Calculating Arrow Speed with Doubled Force: Newton's Second Law

In summary: Thanks for clearing that up!In summary, if you double the force exerted on an arrow by the bow, the arrow will leave the bow at a speed double what it would have left with the original force.
  • #1
Washable_Marker
12
0
This question is driving me insane...

An arrow, starting from rest, leaves the bow with a speed of 25.0 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?

Of course, instinct says 50 m/s, but it's never that simple! I have no idea where to start with this, it seems like too much information is missing.

A general prod in the right direction would be appreciated- please don't tell me something like "use F=ma", because I *know* that. What I *don't* know is how to get the force, or the mass, or the acceleration.

Thanks =)
 
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  • #2
Hint:
Think of stretching the bow-string back as similar to compressing a spring.
DOUBLING the force, keeping the "rest" alike should be similar to doubling the compression distance; agreed?

Now, think of conservation of mechanical energy...
 
  • #3
I still keep getting 50... grr.

Okay, so using

V2
------
V1

set equal to

Fa
-------
2Fa

I've tried cross-multiplying, but I still have too many unknowns to solve for anything. All I know is the change in velocity.
 
  • #4
I deleted my earlier message, as I couldn't quite get it edited (physicsforums.com appears sluggish to me right now), and the equation had a bad typo.
Anyways, what is "all else"? Time? Distance?
 
  • #5
Yes, I assume "all else" means *everything* is the same... should I just pick a random value and keep it constant?
 
  • #6
Well, I assumed the distance of the acceleration would be same. As we have the average acceleration, I used the formulas:
x = x0 + v0t + ½at2
F = ma

If you managed to see the post I deleted, forget what I said in it :).
 
  • #7
^^ what are x and xo being used to represent?
 
  • #8
x is the final disposition, x0 is the disposition at the beginning. Are you not familiar with the equations above? What equations do you have at your disposal?
 
  • #9
This question is too vague, since "all else" can be validly be interpreted in two distinct ways:
1. If times and distances are to be kept equal, it means that you have changed out the actual bowstring you used. Thus, not only the force changes, but also a material object pertinent to the problem.

This is what I now think they're after.
Then, use the work-energy theorem, and gain the factor of square root of two, rather than 2.

2. However, if you just double the force while having the SAME bow, you will effectively draw the string a doubled distance back, as I assumed in my first post.
 
  • #10
I'm familiar with the first one being used as
d = v0t + ½at^2

and of course i know the second =)
 

1. What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the heavier the object, the smaller its acceleration will be for a given force.

2. How is Newton's Second Law expressed mathematically?

The mathematical equation for Newton's Second Law is F = ma, where F represents the net force applied to an object, m represents its mass, and a represents its acceleration. This equation shows that force, mass, and acceleration are all interrelated and affect each other according to the law.

3. What are some real-life examples of Newton's Second Law in action?

Some common examples of Newton's Second Law in action include pushing a shopping cart, kicking a soccer ball, and riding a bicycle. In each of these scenarios, the force applied to the object (the cart, the ball, and the pedals) results in an acceleration of the object in the direction of the force.

4. How does Newton's Second Law relate to the other laws of motion?

Newton's Second Law is a fundamental principle of classical mechanics and is closely related to the other two laws of motion. The First Law, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force. The Second Law explains how objects respond to external forces, and the Third Law states that for every action, there is an equal and opposite reaction. Together, these laws provide a comprehensive understanding of the behavior of objects in motion.

5. Can Newton's Second Law be applied to non-moving objects?

Yes, Newton's Second Law can be applied to objects that are not in motion. In these cases, the acceleration of the object is zero, so the equation becomes F = 0. This means that in order for an object to remain at rest, the net force acting on it must be zero. For example, a book sitting on a table has a net force of zero acting on it, as the force of gravity pulling it down is equal to the force of the table pushing it up.

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