A person rides a Ferris wheel that turns with constant angular velocity. Her weight is 509.0 N. At the top of the ride her apparent weight is 1.5 N different from her true weight. If the angular speed of the Ferris wheel is 0.025 rad/s, what is its radius (in meters)?
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At the top of the wheel the person's apparent weight would be LESS than her actual weight, and the difference (1.5 N) is the force needed to keep her moving in a circular path. That's called centripetal force.
Fc = mω²r
We don't have her mass, but we do know her weight, and we know that on Earth:
Fw = mg
509.0 N = m(9.81 m/s²)
m = 51.9 kg
Now back to the original equation:
1.5 N = (51.9 kg)(0.025 rad/s)²r
1.5 N = (0.0324 kg/s²)r
r = 46.2 m
I hope that helps. Good luck!
Fc = mω²r
We don't have her mass, but we do know her weight, and we know that on Earth:
Fw = mg
509.0 N = m(9.81 m/s²)
m = 51.9 kg
Now back to the original equation:
1.5 N = (51.9 kg)(0.025 rad/s)²r
1.5 N = (0.0324 kg/s²)r
r = 46.2 m
I hope that helps. Good luck!
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apparent weight + actual weight= (mass of person)*(0.025)^2 * R
here mass of person is 50.9 , and R is radius
cheers :)
here mass of person is 50.9 , and R is radius
cheers :)
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[g - R*w²]*W/g = 509 - 1.5 = 507.5 → R = g[1 - 507.5/509]/w²
R = 46.2 m
R = 46.2 m