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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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## Understanding the Motion of a Particle on a Frictionless Track

### Problem Statement

A particle slides along a frictionless track shown in the figure, starting at rest from point \( A \). 

### Figure 1: Particle on a Frictionless Track

![Figure 1: Frictionless Track Diagram](image-url-placeholder)

The figure illustrates a frictionless track with a particle starting from point \( A \) at rest. The track consists of various slopes and valleys, with specific measurements of height and horizontal distances marked at various points:

- Point \( A \) is positioned at a height of \( 96.0 \) cm.
- Point \( B \) is lower in height and is \( 72.0 \) cm horizontally away from \( A \).
- Point \( C \) is another point further along the track, \( 39.0 \) cm from \( B \).

### Part A

Determine the speed of the particle at point \( B \). 

**Input:** 
\[ v_B = \boxed{21.68} \, \text{m/s} \]

**Feedback:**
Incorrect response. You have 5 attempts remaining.

### Part B

Determine the speed of the particle at point \( C \).

**Question:** 
Express your answer using two significant figures.

**Input:** 
\[ v_C = \boxed{25.4} \, \text{m/s} \]

---

### Detailed Description of the Track Diagram

The track diagram depicts the initial and subsequent positions of a particle in motion along a frictionless path. 

1. **Point \( A \)**: This is the highest point on the track at 96.0 cm. The particle starts from rest here, which means its initial potential energy is maximum, and kinetic energy is zero.

2. **Path from \( A \) to \( B \)**: The particle descends, converting potential energy into kinetic energy. The horizontal distance between points \( A \) and \( B \) is 72.0 cm. 

3. **Point \( B \)**: The particle reaches here with a certain speed to be calculated.

4. **Path from \( B \) to \( C \)**: The particle continues moving along the track, and the horizontal distance between \( B \) and \( C \) is 39.0 cm. 

5. **Point \( C \)**: The particle's speed is
Transcribed Image Text:## Understanding the Motion of a Particle on a Frictionless Track ### Problem Statement A particle slides along a frictionless track shown in the figure, starting at rest from point \( A \). ### Figure 1: Particle on a Frictionless Track ![Figure 1: Frictionless Track Diagram](image-url-placeholder) The figure illustrates a frictionless track with a particle starting from point \( A \) at rest. The track consists of various slopes and valleys, with specific measurements of height and horizontal distances marked at various points: - Point \( A \) is positioned at a height of \( 96.0 \) cm. - Point \( B \) is lower in height and is \( 72.0 \) cm horizontally away from \( A \). - Point \( C \) is another point further along the track, \( 39.0 \) cm from \( B \). ### Part A Determine the speed of the particle at point \( B \). **Input:** \[ v_B = \boxed{21.68} \, \text{m/s} \] **Feedback:** Incorrect response. You have 5 attempts remaining. ### Part B Determine the speed of the particle at point \( C \). **Question:** Express your answer using two significant figures. **Input:** \[ v_C = \boxed{25.4} \, \text{m/s} \] --- ### Detailed Description of the Track Diagram The track diagram depicts the initial and subsequent positions of a particle in motion along a frictionless path. 1. **Point \( A \)**: This is the highest point on the track at 96.0 cm. The particle starts from rest here, which means its initial potential energy is maximum, and kinetic energy is zero. 2. **Path from \( A \) to \( B \)**: The particle descends, converting potential energy into kinetic energy. The horizontal distance between points \( A \) and \( B \) is 72.0 cm. 3. **Point \( B \)**: The particle reaches here with a certain speed to be calculated. 4. **Path from \( B \) to \( C \)**: The particle continues moving along the track, and the horizontal distance between \( B \) and \( C \) is 39.0 cm. 5. **Point \( C \)**: The particle's speed is
**Particle Motion Analysis on a Frictionless Track**

In this exercise, we analyze the movement of a particle that slides along a frictionless track. The particle begins at rest from point \( A \).

### Figure Overview:
The figure displays a particle track with various positions and elevations marked for reference. Below is a detailed description of the graph:

- **YAxis (Height, h in cm)**: This axis measures the height of the points on the track above the baseline.
- **XAxis (Position, x in meters)**: This axis indicates the horizontal position of the particle along the track.

**Key Points on the Track:**
- **Point A:** 
  - Height: \( 96.0 \) cm 
  - Position: \(2 \) m
- **Point B:**
  - Height: \(72.0 \) cm 
  - Position: \(6 \) m
- **Point C:** 
  - Height: \(39.0 \) cm 
  - Position: \(9 \) m

### Problem Statement: 
The issue requires finding the approximate location of the particle's right-hand turning point using two significant figures. This analysis will require considering the conservation of energy principles and the initial conditions provided. 

#### Task:
1. **Find the approximate location of the right-hand turning point.**
2. **Express your answer using two significant figures.**

**Interactive Components:**
- An input box for the user to submit their answer (\( \text{x}_D \) in meters).
- Buttons for submitting the answer, requesting an answer, and viewing previous attempts.
- Notice of the number of remaining attempts for the user.

### Additional Tools: 
Provided is an equation editor with various mathematical symbols to assist with complex calculations. 

---

For further guidance, remember to employ energy conservation principles to find the right-hand turning point.
Transcribed Image Text:**Particle Motion Analysis on a Frictionless Track** In this exercise, we analyze the movement of a particle that slides along a frictionless track. The particle begins at rest from point \( A \). ### Figure Overview: The figure displays a particle track with various positions and elevations marked for reference. Below is a detailed description of the graph: - **YAxis (Height, h in cm)**: This axis measures the height of the points on the track above the baseline. - **XAxis (Position, x in meters)**: This axis indicates the horizontal position of the particle along the track. **Key Points on the Track:** - **Point A:** - Height: \( 96.0 \) cm - Position: \(2 \) m - **Point B:** - Height: \(72.0 \) cm - Position: \(6 \) m - **Point C:** - Height: \(39.0 \) cm - Position: \(9 \) m ### Problem Statement: The issue requires finding the approximate location of the particle's right-hand turning point using two significant figures. This analysis will require considering the conservation of energy principles and the initial conditions provided. #### Task: 1. **Find the approximate location of the right-hand turning point.** 2. **Express your answer using two significant figures.** **Interactive Components:** - An input box for the user to submit their answer (\( \text{x}_D \) in meters). - Buttons for submitting the answer, requesting an answer, and viewing previous attempts. - Notice of the number of remaining attempts for the user. ### Additional Tools: Provided is an equation editor with various mathematical symbols to assist with complex calculations. --- For further guidance, remember to employ energy conservation principles to find the right-hand turning point.
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