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August 27th, 2007

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What was the speed of the bullet, V?

We use the set-up shown below to determine the muzzle velocity of a bullet. The bullet hits
the block hanging at the end of a light flexible string and causes it to swing up to an angle of θ. In a
particular test, the value θ is measured as 20 degree. What was the speed of the bullet, V? The mass of the bullet and the wood are, respectively, m=0.05 kg and M=20 kg, and the length of the string is L=2
m.

I'm assuming bullet gets pierced into block
by energy conservation we can say

initial K.E of bullet =change in P.E of (bullet+block)system

1/2 mv^2 = (M+m)g*(height displaced)
if u sketch the fig. u"ll understand,
height displaced(h)=L-LCOS20

=>muzzle velocity( v)=sqrt[2(M+m)g(L-Lcos20)]

plug every thing as correctly
M=2kg,m=0.05kg,g=9.81m/s^2,cos 20=0.9397

u'll get v=6.89 m/s

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