The Physics of Archery: Fake Forces

The Physics of Archery 

When you think about archery you may be very confused when watching a slowed down version of a archery such as the one below. 

 

As you can tell be able to tell just by looking at the motions of archery the force comes from the pulling back of strings as shown in the picture below.

The bow start at rest and accelerates until the bowstring stops applying force. However this does not explain why the arrow wobbles so much. This can be explained by fake forces. While fake forces may seem fake they are real. When first  understand fake forces it may seem like everything that has been taught to you in physics is a lie, because it goes against newton's second law. Newton's second law is necessary in physics but it is only applicable if  forces and accelerations are measured with respect to a constant velocity reference frame. When measures this way a fake force must be applied. The new equation is Ffake=-ma. These fake forces are not a evil new development and have probably been encountered by the average individual. This fake force is experienced while riding on an elevator. A fake force pushing down on you due to the acceleration of the elevator. This makes you feel like you have become heavier, but it is actually just  force due to a real interaction. 

Now you may be confused how this fake force causes this wobble, because not all elevators wobble. This is because there is not only a fake force acting upon this arrow in Archery.  

Now this may be confusing because it would make sense that the two forces would cancel each other out and the arrow would not move, but this is not the case. One way to picture why would happen is placing a arrow against a wall. When you place pressure on the arrow, it does not snap or stay still it bends a little. This is why during flight the arrow is constantly bending.  Once the bowstring stops applying force to the   arrow, the arrow is no longer accelerating. If the arrow is no longer accelerating, the fake force is not longer present. This results in a  bent arrow with no forces. This cause the arrow to attempt to return it’s straight shape, but it cannot stay there. When it gets to the straight position it is moving with speed. This speed  causes it to overshoot this equilibrium, and now it’s bent the other way. Thus begins the oscillating arrow, which makes it look like this is slow motion. 

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