Work: springs, pumping and cables
Problem 5.479 · easy
A 30-ft cable weighing 3 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
- \[ \int\limits_{0}^{30} 3 x\, dx = 1350 \]Add it up.✓ Proved
Answer \( 1350\ \text{ft-lb} \)
✓ 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 models the work done by integrating the weight of each segment times the distance it is lifted. The calculation is correct.
Every verdict on record (4)
gpt-oss:20b: pass 2026-10-11qwen3.6:27b-mlx: pass 2026-10-11 — The setup correctly models the work done by integrating the weight of each segment times the distance it is lifted. The calculation is correct.gpt-oss:20b: pass 2026-10-11qwen3.6:27b-mlx: pass 2026-10-11 — The setup correctly identifies the weight of the segment as 3 dx and the distance it must be lifted as x. The integration bounds and result are 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 2026-10-11 with SymPy 1.14.0.