A 5.36-g bullet is maving horizontally with a velocity of +358 m/\'s, where the

Question

A 5.36-g bullet is maving horizontally with a velocity of +358 m/'s, where the sign + indicates that it is moving to the right (see part a of the drawing). The bullet is approaching bwo blocks resting on a horizontal frictianless surface. Air resistance is negligible. The bullet passes completely through the first block (an inelastic collision) and embeds itself in the second one, as indicated in part b. Note that both blocks are moving after the collision with the bullet. The mass of the first block is 1183 g, and its velocity is +0.616 m/s after the bullet passes through it. The mass of the second block is 1613 g. (a) What is the velocity of the second block after the bullet imbeds itself? (b) Find the ratio of the total kinetic energy after the collision to that before the collision. 358n's Block 2 (a) Before collision 0.616 s blach 2 Tlock 2-1613 llet 5.36 mok1183 (b) After collision (a) Volock2 -Number 1735 Units m's EbeforeNumber 00127 would like to Show Work for this question: (b) KEafter/KEbe Units Click if you

Explanation / Answer

Given

mass of bullet m = 5.36*10^-3 kg ,velocity of bullet is u = 358 m/s

mass of block1 , M1 = 1.183 kg ,velocity of block 1 after the bullet passes through it is v1 = 0.616 m/s

of block 2 is M2 = 1.613 kg , velocity of the vlock2 when the bullet imbeded is v2 =?

the collision is inelastic collision so

initially the conservation of momentum at the block1 is

m*u+M1*u1 = m*v+M1*v1

here u1 =0 m/s,

m*u+ 0 = m*v+M1*v1

m*u = m*v+M1*v1 ===> v = (m*u-M1*v1 )/m

substituting the values

v = (5.36*10^-3*358 -1.183*0.616)/(5.36*10^-3) m/s

v = 222.0433 m/s

the velocity of the bullet after passing through the block1 is 222.0433 m/s

a) from conservation of momentun  

m*u'+M2*u2 = (m+M2)V2

here u'=v

5.36*10^-3*222.0433 + 1.613*0 = (5.36*10^-3+1.613)V2

V2 = 0.7354 m/s

b)

for Bullet after the first block collision and before the collision the ratio of k.e is

k2/k1 = 0.5*m*v^2/0.5*m*u^2 = v^2/u^2 = 222.0433^2/358^2 = 0.3847 no units it is a ratio only number

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