![]() Substituting this into the above equations we find thatĪ P = 2.2 m/s 2 (centripetal acceleration)Īt the top of the Ferris wheel the passengers experience 0.78 g (they feel lighter).Īt the bottom of the Ferris wheel the passengers experience 1.2 g (they feel heavier). Two full revolutions per minute translates into w = 0.21 radians/s. Let's say we have a Ferris wheel with a radius of 50 meters, which makes two full revolutions per minute. It's informative to look at an example to get an idea of how much force acts on the passengers. ![]() ![]() they are at the same height as the center of the Ferris wheel). This occurs when the riders are exactly halfway between the top and bottom (i.e. The riders only feel their "true weight", when the centripetal acceleration is pointing horizontally and has no vector component parallel with gravity, and as a result it has no contribution in the vertical direction. So basically, the motion of a Ferris wheel affects your bodies "apparent" weight, which varies depending on where you are on the ride. This means that the passengers feel "heaviest" at the bottom of the Ferris wheel, and the "lightest" at the top. Therefore, the velocity and acceleration of these two points are the same. This is because point C does not move relative to point P. The acceleration of the passengers at point C is equal to the acceleration of the Ferris wheel at point P. ![]() To solve for N 1 and N 2 we must apply this equation in the vertical direction. At these two positions a P is a vector which is aligned (parallel) with gravity, so their contributions can be directly added together. At the top of the circle a P is pointing down. So at the bottom of the circle, a P is pointing up. The centripetal acceleration always points towards the center of the circle. So at location (1) this acceleration is pointing directly down, and at location (2) this acceleration is pointing directly up. This acceleration is always pointing towards the center of the wheel. N 2 is the force exerted on the passengers (by the seats) at point C, at location (2)Ī P is the centripetal acceleration of point P. Mg is the force of gravity pulling down on the passengers, where m is the mass of the passengers and g is the acceleration due to gravity, which is 9.8 m/s 2 N 1 is the force exerted on the passengers (by the seats) at point C, at location (1) The figure below shows a free-body diagram for the passengers at these locations. We wish to analyze the forces acting on the passengers at locations (1) and (2). The forces acting on the passengers are due to the combined effect of gravity and centripetal acceleration, caused by the rotation of the Ferris wheel with angular velocity w. W is the angular velocity of the Ferris wheel, in radians/s Point C is where the passengers sit (on the gondola) Point P is where the gondolas are attached to the Ferris wheel (1) is the top-most position and (2) is the bottom-most position The figure below shows a schematic of the Ferris wheel, illustrating the essentials of the problem. To analyze the Ferris wheel physics, we must first simplify the problem. As a result, the gondolas always hang downwards at all times as the Ferris wheel spins. These gondolas can freely pivot at the support where they are connected to the Ferris wheel. The Ferris wheel consists of an upright wheel with passenger gondolas (seats) attached to the rim. Ferris wheel physics is directly related to centripetal acceleration, which results in the riders feeling "heavier" or "lighter" depending on their position on the Ferris wheel.
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