"Losing and Gaining Weight" on the Ferris Wheel A person is riding on the Ferris wheel, as shown below. Her mass is m, her tangential speed is v, and she is at a distance r = 14.8 m from the center of the wheel. (a) Show that the normal force N that the seat exerts on the person is given by: • N= m(g-v²/r) at the top of the wheel N = m(g + v²/r) at the bottom of the wheel (b) Show that the ratio of the person's apparent weight to her actual weight • 1-v²/gr at the top of the wheel (apparent weight) actual weight is: 1+v²/gr at the bottom of the wheel (c) Calculate the two ratios in (b) for v=2.85 m/s. (answer: 0.944 at the top; 1.06 at the bottom) V (d) Where does the person "feel lightest"? Where does the person "feel heaviest"? (e) What value of v at the top is required so that the person "feels weightless"? (answer: 12.0 m/s)

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**“Losing and Gaining Weight” on the Ferris Wheel**

A person is riding on the Ferris wheel, as shown below. Her mass is \( m \), her tangential speed is \( v \), and she is at a distance \( r = 14.8 \, \text{m} \) from the center of the wheel.

**(a)** Show that the normal force \( N \) that the seat exerts on the person is given by:

- \( N = m(g - v^2/r) \) at the top of the wheel
- \( N = m(g + v^2/r) \) at the bottom of the wheel

**(b)** Show that the ratio of the person’s *apparent weight* to her *actual weight* \( \left(\frac{\text{apparent weight}}{\text{actual weight}}\right) \) is:

- \( 1 - v^2/gr \) at the top of the wheel
- \( 1 + v^2/gr \) at the bottom of the wheel

**(c)** Calculate the two ratios in (b) for \( v = 2.85 \, \text{m/s} \). (*answer: 0.944 at the top; 1.06 at the bottom*)

**(d)** Where does the person "feel lightest"? Where does the person "feel heaviest"?

**(e)** What value of \( v \) at the top is required so that the person "feels weightless"? (*answer: 12.0 m/s*)

### Diagram Explanation:

The diagrams illustrate a Ferris wheel with:

1. **Left Diagram:** 
   - Position at the top of the wheel.
   - Tangential speed \( v \), and distance \( r \) from the center indicated.

2. **Right Diagram:**
   - Position at the bottom of the wheel.
   - Shows the same notations for \( v \) and \( r \).

These diagrams help to visualize the forces acting on a person at different positions on the Ferris wheel.
Transcribed Image Text:**“Losing and Gaining Weight” on the Ferris Wheel** A person is riding on the Ferris wheel, as shown below. Her mass is \( m \), her tangential speed is \( v \), and she is at a distance \( r = 14.8 \, \text{m} \) from the center of the wheel. **(a)** Show that the normal force \( N \) that the seat exerts on the person is given by: - \( N = m(g - v^2/r) \) at the top of the wheel - \( N = m(g + v^2/r) \) at the bottom of the wheel **(b)** Show that the ratio of the person’s *apparent weight* to her *actual weight* \( \left(\frac{\text{apparent weight}}{\text{actual weight}}\right) \) is: - \( 1 - v^2/gr \) at the top of the wheel - \( 1 + v^2/gr \) at the bottom of the wheel **(c)** Calculate the two ratios in (b) for \( v = 2.85 \, \text{m/s} \). (*answer: 0.944 at the top; 1.06 at the bottom*) **(d)** Where does the person "feel lightest"? Where does the person "feel heaviest"? **(e)** What value of \( v \) at the top is required so that the person "feels weightless"? (*answer: 12.0 m/s*) ### Diagram Explanation: The diagrams illustrate a Ferris wheel with: 1. **Left Diagram:** - Position at the top of the wheel. - Tangential speed \( v \), and distance \( r \) from the center indicated. 2. **Right Diagram:** - Position at the bottom of the wheel. - Shows the same notations for \( v \) and \( r \). These diagrams help to visualize the forces acting on a person at different positions on the Ferris wheel.
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