Calculate Arrow Velocity from Stored Energy

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To calculate the velocity of a 15 gm arrow leaving the bow, first determine the kinetic energy transferred to the arrow, which is 64% of the stored energy of 305 mJ, resulting in 195.2 mJ. Using the kinetic energy formula, 0.5 * m * v^2, where m is the mass in kg (0.015 kg), the equation becomes 195.2 mJ = 0.5 * 0.015 * v^2. Rearranging the equation allows for solving v, leading to a calculated velocity of approximately 73.4 m/s. This demonstrates the application of conservation of energy principles in determining arrow velocity.
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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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