A Ferris wheel 28.0m in diameter rotates once every 21.0s.
What is the ratio of a person's apparent weight to her real weight at the top?
What is the ratio of a person's apparent weight to her real weight at the bottom?
radius, r = 28/2 m =14 m
Period, T = 21 s
angular velocity, ω = 2π/21 rad/s
Centrifugal force, f= mrω²
actual weight, w = mg
apparent weight at top, wt = mg -f
apparent weight at bottom, wb = mg+f
Solve for f and calculate wt/w and wb/w.
so i have a question how do you solve for f if there is no m?
the m's cancel at some point in the equation
To determine the ratio of a person's apparent weight to her real weight at different points on the Ferris wheel, we need to consider the forces acting on the person.
At the top of the Ferris wheel:
1. Find the centripetal force acting on the person at the top of the Ferris wheel.
- Centripetal force (Fc) = mass (m) x centripetal acceleration (ac)
- Centripetal acceleration (ac) = (velocity (v))^2 / radius (r)
- Velocity (v) = circumference (C) / time taken for one rotation (T)
- Radius (r) = diameter (d) / 2
- Substitute the values to find centripetal force (Fc) at the top.
2. Find the net force acting on the person at the top of the Ferris wheel.
- Net force (Fn) = real weight (W) - centripetal force (Fc)
3. Calculate the ratio of the person's apparent weight to her real weight at the top.
- Ratio at the top = apparent weight (Wa) / real weight (W)
- Apparent weight (Wa) at the top is equal to the net force (Fn).
Repeat the same steps to find the ratio at the bottom, but using the appropriate values for the radius and velocity.
Note: The apparent weight will be greater than the real weight at the bottom and less than the real weight at the top.
I can help you calculate the ratios if you provide the value for mass (m) or the person's weight (W).