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Transcribed Image Text:**Title:** Understanding Forces on a Ferris Wheel
**Introduction:**
A woman of mass \( m \) rides in a Ferris wheel of radius \( R \). In order to better understand physics, she takes along a bathroom scale and sits on it. Determine the difference in scale readings between the bottom and top of the Ferris wheel (\( \Delta F_{\text{scale}} \)) as a function of the constant angular speed of the Ferris wheel (\( \omega \)), \( m \), \( R \), and \( g \).
**Free-Body Diagrams:**
- **Top of Ferris Wheel:**
- A simple stick figure representing the woman sitting on a scale at the top of the Ferris wheel. The forces acting on her include gravitational force downward and normal force from the scale.
- **Bottom of Ferris Wheel:**
- Another stick figure representing the woman at the bottom of the Ferris wheel. Again, gravitational force acts downward while the normal force from the scale acts upward.
**Mathematical Analysis:**
This section is presumably left for students to calculate the difference in forces using principles of circular motion and Newton's laws.
**Questions:**
1. If \( \omega = 0 \, \text{rad/s} \), what should \( \Delta F_{\text{scale}} \) equal? Does your function agree with this observation?
2. If \( \omega \) was twice as large, what would happen to \( \Delta F_{\text{scale}} \)?
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This exercise teaches students about the effects of centripetal force on scale readings during circular motion, exploring how velocity impacts perceived weight in different positions on the Ferris wheel.
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