A thin rod of length 0.926 m and mass 174 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 1.49 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises. (a) Number i (b) Number i Units Units

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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

A thin rod of length 0.926 m and mass 174 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with an angular speed of 1.49 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises.

### Solution

1. **Kinetic Energy Calculation (Part a):**
   - Formula: \( KE = \frac{1}{2} I \omega^2 \)
   - Where \( I \) is the moment of inertia and \( \omega \) is the angular speed.

2. **Height Calculation (Part b):**
   - Use energy conservation principles to find the height.

### Input Fields

- (a) Kinetic Energy:  
  - **Number:** [Input box]
  - **Units:** [Dropdown]

- (b) Height:  
  - **Number:** [Input box]
  - **Units:** [Dropdown] 

### Notes
- Ensure all calculations consider the length and mass unit conversions where necessary.
- Assume ideal conditions for energy conversion (no energy loss).
Transcribed Image Text:## Problem Statement A thin rod of length 0.926 m and mass 174 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with an angular speed of 1.49 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises. ### Solution 1. **Kinetic Energy Calculation (Part a):** - Formula: \( KE = \frac{1}{2} I \omega^2 \) - Where \( I \) is the moment of inertia and \( \omega \) is the angular speed. 2. **Height Calculation (Part b):** - Use energy conservation principles to find the height. ### Input Fields - (a) Kinetic Energy: - **Number:** [Input box] - **Units:** [Dropdown] - (b) Height: - **Number:** [Input box] - **Units:** [Dropdown] ### Notes - Ensure all calculations consider the length and mass unit conversions where necessary. - Assume ideal conditions for energy conversion (no energy loss).
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