A ferris wheel has a radius of 9m. The centre of the wheel is 11m above the ground. The Ferris wheel rotates at a constant speed of 12° per second. What is the amplitude?
To find the amplitude of the Ferris wheel, we need to find the maximum vertical distance from the center of the wheel to the ground.
The radius of the wheel is 9m. This means that the distance from the center of the wheel to the topmost point is also 9m.
Since the center of the wheel is 11m above the ground, we can calculate the amplitude by subtracting the radius from the height of the center:
Amplitude = Center height - Radius
= 11m - 9m
= 2m
Therefore, the amplitude of the Ferris wheel is 2m.
To find the amplitude of the ferris wheel, we need to first understand what the amplitude represents. In the context of periodic motion, the amplitude is the maximum distance that the object moves away from its equilibrium position.
In this case, the ferris wheel's equilibrium position can be defined as the position of the center of the wheel when it is at ground level. Since the center of the wheel is 11m above the ground, the equilibrium position can be considered as a point 11m above the ground.
The ferris wheel rotates at a constant speed of 12° per second. Since the ferris wheel is circular, the angular displacement can be related to the linear displacement using the relationship:
angular displacement = (linear displacement) / (radius)
Since the angular displacement for one complete rotation is 360°, we can calculate the linear displacement using the equation:
360° = (linear displacement) / (radius)
Solving for the linear displacement:
linear displacement = 360° * radius
linear displacement = 360° * 9m
linear displacement = 3240m
The amplitude is the maximum distance from the equilibrium position, so it is half of the linear displacement. Therefore, the amplitude of the ferris wheel is:
amplitude = linear displacement / 2
amplitude = 3240m / 2
amplitude = 1620m
Therefore, the amplitude of the ferris wheel is 1620m.