Work: springs, pumping and cables
Problem 5.545 · easy
A 10-ft cable weighing 2 lb/ft hangs from the top of a building. How much work does it take to pull it all to the top?
- Measure x down from the top. The piece of cable at depth x weighs ρ·dx and rises x feet.Reviewed
- \[ \int\limits_{0}^{10} 2 x\, dx = 100 \]Add it up.✓ Proved
Answer \( 100\ \text{ft-lb} \)
✓ Nihil obstat Lines: 1 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 |
| 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 setup correctly identifies the weight of the differential element and the distance it must be lifted. The integration limits and integrand are correct for the problem statement.
Every verdict on record (4)
gpt-oss:20b: pass 2026-10-13qwen3.6:27b-mlx: pass 2026-10-13 — The setup correctly identifies the weight of the differential element and the distance it must be lifted. The integration limits and integrand are correct for the problem statement.gpt-oss:20b: pass 2026-10-13qwen3.6:27b-mlx: pass 2026-10-13 — The setup correctly models the work done by integrating the weight of each segment times the distance it is lifted. The calculation is correct.
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 2026-10-13 with SymPy 1.14.0.