A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.5 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 127 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair. (a) Number i 2540 (b) Number i Units Units N 160.0

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Chapter1: Units, Trigonometry. And Vectors
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# Carnival Swing Ride Physics Problem

A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.5 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 127 kg.

## Problem Statement

1. **(a)** Determine the tension in the cable attached to the chair.
2. **(b)** Find the speed of the chair.

## Diagram Explanation

The diagram illustrates a swing ride setup, where a cable forms an angle of 60.0° with the vertical axis as it supports a chair moving in a circular path. The circular motion of the chair creates a horizontal circle (blue) and requires analyzing both horizontal and vertical components of forces.

### Variables

- **Cable Length**: 12.5 m
- **Angle with Vertical**: 60.0°
- **Mass of Chair and Occupant**: 127 kg

### Solution Steps

1. **Determine the Tension (T) in the Cable**
   - Analyze vertical and horizontal components of tension and gravitational force.

2. **Calculate the Speed (v) of the Chair**
   - Use centripetal force to relate tension and speed.

## Input Fields

- **(a)** Tension in cable (You can input the value: **2540** N)
- **(b)** Speed of the chair (Input field for value in appropriate units) 

This exercise involves using trigonometry and dynamics to solve for the tension and speed, based on circular motion principles.
Transcribed Image Text:# Carnival Swing Ride Physics Problem A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.5 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 127 kg. ## Problem Statement 1. **(a)** Determine the tension in the cable attached to the chair. 2. **(b)** Find the speed of the chair. ## Diagram Explanation The diagram illustrates a swing ride setup, where a cable forms an angle of 60.0° with the vertical axis as it supports a chair moving in a circular path. The circular motion of the chair creates a horizontal circle (blue) and requires analyzing both horizontal and vertical components of forces. ### Variables - **Cable Length**: 12.5 m - **Angle with Vertical**: 60.0° - **Mass of Chair and Occupant**: 127 kg ### Solution Steps 1. **Determine the Tension (T) in the Cable** - Analyze vertical and horizontal components of tension and gravitational force. 2. **Calculate the Speed (v) of the Chair** - Use centripetal force to relate tension and speed. ## Input Fields - **(a)** Tension in cable (You can input the value: **2540** N) - **(b)** Speed of the chair (Input field for value in appropriate units) This exercise involves using trigonometry and dynamics to solve for the tension and speed, based on circular motion principles.
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