant $k = \frac{10\text{ N}}{2\text{ cm}} = 5\text{ N/cm}$.
For 5 cm extension: $\text{Force} = 5\text{ cm} \times 5\text{ N/cm} = \mathbf{25\text{ N}}$.
A heavy load is hung on a steel spring. When the load is removed, the spring remains permanently stretched and does NOT return to its original length. What happened?
Once a force exceeds the elastic limit, the spring enters the plastic region and suffers permanent structural deformation.
On a Force vs Extension graph, what do we call the exact point where the straight line ends and begins to curve?
The Limit of Proportionality (Point P) marks where extension stops being directly proportional to force!
Congratulations! Physics Lab Completed!
You have successfully explored spring extension, Hooke's Law, limits of elasticity, and real-world applications!