Slowly Falling Cupcake Cup

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What type of experiment is this?

Experimental procedure and explanation:

• We learn in science classes that an object will fall with constant acceleration due to gravity, ignoring air resistance. In other words, when you let go of something, it will fall downwards, getting faster as it falls. However, in reality, air resistance acts as a brake on the falling object.
• In this experiment, we investigate the effect of air resistance by dropping a cupcake cup.
• We observe that the cupcake cup falls slowly because it is light, and the air resistance is large. Beneath the cupcake cup, the flow separates, increasing the air resistance.
• When we let go of the cupcake cup, at first it accelerates, but after it has fallen a certain distance, its speed stops increasing and becomes almost constant. This constant speed is called the terminal velocity, and the falling object’s speed will not exceed this terminal velocity. In this state, the air resistance is equal to gravity; therefore, the forces are balanced, and the falling object neither accelerates nor decelerates. The magnitude of the air resistance F_D and the terminal velocity U∞ can be calculated from the equations below (ignoring the buoyancy from the air).
  F_D＝C_DρU ² S／2
  U∞ ＝√（2mg／C_DρS）
  In these equations, √ is the square root, m is the mass of the object, g is the gravitational acceleration,C_Dis the drag coefficient (roughly determined by the shape of the object), ρ is the density of air, U is the falling speed, and S is the frontal projected area (the area of the object when viewed from the direction of movement).
• In our experiment, we dropped both large and small aluminum cupcake cups. We found that the mass m is almost proportional to the frontal projected area S, and the air resistance is also almost proportional to the frontal projected area S. For these reasons, and because C_D is not related to the falling object’s size, the two cups both fell at approximately the same speed.
• When we put a paperclip on an aluminum cupcake cup to make it heavier without altering its size or shape, the cupcake cup fell faster because of its increased mass.

[Keywords]	Air resistance, Terminal velocity
[Related items]	Slowly Sinking Cupcake Cup, Heavy Ball and Light Ball, Air Flow Behind a Board
[Reference]	“The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, P136－139. “Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, P66－69. “Introduction to Fluid Dynamics,” by Ryozo Ishiwata, Morikita Publishing, P123－124.