Calculate Arrow Velocity from Stored Energy

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Homework Help Overview

The problem involves calculating the velocity of an arrow released from a bow, given the extension of the bow and the energy transferred to the arrow. The context is rooted in the conservation of energy principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between potential energy stored in the bow and the kinetic energy of the arrow. Questions arise regarding the correct application of energy equations and the consistency of units.

Discussion Status

Some participants are exploring the equations related to energy transfer and velocity, while others are questioning the correctness of their formulations. There is an ongoing examination of the assumptions and definitions involved in the problem.

Contextual Notes

Participants note the importance of unit consistency and the specific percentage of energy transfer in the calculations. There is a lack of explicit consensus on the correct approach to the problem.

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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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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.)
 
So can i use FD=0.64(1/2mv^2)
 
wait...thats not right...0.64FD=1/2mv^2?
 
KingBigness said:
wait...thats not right...0.64FD=1/2mv^2?

That'll do it.
 

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