You are riding a carousel that is turning at a constant angular velocity. You must pull toward the center with 100N of force to stay in place. You decide to move radially toward the center of the carousel to ride on a small animal figure that is at half the distance from the center of your previous seat. How much force force will be required to hang on to this internal seat?

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To determine the force required to hang on to the internal seat, we need to consider the centripetal force acting on you. The centripetal force is responsible for keeping an object moving in a circular path.

In this scenario, as you move radially toward the center of the carousel to the internal seat, the radius of your circular path decreases. This means the magnitude of the centripetal force required to keep you in circular motion will increase.

The formula for centripetal force is given by:

Fc = (m * v^2) / r

Where:
- Fc is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circular path

In this case, the velocity of the carousel is constant, so we can ignore the velocity term.

Now, let's assume your mass (m) remains constant. Initially, the radius of your circular path is R, which corresponds to the original seat. When you move to the internal seat, the radius becomes R/2.

The centripetal force at the original seat (F1) is given by:

F1 = (m * v^2) / R

The centripetal force at the internal seat (F2) is given by:

F2 = (m * v^2) / (R/2)

Since we are only interested in comparing the forces, we can simplify the above equations further:

F2 = 2 * F1

Therefore, the force required to hang on to the internal seat will be twice the force required to hang on to the original seat. In this case, since the force required to hang on to the original seat is 100N, the force required to hang on to the internal seat would be 2 * 100N = 200N.