A Ferris wheel has a circumference of 93 m and it completes one rotation in 2.3 minutes without stopping. What is the percentage change in apparent weight (=weight difference/weight = W/W) of a passenger between the highest and the lowest positions on this Ferris wheel?

To calculate the percentage change in apparent weight of a passenger on the Ferris wheel, we need to determine the weight at the highest and lowest positions.

First, let's find the distance traveled by a passenger in one rotation. The circumference of the Ferris wheel is given as 93 m, which means that in one complete rotation, the passenger travels a distance equal to the circumference.

Next, we need to find the time taken for one rotation. It is given that the Ferris wheel completes one rotation in 2.3 minutes.

Now, we can use the formula for velocity:

velocity (v) = distance (d) / time (t)

In this case, the distance traveled by the passenger in one rotation is equal to the circumference (93 m) and the time taken is 2.3 minutes. Since we are interested in the speed, we need to convert minutes to seconds:

time (t) = 2.3 minutes * 60 seconds/minute = 138 seconds

Plugging the values into the formula, we get:

velocity (v) = distance (d) / time (t)
v = 93 m / 138 s
v ≈ 0.674 m/s

Now, let's consider the forces acting on the passenger at the highest and lowest points of the Ferris wheel.

At the highest point, the apparent weight of the passenger is equal to the passenger's actual weight plus the centrifugal force acting in the opposite direction to gravity (upwards).

At the lowest point, the apparent weight of the passenger is equal to the passenger's actual weight minus the centrifugal force acting in the same direction as gravity (downwards).

The centrifugal force can be calculated using the formula:

centrifugal force = mass * velocity^2 / radius

Since the mass of the passenger cancels out in the weight difference calculation, we can omit it from further calculations.

Next, we need to find the radius of the Ferris wheel. The circumference in this case is equal to 2 * π * radius, so we can rearrange the formula to solve for the radius:

radius = circumference / (2 * π)
radius = 93 m / (2 * 3.14)
radius ≈ 14.8 m

Now, let's calculate the weight difference at the highest and lowest points:

At the highest point:
centrifugal force = velocity^2 / radius
weight difference = centrifugal force - 0 (no additional force against gravity)

At the lowest point:
centrifugal force = velocity^2 / radius
weight difference = 0 - centrifugal force (force opposing gravity)

Finally, we can calculate the weight difference as a percentage change in weight:

percentage change = weight difference / weight * 100

Please note that we're assuming the initial weight of the passenger stays constant throughout this calculation.

Plug in the values and calculate the percentage change in weight to get the answer.