Carousels
are amusement park rides with seats in the form of horses revolving about a
fixed center, they are almost like a vertical Ferris wheels. The carousel
rotates in a circular motion faster and faster until it reaches a certain speed.
Horses on the carousel move around in a circle all in the same amount of
time. But the horses on toward the outside of the carousel have a greater
distance to cover than the horses toward the center. The horses that are
toward the outside will have to have a greater speed to travel around the circle
in the same amount of time as the other horses.
On some carousels, the horses gallop. For these horses to gallop, you need
a force to move them up and down. To determine the amount of force you
need, you have to consider both the mass of the horse and rider.
Centripetal
Force
According to Newton's first law the speed and
direction of a moving body remain constant if no force acts on it. When a
moving body is moving in a circular motion then there's an unbalanced force
causing it go in circles, this force that is directed toward the center is
called centripetal force. For there to be a net force, there must be
acceleration. Both acceleration and force are directed toward the center.
Mathematics of Carousels / Circular Motion
You can manipulate this equation depending on what you want to find and what
variables you have. But since you're moving in a complete cycle, you can replace
distance with the circumference. So the equation is:
velocity=circumference / time traveled.
Circumference can be found by multiplying the radius by two pi (circumference
= 2*pi*Radius).
To find the acceleration of one of the horses, there are two equations you
can use:
Acceleration = Velocity^2 / Radius and
Acceleration=4*pi^2*radius /
time^2.
On some carousels, the horses gallop. For these horses to gallop, you need a
force to move them up and down. To determine the amount of force you need, you
have to consider both the masses of the horse and rider. The acceleration of the
horses is also related to the force. Newton's second law gives us the equation:
(F=ma).
This equation can be manipulated knowing the above equations:
Force centripetal force= mass* velocity^2 / radius and
force
centripetal force=mass(4*pi^2*radius / time traveled^2).
Using equations like these, we can better understand the motion of objects
that move in a circular motion.
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