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title: "A uniform horizontal strut of length \\(L\\) and mass \\(M\\) is attached to a vertical wall by a frictionless hinge at \\(x = 0\\). A light cable is connected between the outer end of the strut at \\(x = L\\) and the wall, making an angle \\(\\theta\\) above the horizontal strut. A small block of mass \\(m\\) is moved slowly along the strut from the hinge at \\(x = 0\\) to the tip at \\(x = L\\), and the tension \\(T\\) in the cable is recorded as a function of the block’s position \\(x\\), as shown in the graph. Which of the following statements correctly interprets a physical feature of the system based on the graph?"
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url: "https://nerd-notes.com/ubq/124392/"
date_modified: "2026-09-28T14:05:08+00:00"
---

# A uniform horizontal strut of length \(L\) and mass \(M\) is attached to a vertical wall by a frictionless hinge at \(x = 0\). A light cable is connected between the outer end of the strut at \(x = L\) and the wall, making an angle \(\theta\) above the horizontal strut. A small block of mass \(m\) is moved slowly along the strut from the hinge at \(x = 0\) to the tip at \(x = L\), and the tension \(T\) in the cable is recorded as a function of the block’s position \(x\), as shown in the graph. Which of the following statements correctly interprets a physical feature of the system based on the graph?

A uniform horizontal strut of length \(L\) and mass \(M\) is attached to a vertical wall by a frictionless hinge at \(x = 0\). A light cable is connected between the outer end of the strut at \(x = L\) and the wall, making an angle \(\theta\) above the horizontal strut. A small block of mass \(m\) is moved slowly along the strut from the hinge at \(x = 0\) to the tip at \(x = L\), and the tension \(T\) in the cable is recorded as a function of the block's position \(x\), as shown in the graph. Which of the following statements correctly interprets a physical feature of the system based on the graph?

![A Cartesian graph with a horizontal axis labeled x and a vertical axis labeled T. The horizontal axis begins at 0 and has a single tick mark at the far right labeled L. The vertical axis begins at 0 and has two tick marks: one at a moderate height labeled T_0, and one near the top labeled T_1. A single solid straight line segment begins at the vertical intercept (0, T_0) and extends upward and to the right with a constant positive slope, terminating at the point (L, T_1). A horizontal dashed line extends from (L, T_1) leftward to the vertical axis at tick mark T_1, and a vertical dashed line extends downward from (L, T_1) to the horizontal axis at tick mark L. No gridlines, other curves, shading, text, or extraneous markings appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604308-ArxQDo.jpg)

- **A.** The vertical component of the force exerted by the hinge on the strut increases linearly with \(x\) at a rate equal to \(+\sin\theta\left(\dfrac{dT}{dx}\right)\), because the gravitational torque about the hinge increases as the block moves.
- **B.** The horizontal component of the force exerted by the hinge on the strut remains constant for all positions \(x\), because the block moves horizontally without acceleration.
- **C.** The vertical component of the force exerted by the hinge on the strut decreases linearly with \(x\) at a rate equal to \(-\sin\theta\left(\dfrac{dT}{dx}\right)\), because the cable supports an increasing share of the total weight.
- **D.** The area under the curve, \(\int_0^L T(x)\,dx\), represents the total mechanical work done by the cable tension on the strut as the block moves from \(x = 0\) to \(x = L\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124392/*