Physics · Grades 9–12
Springs and the linear elastic limit
Use extension, not total length, and distinguish force from stored energy.
Learn the idea
Extension
Extension is stretched length minus natural length. It may need conversion to metres.
Linear model
Within its linear elastic range, an ideal spring follows F = kx.
Energy
Stored elastic energy is one half kx squared in the same linear model.
Limits
A straight force-extension law should not be extrapolated past the stated range without evidence.
Worked examples
A spring's natural length is 12 cm and stretched length is 17 cm. Find extension.
Extension is 17 − 12 = 5 cm.
5 cm
An ideal spring has k = 200 N/m and extension 0.03 m. Find force.
F = kx = 200 × 0.03 = 6 N.
6 N
Check your understanding
For k = 100 N/m and x = 0.2 m, find stored elastic energy.
At fixed spring constant, doubling extension multiplies stored energy by what?
- 1
- 4
- 2
Why is substituting a total spring length into F = kx incorrect?
Answers and marking notes
Answers and marking notes
- 2 J
0.5 × 100 × 0.2² = 2 J.
- 4
Energy is proportional to extension squared.
- x is the change from natural length, not the full length.
Credit the definition of extension.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.