Springs and Hooke’s law
When you stretch a spring, the extension is proportional to the force, as long as you don’t go past the limit of proportionality. The spring constant k says how stiff the spring is.
Key facts
- F = kx (x is the extension in metres).
- Extension = new length − original length.
- Past the limit of proportionality the graph curves; past the elastic limit the spring won’t go back.
- Elastic potential energy = ½kx².
Worked examples
Example 1
A spring is 12 cm long. A 6 N weight makes it 15 cm long. Find k.
- Extension: 15 − 12 = 3 cm = 0.03 m.
- k = F/x = 6 ÷ 0.03 = 200 N/m
Answer: 200 N/m
Example 2
How much energy is stored in that spring at 3 cm extension?
- ½ × 200 × 0.03² = 0.09 J
Answer: 0.09 J