(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"?

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Chapter1: Units, Trigonometry. And Vectors
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(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
apparent weight)
actual weight
18:
• 1-v²/gr at the top of the wheel
. 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)
(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)
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 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 apparent weight) actual weight 18: • 1-v²/gr at the top of the wheel . 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) (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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