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title: "A research elevator cab ascends along a vertical axis where the positive y-direction is defined as upward. Inside the cab, two identical blocks of mass m are monitored: Block 1 is suspended from an ideal spring scale attached to the ceiling, and Block 2 rests on an ideal platform scale fixed to the floor. The vertical position of the cab as a function of time is given by \\(y(t) = b t^2 – c t^3\\), where b and c are positive constants such that \\(b < g\\). At time \\(t_1 = \\dfrac{b}{2c}\\), which of the following correctly compares the scale readings \\(F_{\\text{spring}}\\) and \\(F_{\\text{platform}}\\) to the true gravitational weight mg, and indicates the direction of the blocks' instantaneous acceleration vector \\(\\vec{a}\\)?"
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url: "https://nerd-notes.com/ubq/124189/"
date_modified: "2026-09-28T13:31:07+00:00"
---

# A research elevator cab ascends along a vertical axis where the positive y-direction is defined as upward. Inside the cab, two identical blocks of mass m are monitored: Block 1 is suspended from an ideal spring scale attached to the ceiling, and Block 2 rests on an ideal platform scale fixed to the floor. The vertical position of the cab as a function of time is given by \(y(t) = b t^2 – c t^3\), where b and c are positive constants such that \(b < g\). At time \(t_1 = \dfrac{b}{2c}\), which of the following correctly compares the scale readings \(F_{\text{spring}}\) and \(F_{\text{platform}}\) to the true gravitational weight mg, and indicates the direction of the blocks' instantaneous acceleration vector \(\vec{a}\)?

A research elevator cab ascends along a vertical axis where the positive y-direction is defined as upward. Inside the cab, two identical blocks of mass m are monitored: Block 1 is suspended from an ideal spring scale attached to the ceiling, and Block 2 rests on an ideal platform scale fixed to the floor. The vertical position of the cab as a function of time is given by \(y(t) = b t^2 - c t^3\), where b and c are positive constants such that \(b < g\). At time \(t_1 = \dfrac{b}{2c}\), which of the following correctly compares the scale readings \(F_{\text{spring}}\) and \(F_{\text{platform}}\) to the true gravitational weight mg, and indicates the direction of the blocks' instantaneous acceleration vector \(\vec{a}\)?

![A vertical rectangular enclosure representing a test cab with a flat ceiling and a flat floor. Attached to the center of the ceiling is a small vertical coil spring representing an ideal spring scale, with a square mass labeled Block 1 suspended directly beneath it. On the floor of the enclosure rests a flat, wide rectangular base representing an ideal platform scale, with an identical square mass labeled Block 2 resting centered on its upper surface. To the right of the enclosure, a single vertical coordinate axis arrow points upward, labeled +y. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/setup-fig-1-1790602266-HzNbwj.jpg)

- **A.** Scale readings: \(F_{\text{spring}} = F_{\text{platform}} > mg\) ; Direction of \(\vec{a}\): Vertically upward
- **B.** Scale readings: \(F_{\text{spring}} = F_{\text{platform}} > mg\) ; Direction of \(\vec{a}\): Vertically downward
- **C.** Scale readings: \(F_{\text{spring}} = F_{\text{platform}} < mg\) ; Direction of \(\vec{a}\): Vertically downward
- **D.** Scale readings: \(F_{\text{spring}} = F_{\text{platform}} < mg\) ; Direction of \(\vec{a}\): Vertically upward

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124189/*