**“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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"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)

"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)

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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Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

**“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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