The "Screaming Swing" is a carnival ride that is-not surprisingly-a giant swing. It's actually two swings moving in opposite directions. At the bottom of its arc, riders are moving at 30 m/s with respect to the ground in a 44 m-diameter circle.

Question

The "Screaming Swing" is a carnival ride that is-not surprisingly-a giant swing. It's actually two swings moving in opposite directions. At the bottom of its arc, riders are moving at 30 m/s with respect to the ground in a 44 m-diameter circle.

At the bottom of the ride, as they pass each other, how fast do the riders move with respect to each other?

I've figured out that the acceleration is 41 m/s^2 and this equates to 4.2g's. Please help me with this last part!

Answer 1

To find the speed at which the riders move with respect to each other at the bottom of the ride, we need to consider their relative velocities.

First, let's calculate the linear velocity of each swing at the bottom of its arc. We're given that the riders are moving at 30 m/s with respect to the ground in a 44 m-diameter circle.

The linear velocity of an object moving in a circle can be calculated using the equation:

v = ω * r

where v is the linear velocity, ω is the angular velocity, and r is the radius of the circle.

In this case, the radius is half the diameter, so r = 44 m / 2 = 22 m.

To find the angular velocity, we can use the formula:

ω = v / r

Plugging in the values, we get:

ω = 30 m/s / 22 m ≈ 1.36 rad/s

Now, since the ride consists of two swings moving in opposite directions, their angular velocities would have opposite signs. Let's assume one swing has a clockwise rotation and the other has a counterclockwise rotation.

At the bottom of the ride, the riders are at the same height, and their relative speed is the sum of their individual velocities. Since the swings are moving in opposite directions, we subtract the angular velocity of one swing from the other. Thus, the relative angular velocity is:

ω relative = ω clockwise - ω counterclockwise

To calculate the relative velocity, we multiply the relative angular velocity by the distance between the swings. Let's assume that distance is equal to the diameter of the circle, which is 44 m.

Relative velocity = ω relative * distance

Relative velocity = (ω clockwise - ω counterclockwise) * 44 m

Let's calculate this:

Relative velocity = (1.36 rad/s - (-1.36 rad/s)) * 44 m

Relative velocity = 2.72 rad/s * 44 m

Relative velocity ≈ 119.68 m/s

Therefore, at the bottom of the ride, as the riders pass each other, they are moving with a relative velocity of approximately 119.68 m/s with respect to each other.