A Ferris wheel 26.0m in diameter rotates once every 15.0s .
What is the ratio of a person's apparent weight to her real weight at the top?
See answer to a similar question below under related questions
To find the ratio of a person's apparent weight to her real weight at the top of the Ferris wheel, we need to consider the centripetal force acting on the person.
The centripetal force is given by the equation:
Fc = m * (v^2 / r)
Where:
- Fc is the centripetal force,
- m is the mass of the person,
- v is the velocity of the person, and
- r is the radius of the Ferris wheel.
In this case, we know the Ferris wheel's diameter is 26.0m, so its radius is half of that, which is 13.0m.
Furthermore, we know that the Ferris wheel rotates once every 15.0s, which means it completes one revolution every 15.0s. This gives us the angular speed (ω) in radians per second:
ω = (2π radians) / (time for one revolution)
Substituting the given values:
ω = (2π radians) / (15.0s)
Now, we can find the velocity of the person at the top of the Ferris wheel by multiplying the radius of the Ferris wheel by the angular speed:
v = r * ω
Substituting the given values:
v = (13.0m) * [(2π radians) / (15.0s)]
Finally, to find the ratio of the person's apparent weight to her real weight at the top, we divide the centripetal force by her actual weight. Since the apparent weight is the weight felt by the person in the rotating frame of reference, it can be calculated using the equation:
Apparent Weight = Real Weight - Fc
Therefore, the ratio of apparent weight to real weight is given by:
Ratio = Apparent Weight / Real Weight
To calculate this ratio, we need the mass of the person and the acceleration due to gravity (g). The value of g is approximately 9.8 m/s².
Once you have the values for mass and g, you can plug them into the formulas mentioned above and calculate the ratio of a person's apparent weight to her real weight at the top of the Ferris wheel.