- #1
Warbow
- 7
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A 0.1 kg arrow is moving at 48 m/s to the right and strike a 3 kg object (helmet resting on a 5 kg head) moving to the left towards the arrow at 9 m/s (full mounted charge). It takes 80 Joules to penetrate the 3 kg helmet, what is the velocity of the arrow after penetration when it slams into the head? What is the velocity of the 3 kg helmet after penetration?
I'm stuck on this one. I know the KE of the arrow (115.2 Joule). I know the KE of the helmet (121.5 Joule). I know the momentum of the arrow (4.8 kg *m/s) and the object (27 kg * m/s).
I know how to calculate the final velocity of the helmet/arrow if the arrow get stuck in the helmet as an inelastic collision: (0.1*48+3*-9)/(0.1+3) = -7.1613 m/s
And from this that the KE of the object is now: 0.5*(0.1+3)*-7.1613^2 = 79.49 Joules.
Subtract this from (115.2+121.5) and you get 157.21 Joule going into penetration, heat and sound.
I have no idea when the arrow passes through the helmet.
How do I find out the amount of KE coming from the arrow vs helmet when dealing with those 80 Joules?
How does the 5 kg head have an impact on the outcome of this collision? I can't threat them as one solid object either. The helmet has a liner and as such reduces the impulse slightly.
I need a formula I can use in excel.
[Moderator's note: Moved from a technical forum and thus no template.]
I'm stuck on this one. I know the KE of the arrow (115.2 Joule). I know the KE of the helmet (121.5 Joule). I know the momentum of the arrow (4.8 kg *m/s) and the object (27 kg * m/s).
I know how to calculate the final velocity of the helmet/arrow if the arrow get stuck in the helmet as an inelastic collision: (0.1*48+3*-9)/(0.1+3) = -7.1613 m/s
And from this that the KE of the object is now: 0.5*(0.1+3)*-7.1613^2 = 79.49 Joules.
Subtract this from (115.2+121.5) and you get 157.21 Joule going into penetration, heat and sound.
I have no idea when the arrow passes through the helmet.
How do I find out the amount of KE coming from the arrow vs helmet when dealing with those 80 Joules?
How does the 5 kg head have an impact on the outcome of this collision? I can't threat them as one solid object either. The helmet has a liner and as such reduces the impulse slightly.
I need a formula I can use in excel.
[Moderator's note: Moved from a technical forum and thus no template.]
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