A Ferris wheel 26.0m in diameter rotates once every 19.0s What is the ratio of a person's apparent weight to her real weight at the top and at the bottom?
Please help! I know there are other questions similar to this but none of the answers are helping me, they are too confusing.
So far I have that the velocity is 2pi(13)/19= 4.29 m/s and acceleration is 1.42 m/s^2.
To calculate the ratio of a person's apparent weight to their real weight at the top and bottom of the Ferris wheel, we need to understand the concept of centripetal acceleration.
First, let's find the centripetal acceleration of the person on the Ferris wheel. Centripetal acceleration is given by the equation:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity
r = radius
You correctly found the velocity of the Ferris wheel to be 4.29 m/s. However, to find the radius, we need to convert the diameter to radius by dividing it by 2:
r = 26.0m / 2 = 13.0m
Now, let's calculate the centripetal acceleration:
a = (4.29m/s)^2 / 13.0m = 1.43 m/s^2
Now that we have the centripetal acceleration, we can calculate the apparent weight of the person at the top and bottom of the Ferris wheel. In this case, the apparent weight is the sum of the person's real weight (mg) and the additional force due to the centripetal acceleration (ma).
At the top of the Ferris wheel, the apparent weight is:
W_top = mg + ma
At the bottom of the Ferris wheel, the apparent weight is:
W_bottom = mg - ma
To find the ratio of the apparent weight to the real weight, divide the apparent weight by the real weight:
Ratio_top = W_top / mg
Ratio_bottom = W_bottom / mg
Now, let's calculate the ratios:
Ratio_top = (mg + ma) / mg
= (m + ma / m
= 1 + (a / g)
Ratio_top = 1 + (1.43 m/s^2 / 9.8 m/s^2)
= 1.146
Ratio_bottom = (mg - ma) / mg
= (m - ma) / m
= 1 - (a / g)
Ratio_bottom = 1 - (1.43 m/s^2 / 9.8 m/s^2)
= 0.854
Therefore, the ratio of a person's apparent weight to their real weight at the top of the Ferris wheel is approximately 1.146, and at the bottom, it is approximately 0.854.