Falling Slowly, Falling Quickly

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Watch the video on YouTube.

What type of experiment is this?

Experimental procedure and explanation:

• Fold pieces of paper of the same size in different ways and compare how fast they fall.
• The magnitude of the air resistance changes depending on how the paper is folded, causing it to fall at different speeds.
• The air resistanceF_Dcan be calculated from the equation below.
  F_D＝C_DρU² S／2
  In this equation,C_Dis the drag coefficient, ρ is the density of air, U is the falling speed, and S is the frontal projection area (the area of the object when viewed from the direction of movement).
• The drag coefficientC_Ddepends on the shape of the object. The approximate value ofC_Dis 1.1 for a square, 0.47 for a sphere, 1 for a cylinder, and 0.01 to 0.1 for a streamlined shape (rounded at the front and pointed at the back).
• In this experiment, in addition to the drag coefficient, the difference in the frontal projection area of the four shapes also has a significant effect. When the paper is not folded, and when it is folded into a cup shape, it has a large frontal projection area and therefore induces increased air resistance.
• We have seen that pieces of paper of the same size (squares with sides of 21 cm) fall at very different speeds when folded in different ways. Try making a shape that will fall as quickly as possible, and a shape that will fall as slowly as possible.

[Keywords]	Air resistance, Separation
[Related items]	Slowly Falling Cupcake Cups, Large Ball and Small Ball
[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. “JSME Textbook Series: Fluid Dynamics,” by Japan Society of Mechanical Engineers, P113.