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title: "Four winches are used to haul shipping containers at constant speed under different operational conditions:  – Winch 1 lifts a container of mass \\(M\\) vertically upward through a vertical height \\(H\\) in a time interval \\(2T\\). – Winch 2 hauls a container of mass \\(2M\\) up a frictionless incline of length \\(2H\\) reaching a vertical height \\(H\\) in a time interval \\(2T\\). – Winch 3 pulls a container of mass \\(M\\) horizontally across a dock floor with coefficient of kinetic friction \\(\\mu_k = 0.40\\) over a distance \\(3H\\) in a time interval \\(T\\). – Winch 4 hauls a container of mass \\(M\\) up a rough incline (\\(\\sin\\theta = 0.60\\), \\(\\cos\\theta = 0.80\\), and coefficient of kinetic friction \\(\\mu_k = 0.25\\)) along a ramp length \\(2H\\) in a time interval \\(T\\).  Which of the following correctly ranks the average mechanical power outputs \\(P_1\\), \\(P_2\\), \\(P_3\\), and \\(P_4\\) of the winches during these operations?"
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url: "https://nerd-notes.com/ubq/119111/"
date_modified: "2026-08-18T04:49:06+00:00"
---

# Four winches are used to haul shipping containers at constant speed under different operational conditions:

– Winch 1 lifts a container of mass \(M\) vertically upward through a vertical height \(H\) in a time interval \(2T\).
– Winch 2 hauls a container of mass \(2M\) up a frictionless incline of length \(2H\) reaching a vertical height \(H\) in a time interval \(2T\).
– Winch 3 pulls a container of mass \(M\) horizontally across a dock floor with coefficient of kinetic friction \(\mu_k = 0.40\) over a distance \(3H\) in a time interval \(T\).
– Winch 4 hauls a container of mass \(M\) up a rough incline (\(\sin\theta = 0.60\), \(\cos\theta = 0.80\), and coefficient of kinetic friction \(\mu_k = 0.25\)) along a ramp length \(2H\) in a time interval \(T\).

Which of the following correctly ranks the average mechanical power outputs \(P_1\), \(P_2\), \(P_3\), and \(P_4\) of the winches during these operations?

Four winches are used to haul shipping containers at constant speed under different operational conditions:

- Winch 1 lifts a container of mass \(M\) vertically upward through a vertical height \(H\) in a time interval \(2T\).
- Winch 2 hauls a container of mass \(2M\) up a frictionless incline of length \(2H\) reaching a vertical height \(H\) in a time interval \(2T\).
- Winch 3 pulls a container of mass \(M\) horizontally across a dock floor with coefficient of kinetic friction \(\mu_k = 0.40\) over a distance \(3H\) in a time interval \(T\).
- Winch 4 hauls a container of mass \(M\) up a rough incline (\(\sin\theta = 0.60\), \(\cos\theta = 0.80\), and coefficient of kinetic friction \(\mu_k = 0.25\)) along a ramp length \(2H\) in a time interval \(T\).

Which of the following correctly ranks the average mechanical power outputs \(P_1\), \(P_2\), \(P_3\), and \(P_4\) of the winches during these operations?

- **A.** \(P_3 < P_1 < P_2 < P_4\)
- **B.** \(P_1 < P_4 < P_2 < P_3\)
- **C.** \(P_2 < P_1 < P_3 < P_4\)
- **D.** \(P_1 < P_2 < P_3 < P_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119111/*