Calculate Arrow Velocity from Stored Energy

In summary, the problem involves conservation of energy and finding the velocity of a 15 gram arrow leaving a bow with an extension of 5.5 cm and a stored energy of 305 mJ. With 64% of the stored energy being transferred to the arrow, the kinetic energy of the arrow can be calculated using the mass and energy. The equation 0.64FD = 1/2mv^2 can be used to find the velocity of the arrow.
  • #1
KingBigness
96
0

Homework Statement



If the extension of the bow is 5.5 cm and you have determined that this corresponds to 305 mJ , what is the velocity with which a 15 gm arrow will leave the bow if 64 percent of the stored energy is transferred to the arrow?
Calculate the velocity in m/s but do not include the units in your answer.


Homework Equations



none

Please help!
 
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  • #2
KingBigness said:

Homework Statement



If the extension of the bow is 5.5 cm and you have determined that this corresponds to 305 mJ , what is the velocity with which a 15 gm arrow will leave the bow if 64 percent of the stored energy is transferred to the arrow?
Calculate the velocity in m/s but do not include the units in your answer.


Homework Equations



none

Please help!

This is a problem in the conservation of energy. The potential energy stored in the bow ends up as kinetic energy of the arrow (or, in this case, 64% of it ends up as kinetic energy of the arrow).

So what is the kinetic energy of the arrow?

Do you see how to use the mass and the energy to find the velocity of the arrow? (Be careful to keep units consistent.)
 
  • #3
So can i use FD=0.64(1/2mv^2)
 
  • #4
wait...thats not right...0.64FD=1/2mv^2?
 
  • #5
KingBigness said:
wait...thats not right...0.64FD=1/2mv^2?

That'll do it.
 

1. How is arrow velocity calculated from stored energy?

The velocity of an arrow can be calculated by using the formula: velocity = square root (2 x stored energy / arrow weight).

2. What is stored energy in the context of calculating arrow velocity?

Stored energy refers to the potential energy that is stored in the bow when it is drawn back. This energy is then transferred to the arrow when it is released, causing it to move at a certain velocity.

3. What units are typically used when measuring stored energy and arrow velocity?

Stored energy is usually measured in foot-pounds (ft-lbs) or joules (J), while arrow velocity is measured in feet per second (fps) or meters per second (m/s).

4. Are there any other factors that can affect the calculation of arrow velocity from stored energy?

Yes, there are other factors that can affect the calculation, such as the efficiency of the bow, the type and quality of the bowstring, and the type of arrow used.

5. Is it important to accurately calculate arrow velocity from stored energy?

Yes, it is important to have an accurate calculation of arrow velocity as it can impact the accuracy and distance of the arrow when it is released from the bow. It is also essential for safety reasons to ensure that the arrow is not traveling at an unsafe velocity.

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