An object travels in a vertical circle of 1.76 m radius. When the object is traveling downward and is 39.0° from its lowest point, its total acceleration is a = (18.5î + 16.2j) m/s2. At this instant, determine the following. (Take the angle 39.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.) (a) magnitude of the radial acceleration 22.89 Draw a figure in order to get a good view of the particle, the acceleration vector, and its components. How can you obtain the radial acceleration from the components of the total acceleration? m/s2 (b) magnitude of the tangential acceleration m/s? (c) speed of the object m/s (d) velocity of the object (Express your answer in vector form.) m/s
An object travels in a vertical circle of 1.76 m radius. When the object is traveling downward and is 39.0° from its lowest point, its total acceleration is a = (18.5î + 16.2j) m/s2. At this instant, determine the following. (Take the angle 39.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.) (a) magnitude of the radial acceleration 22.89 Draw a figure in order to get a good view of the particle, the acceleration vector, and its components. How can you obtain the radial acceleration from the components of the total acceleration? m/s2 (b) magnitude of the tangential acceleration m/s? (c) speed of the object m/s (d) velocity of the object (Express your answer in vector form.) m/s
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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![### Problem Statement:
**Context:**
An object travels in a vertical circle of 1.76 m radius. When the object is traveling downward and is 39.0° from its lowest point, its total acceleration is \( \vec{a} = (18.5 \hat{i} + 16.2 \hat{j}) \, \text{m/s}^2 \). At this instant, determine the following. (Take the angle 39.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.)
**Questions:**
1. (a) Magnitude of the radial acceleration
2. (b) Magnitude of the tangential acceleration
3. (c) Speed of the object
4. (d) Velocity of the object (Express your answer in vector form.)
---
**Solutions:**
**(a) Magnitude of the radial acceleration:**
\[ \boxed{[22.89]} \times \]
*Note: Draw a figure to get a good view of the particle, the acceleration vector, and its components. How can you obtain the radial acceleration from the components of the total acceleration?*
Unit: \( \text{m/s}^2 \)
---
**(b) Magnitude of the tangential acceleration:**
\[ \boxed{[ \phantom{x} ]} \\]
Unit: \( \text{m/s}^2 \)
---
**(c) Speed of the object:**
\[ \boxed{[ \phantom{x} ]} \times \]
Unit: \( \text{m/s} \)
---
**(d) Velocity of the object (Express your answer in vector form):**
\[ \vec{v} = \boxed{[ \phantom{x} ]} \]
Unit: \( \text{m/s} \)
---
**Explanation of Diagrams and Figures:**
- A diagram should be drawn that includes the circle of motion, indicating the object's position at 39.0° from the lowest point.
- Mark the direction of the total acceleration vector \(( \vec{a} )\).
- Decompose the total acceleration vector into radial and tangential components.
### Observations:
- A red cross mark suggests an incorrect answer for (a)'s provided value 22.89 \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1774cd4-7542-40dd-a6d2-b73f5360ee27%2Ff61dbe0a-0e7c-49af-a47c-39ffa6874e19%2Fmieridm.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**Context:**
An object travels in a vertical circle of 1.76 m radius. When the object is traveling downward and is 39.0° from its lowest point, its total acceleration is \( \vec{a} = (18.5 \hat{i} + 16.2 \hat{j}) \, \text{m/s}^2 \). At this instant, determine the following. (Take the angle 39.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.)
**Questions:**
1. (a) Magnitude of the radial acceleration
2. (b) Magnitude of the tangential acceleration
3. (c) Speed of the object
4. (d) Velocity of the object (Express your answer in vector form.)
---
**Solutions:**
**(a) Magnitude of the radial acceleration:**
\[ \boxed{[22.89]} \times \]
*Note: Draw a figure to get a good view of the particle, the acceleration vector, and its components. How can you obtain the radial acceleration from the components of the total acceleration?*
Unit: \( \text{m/s}^2 \)
---
**(b) Magnitude of the tangential acceleration:**
\[ \boxed{[ \phantom{x} ]} \\]
Unit: \( \text{m/s}^2 \)
---
**(c) Speed of the object:**
\[ \boxed{[ \phantom{x} ]} \times \]
Unit: \( \text{m/s} \)
---
**(d) Velocity of the object (Express your answer in vector form):**
\[ \vec{v} = \boxed{[ \phantom{x} ]} \]
Unit: \( \text{m/s} \)
---
**Explanation of Diagrams and Figures:**
- A diagram should be drawn that includes the circle of motion, indicating the object's position at 39.0° from the lowest point.
- Mark the direction of the total acceleration vector \(( \vec{a} )\).
- Decompose the total acceleration vector into radial and tangential components.
### Observations:
- A red cross mark suggests an incorrect answer for (a)'s provided value 22.89 \(
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