Exploring the Relationship Between Arrows, Mass, and Force

[bradcad]

Hi all

My first post, please go gentle on me as I have a very limited understanding of physics. I do enjoy trying to understand, and hence my question. I hope you can help.

I have just started archery- about to pick up my first bow. For the last few weeks I have been reading archery books and websites including forums to learn as much as I can.

One consistant question I come across is- how heavy should arrows be for a certain task. For example, those into hunting are very particular about using an arrow weighted to a task. The larger the animal they want to hunt, the heavier the arrow. Seems fair enough.

My confusion-

'Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it'

So two arrows identical except mass have an equal force applied to them.

Newtons second law- (the one I'm most interested in) The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.

Those arrows with differing mass accellerate at differing speeds, but must have effectively the same force, as the accelleration is relative to mass, and force = mass x accelleration

For every action there is an equal and opposite reaction.

Thinking about these 3 laws says to me that both arrows must carry the same force at the same point when fired from the bow.

Then I think about this.

Law of Falling Bodies:
Two objects that are identical except for their masses are dropped from the same height at the same time. With air resistance set to zero, both balls strike the ground at the same time. As the air resistance is increased, the more massive object will strike the ground first. With enough air resistance the lighter ball is seen to reach a terminal velocity.

If this is the answer, air resistance is higher on the lighter arrow as it is traveling faster, and lighter bodies are affected more by forces than heavier ones.



Finally to my question-

Why is a heavier arrow required to penetrate a thicker hide? Is it a question of air resistance reducing the force of the smaller arrow, or something I have overlooked?

Thank you

BRad

 

[cesiumfrog]

Naively, if the bow imparts equal energy to two arrows, the heavier arrow must go slower (and hence fall shorter) whereas the lighter arrow must have less momentum (and hence stop penetrating sooner against an equal force).

 

[gdpudasaini]

Are you sure that heavier arrow is required to penerate the thick surface? I think lighter arrow also can do it

 

[MrXow]

The lighter arrow will have less momentum. Another reason for a heavier arrow is it will be in layman's terms, less flimsy. If you try to throw a PVC pipe like a javelin, it will spin around. An actual, weighted javelin will not spin around.

 

[cesiumfrog]

Are you sure that heavier arrow is required to penerate the thick surface? I think lighter arrow also can do it

The speed and stopping time I mentioned should indeed cancel such that the penetrating distance is proportional to the initial energy only, although additionally the arrow with more momentum is more more likely to knock the target over.

Theoretically, if the bow itself has some inertia (which it does), it should impart less energy to the lighter arrow (being unable to shoot infinitely fast), hence the heavier arrow does penetrate further. (The lighter arrow still flies faster, which suggests that some particular weight will optimise the bow range after accounting for air resistance. Too light will flutter rather than penetrating the air, too heavy will drop out.)