A Ferris wheel 20.0m in diameter rotates once every 21.0s
What is the ratio of a person's apparent weight to her real weight at the top?(Wa / W)
What is the ratio of a person's apparent weight to her real weight at the bottom? (Wa/W)
What is the ratio of a person's apparent weight to her real weight at the top?(Wa / W)
What is the ratio of a person's apparent weight to her real weight at the bottom? (Wa/W)
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OK so d= 20 and c = pi*d = 6.28 m
then v = d/t = c/t = 6.28 / 21 = 2.99 m/s
so
centripetal a = v^2 / r = 2.99^2 / 10 = 0.895 m/s/s
then 0.895 m/s/s / 9.81 m/s/s / g = 0.09125 g
at the top Wa = m ( 1g - 0.09125 g) = m 0.909g
and W = m g so Wa/W = 0.909 / 1 or about 90.9% of normal weight
at the botton Wa = m ( 1g + 0.09125g) = m 1.09125g
and Wa/W = 1.109 / 1 or about 109% of normal
then v = d/t = c/t = 6.28 / 21 = 2.99 m/s
so
centripetal a = v^2 / r = 2.99^2 / 10 = 0.895 m/s/s
then 0.895 m/s/s / 9.81 m/s/s / g = 0.09125 g
at the top Wa = m ( 1g - 0.09125 g) = m 0.909g
and W = m g so Wa/W = 0.909 / 1 or about 90.9% of normal weight
at the botton Wa = m ( 1g + 0.09125g) = m 1.09125g
and Wa/W = 1.109 / 1 or about 109% of normal
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The centripetal force is pulling the seat toward the center of the circle. At the top, the centripetal force is pulling the seat down, so the person feels like his weight has decreased. At the bottom, the centripetal force is pulling the seat up, so the person feels like his weight has increased.
The weight of the person = mass * 9.8
The person is moving a distance equal to the circumference of the circle in 21 seconds.
Centripetal force = mass * velocity^2 ÷ radius
Circumference = 2 * π * 10.0
Velocity = (2 * π * 10.0 ÷ 21) m/s
Centripetal force = mass * velocity^2 ÷ radius = m * (2 * π * 10.0 ÷ 21)^2 ÷ 10.0 = m * 0.895
At the top, the apparent weight = m * 9.8 – m * 0.895 = m * 8.905
At the bottom, the apparent weight = m * 9.8 + m * 0.895 = m * 10.695
What is the ratio of a person's apparent weight to her real weight at the top?
m * 8.905 / m * 9.8 (m’s cancel)
Wa /W = 8.905/9.8
What is the ratio of a person's apparent weight to her real weight at the bottom?
Wa/W = 10.695 / 9.8
These ratios are actually the ratio of the net acceleration /g
Centripetal acceleration = v^2/r = (2 * π * 10.0 ÷ 21)^2 ÷ 10.0 = 0.895 m/s^2
Net acceleration at the top = 9.8 – 0.895
Ratio = (9.8 – 0.895)/9.8 = 0.909
At the top, the person is 0.909 g’s
Net acceleration at the bottom = 9.8 + 0.895
Ratio = (9.8 + 0.895)/9.8 = 1.09
At the bottom, the person is 1.09 g’s
The weight of the person = mass * 9.8
The person is moving a distance equal to the circumference of the circle in 21 seconds.
Centripetal force = mass * velocity^2 ÷ radius
Circumference = 2 * π * 10.0
Velocity = (2 * π * 10.0 ÷ 21) m/s
Centripetal force = mass * velocity^2 ÷ radius = m * (2 * π * 10.0 ÷ 21)^2 ÷ 10.0 = m * 0.895
At the top, the apparent weight = m * 9.8 – m * 0.895 = m * 8.905
At the bottom, the apparent weight = m * 9.8 + m * 0.895 = m * 10.695
What is the ratio of a person's apparent weight to her real weight at the top?
m * 8.905 / m * 9.8 (m’s cancel)
Wa /W = 8.905/9.8
What is the ratio of a person's apparent weight to her real weight at the bottom?
Wa/W = 10.695 / 9.8
These ratios are actually the ratio of the net acceleration /g
Centripetal acceleration = v^2/r = (2 * π * 10.0 ÷ 21)^2 ÷ 10.0 = 0.895 m/s^2
Net acceleration at the top = 9.8 – 0.895
Ratio = (9.8 – 0.895)/9.8 = 0.909
At the top, the person is 0.909 g’s
Net acceleration at the bottom = 9.8 + 0.895
Ratio = (9.8 + 0.895)/9.8 = 1.09
At the bottom, the person is 1.09 g’s