A particular Ferris wheel takes you through one complete revolution every 25.3 seconds. If the radius of the Ferris wheel is 10.4 m, and your mass is 63.3 kg, calculate:

(a)
Your apparent weight, in N, when you are at the top of the Ferris wheel.
(b)
Your apparent weight, in N, at the bottom of the Ferris wheel.

To calculate the apparent weight at the top and bottom of the Ferris wheel, we need to consider the gravitational force and the centripetal force.

(a) At the top of the Ferris wheel, the centripetal force is directed downwards while the gravitational force is also directed downwards. Therefore, the apparent weight will be the sum of these two forces.

The centripetal force (Fc) can be calculated using the formula:
Fc = m * v^2 / r

Where:
m = mass = 63.3 kg
v = linear velocity = circumference / time = 2π * r / time
r = radius of the Ferris wheel = 10.4 m
time = 25.3 seconds

Plugging in the values, we get:
v = 2π * 10.4 m / 25.3 s = 8.24 m/s
Fc = 63.3 kg * (8.24 m/s)^2 / 10.4 m
Fc ≈ 318.63 N

The gravitational force (Fg) can be calculated using the formula:
Fg = m * g

Where:
g = acceleration due to gravity = 9.8 m/s^2

Plugging in the values, we get:
Fg = 63.3 kg * 9.8 m/s^2
Fg ≈ 620.34 N

Therefore, the apparent weight at the top of the Ferris wheel is the sum of the centripetal force and the gravitational force:
Apparent weight = Fc + Fg
Apparent weight ≈ 318.63 N + 620.34 N
Apparent weight ≈ 938.97 N

(b) At the bottom of the Ferris wheel, the centripetal force is directed upwards while the gravitational force is directed downwards. Therefore, the apparent weight will be the difference between these two forces.

Using the previously calculated values for Fc and Fg, the apparent weight at the bottom can be calculated as:
Apparent weight = Fg - Fc
Apparent weight ≈ 620.34 N - 318.63 N
Apparent weight ≈ 301.71 N

Therefore, the apparent weight at the bottom of the Ferris wheel is approximately 301.71 N.

To calculate the apparent weight at the top and bottom of the Ferris wheel, we need to consider the angular velocity and the centripetal force acting on the person.

First, let's find the angular velocity (ω) of the Ferris wheel. The angular velocity is given by the formula:

ω = 2π / T,

where T is the time period for one complete revolution (in this case, 25.3 seconds).

ω = 2π / 25.3 = 0.248 rad/s.

Next, we'll calculate the centripetal force (Fc) acting on you when you are at the top and bottom of the Ferris wheel. The centripetal force is given by the formula:

Fc = m * ω^2 * r,

where m is the mass of the person and r is the radius of the Ferris wheel.

(a)
When you are at the top of the Ferris wheel, the centripetal force is acting in the opposite direction of your weight, so the apparent weight will be the difference between the Centripetal force and the weight. The weight (W) is given by:

W = m * g,

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

W = 63.3 kg * 9.8 m/s^2 = 619.74 N.

Now, let's calculate the Centripetal force (Fc) at the top:

Fc = m * ω^2 * r.

Fc = 63.3 kg * (0.248 rad/s)^2 * 10.4 m.

Fc = 40.13 N.

Therefore, your apparent weight at the top of the Ferris wheel is:

Apparent weight = W - Fc.

Apparent weight = 619.74 N - 40.13 N = 579.61 N.

(b)
When you are at the bottom of the Ferris wheel, the centripetal force is acting in the same direction as your weight, so the apparent weight will be the sum of the Centripetal force and the weight.

Now, let's calculate the Centripetal force (Fc) at the bottom:

Fc = m * ω^2 * r.

Fc = 63.3 kg * (0.248 rad/s)^2 * 10.4 m.

Fc = 40.13 N.

Therefore, your apparent weight at the bottom of the Ferris wheel is:

Apparent weight = W + Fc.

Apparent weight = 619.74 N + 40.13 N = 659.87 N.

So, your apparent weight at the top of the Ferris wheel is 579.61 N, and your apparent weight at the bottom of the Ferris wheel is 659.87 N.

Yes