Work: springs, pumping and cables
Problem 5.272 · easy
A force of 12 N holds a spring stretched \frac{1}{10} m beyond its natural length. How much work does it take to stretch it from \frac{3}{10} m to \frac{2}{5} m beyond its natural length?
- Hooke's law: F(x) = kx, with x the stretch beyond natural length.Reviewed
- \[ 120 \]k from the given force and stretch (N/m).✓ Proved
- \[ \int\limits_{\frac{3}{10}}^{\frac{2}{5}} 120 x\, dx = \frac{21}{5} \]W = ∫ F(x) dx.✓ Proved
Answer \( \frac{21}{5} \approx 4.2\ \text{J} \)
✓ Nihil obstat Lines: 2 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | Reviewed | reviewers: gpt-oss:20b, qwen3.6:27b-mlx | a sentence; read, not computed |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| 3 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| answer, a second way | ✓ Checked independently | sympy 1.14.0 + mpmath 1.3.0 | numerical quadrature |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: pass — The solution correctly applies Hooke's Law to determine the spring constant and integrates the force over the specified interval to find the work done.
Every verdict on record (4)
qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly applies Hooke's Law to determine the spring constant and integrates the force over the specified interval to find the work done.gpt-oss:20b: pass 2026-10-05qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly applies Hooke's Law to find the spring constant and then integrates the force over the specified interval to calculate work. The bounds and arithmetic are correct.gpt-oss:20b: pass 2026-10-05
Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate
method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence,
not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by
generator:structured/work, checked 2026-10-05 with SymPy 1.14.0.