Question

Using words, explain the laws of physics behind this in a paragraph. Don't just write equations with few words.

Here is the video: https://www.youtube.com/watch?v=8B_6BU7SYf8

The Horo was used by the Ancient Japanese to deflect arrows from enemies. Explain how such silk could stop the arrows. The video itself explains it little but please expand on that more and use equations/formulas (like perhaps one for KE) to aid the explanation.

Answer 1

Just before the arrow hits the Horo, it is moving at 80 mph (as they mentioned in the video), that is 35.76 m/s, or 128 km/h. This means that it has kinetic energy. The work - energy principle tells us that the kinetic energy of the arrow must be transformed in other form of energy or work, if the arrow must be stopped by the Horo. This work is the work done by the drag force produced by the wind and the friction force between the Horo and the arrow:

(work equals force times displacement) and

where d is the distance traveled by the arrow once it has reached the Horo.

The drag force is given by

where is the density of the air, is the velocity of the air relative to the Horo, and A is the reference area. The faster the samurai rides, and the larger the area of the Horo resisting the wind, the greater this drag force inflating it.

note that this is a very simplified model, because the actual drag force that resists the penetration of the arrow is not produced by a constant area (it changes as the arrow moves further through the fabric) and also the friction force changes with the movement of the arrow.