Answered: Please refer to the picture with the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Please refer to the picture with the formulas and constants that need to be used in this problem.

Harzan wants to swing from one bank of the river to the other using an overhaning vine. As he swings, he traces out an arc of a circle.

Part 1) Please draw and label a free body diagram of Harzan at the bottom of the swing.

Answer: we have to discuss the motion of the swinging person

Part 2) What forces act as the radial force in the circular motion?

Answer: In the radial direction centrifugal force will act as a source of tension

Part 3) Is this uniform circular motion? Explain

Answer: The motion is similar to that of a pendulum, thus the vine-swinger system acts like a physical pendulum, the motion will not be uniform circular.

Part 4) The vine is 6.2 m long, and Harzan's mass is 85 kg. At the bottom of his swing, he is travelling at 4.3 m/s. What is the magnitide of the radial acceleration that Harzan experiences?

Part 5) How much tension must the vine support in order to safely transport Harzan over the river?

Please answer parts 4 and 5. Please answer using the correct formula from this formula sheet. Thank you

**Formulas:**

- \(\vec{a}_{avg} = \frac{\Delta \vec{V}}{\Delta t} \rightarrow \vec{V}_f = \vec{V}_i + \vec{a}_{avg} \Delta t\)

- \(\vec{V}_{avg} = \frac{1}{2} (\vec{V}_i + \vec{V}_f)\)

- \(\vec{V}_{avg} = \frac{\Delta \vec{x}}{\Delta t} \rightarrow \vec{x}_f = \vec{x}_i + \vec{V}_{avg} \Delta t\)

- \(\vec{x}_f = \vec{x}_i + \vec{V}_i \Delta t + \frac{1}{2} \vec{a} \Delta t^2\)

- \(V_f^2 = V_i^2 + 2a\Delta x\)

- \(F = ma\)

- \(F_f = \mu_k F_N\)

- \(a_R = \frac{V^2}{r}\)

- \(\vec{F}_{AB} = -\vec{F}_{BA}\)

- \(F_f \leq \mu_sF_N\)

- \(F_G = G \frac{m_1m_2}{r^2}\)

- \(f = \frac{1}{T}\)

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**Constants:**

- \(c \approx 3 \times 10^8\) m/s
- \(g \approx 9.8\) m/s\(^2\)
- \(G \approx 6.7 \times 10^{-11}\) N\(\cdot\)m\(^2\)/kg\(^2\)

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**Geometry:**

- \(A = lw\)

- \(A = \frac{1}{2}bh\)

- \(A = \pi r^2\)

- \(c = 2\pi r\)

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**Units:**

- \(t = s\)

- \(\vec{x} = m\)

- \(\vec{V} = \text{m/s}\)

- \(\vec{a} = \text{m/s}^2\)

- \(m = \text{kg}\)

- \(\vec{F} = N\)

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