Mechanics & Simple Machines · GCSE Physics Hooke's Law & Elasticity
Hooke's Law Spring Scale & Dual-Pull Simulator
Universal exam trap: Two 5N forces pulling opposite ends read exactly 5N (NOT 10N, NOT 0N). One side provides tension; the other acts as the anchor reacting force.
- Client-side
- No Sign-up
- Live Derivation
- Projector Mode
- Print Worksheet
3D Simulation Stage● 60 FPS
Parameter Controls
N
N/m
N/m
cm
Live Derivations & Metrics
Scale Reading
--
Extension Δx
--
Total Length L
--
Effective k
--
Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Related Tool:
🌀 Standard Tool: Spring Rate Calculator ↗
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: A spring is 10cm unloaded and 12cm with 2N. What is the extension and total length under 5N within elastic limit?
Step-by-Step Derivation:
- Extension per newton = 2cm / 2N = 1cm/N. Under 5N, extension Δx = 5cm, total length L = 10 + 5 = 15cm.
Worked Problem
Problem: Two identical springs with k=200N/m are connected in series and parallel under 20N. Find effective k and extension.
Step-by-Step Derivation:
- Series: k_series = 100N/m, Δx = 20/100 = 0.2m = 20cm. Parallel: k_parallel = 400N/m, Δx = 20/400 = 0.05m = 5cm.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: What are three mandatory pre-use inspection steps for a spring dynamometer?
Answer Key: 1) Check maximum range and graduation; 2) zero-calibrate in the orientation of use; 3) gently exercise hook to prevent housing friction.
Q2. Variant 2: A spring scale is 18cm under 10N and 22cm under 15N. Find unloaded length L0 and stiffness k.
Answer Key: ΔF = 5N stretches 4cm (0.8 cm/N). Stiffness k = 125 N/m. Natural length L0 = 18 - (10 * 0.8) = 10cm.
Q3. Variant 3: Two identical spring scales are hooked in series supporting 6N. What does each scale display?
Answer Key: Both scales read 6N. In a series string, tensile force is uniform across all members.
Frequently Asked Questions & Misconceptions
Why is a dual 5N pull not 10N or 0N?
The scale measures internal tension. Two opposing 5N forces balance the assembly, inducing exactly 5N of tension. Without opposing force, the scale would accelerate freely without stretching.
Can a spring scale be used upside down?
No. The metal casing has mass. Inverting it adds the casing weight to the spring reading, introducing systematic positive error unless re-zeroed in that position.
What happens when the elastic limit is exceeded?
Plastic deformation occurs. The spring will not return to its original length, violating Hooke's law and permanently ruining scale calibration.
If a spring is cut in half, does stiffness increase or decrease?
It doubles (k' = 2k). Under the same force, each half extends half as far as the whole spring, meaning twice the force is required for unit extension.