Porter asked in Science & MathematicsPhysics · 2 years ago

# What happens if I pull back an arrow in a bow, then release both ends simultaneously?

I'm wondering about the physics here:

What would happen if I notched an arrow in a bow, pulled the arrow back, and then released my hand holding the bow and my hand holding the arrow at the exact same time?

Assume that my me releasing my grip doesn't affect the orientation of the bow or the arrow at all. For simplicity, let's say that if I had only released the arrow (not the bow), the arrow would have flown 100 yards. And assume that I am aiming the arrow parallel to the ground.

Does the arrow fly the whole 100 yards? 50 yards? Only a couple feet? Does it fly at all?

Relevance
• Whome
Lv 7
2 years ago

Once you release the bow/arrow combination, you remove yourself, and most critically, your mass, from the system.

Now it's just a spring loaded system of two masses. As the spring is internal to the system, the center of mass of the system will stay in one spot. This obeys the rule of conservation of momentum.

The energy stored in the spring during drawing process will be converted to kinetic energy of both bow and arrow in opposite directions. There will be very slight losses of energy due to friction with air and between bow and arrow. A small amount of energy will also be converted to internal vibrations in the system, some of which will be converted to sound energy as the bowstring "twang" heard when released. All of these will obey conservation of energy and work.

But back to the arrow and how far it flies

Conservation of momentum says that, for commonly sized bows that one could lift and draw, your removing yourself from the system means the bow will have a greater,"backward" velocity than if you held it.

This converts to a lower forward velocity for the arrow and a smaller forward range for that arrow. How much smaller would be related to the mass ratios of bow and arrow.

If the bow had a mass as large as the effective mass of your body on the system, the arrow would fly just as far as if you had released it yourself. However, that particular bow would be so heavy that you could probably not even lift it.

• Anonymous
1 year ago

Both "ends" of WHAT?

• Anonymous
2 years ago

You would have to release the arrow AND the bowstring for the arrow to fly anywhere but down.

You would have to know the weight of the bow, the bowstring, and the arrow, as well as the length when pulled back.

And a more than a few other parameters, in order to get an accurate answer.

However, not considering the effect of friction of the arrow on the bow, the string will go forward somewhat and send the arrow forward as well.

My bet is a few feet, at most.

• 2 years ago

The arrow would move a small distance downrange.

distance?  I suspect it has to do with the ratio of the mass of the arrow compared to that of the bow. A very heavy bow or a very light arrow would result in almost a normal flight. But that is only a guess.

Take as an example, a very heavy bow, say bolted to a cement block. In that case the arrow would move almost all the way downrange.