Calculating k in Hooke's Law: Understanding Archery and Projectile Motion

In summary: If not, I can help you out with that also. Assuming you are asking for the distance the arrow will travel, the answer would be 300 meters.
  • #1
aatgomez
7
0
In preparing to shoot an arrow, an archer pulls a bowstring back 20 cm=.2 m. The arrow can reach a horizontal distance of 300 m and the arrow weighs 200 g. Find k.

m=.2 kg
W=1/2kd final- 1/2kd initial
Fs=-kx

Not really sure where to begin, and I've been trying for a while now. :confused:
 
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  • #2
There are squares missing in your second equation.

To shoot 300m, how fast does the arrow have to be initially? And what is the ideal angle to shoot the arrow, neglecting air resistance?
 
  • #3
oh yes, sorry W=1/2kd^2 final - 1/2kd^2 initial
It would have to be 0 initially and I'm thinking 45 degrees?
 
  • #4
45 degrees is right. With "initially", I meant the flight path, so directly after it leaves the bow. If it is too slow, it won't make 300 meters, obviously.
 
  • #5
Ok, so if I find the initial velocity and the final velocity as if I were doing projectile problem then I can find W=1/2mvf^2 - 1/2mvi^2 then I could set W equal to 1/2kd^2 final - 1/2kd^2 initial and find k. Is that correct?
 
  • #6
No. The energy from the spring does not get "used up" in the flight. It is still in the arrow when it hits the ground.

The velocity is the key connection here.
 
  • #7
I see that there's potential energy before the arrow is shot. That's where the .2 m come in. But I still don't know how to solve it. A little more help please?
 
  • #8
Find the velocity the arrow needs to fly 300m. Once you have that, the rest should follow from that velocity. Note that is the same hint I gave in post #2.
 
  • #9
Right I realize that, that's what I don't know how to find.
 
  • #10
The arrow is in free fall. Maybe the opposite problem is easier: If you know the initial velocity and angle, how far will it go?
I'm quite sure you have solved a problem of this type before in your course or as homework.
 

1. What is Hooke's Law?

Hooke's Law is a physical principle that describes the relationship between the amount of force applied to an object and the resulting deformation or displacement of the object. It states that the force applied is directly proportional to the amount of deformation, as long as the object remains within its elastic limit.

2. Who discovered Hooke's Law?

Hooke's Law was named after the English scientist Robert Hooke, who first described the principle in 1678. However, it is believed that other scientists, including Galileo and Leonardo da Vinci, had observed similar concepts earlier.

3. What is the formula for Hooke's Law?

The formula for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant (a measure of the stiffness of the object), and x is the displacement or deformation of the object.

4. What is the significance of Hooke's Law?

Hooke's Law is an important principle in physics and engineering, as it helps us understand and predict the behavior of elastic materials under different levels of force. It is also the basis for many practical applications, such as in the design of springs, shock absorbers, and elastic bands.

5. Is Hooke's Law applicable to all materials?

No, Hooke's Law is only applicable to materials that exhibit elastic behavior, meaning they can return to their original shape after the applied force is removed. Materials that do not follow this pattern, such as plastic or putty, do not obey Hooke's Law.

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