008 (part 1 of 2) 10.0 points A bullet of mass 6 g moving with an initial speed

Question

008 (part 1 of 2) 10.0 points
A bullet of mass 6 g moving with an initial
speed 500 m/s is fired into and passes through
a block of mass 8 kg, as shown in the figure.
The block, initially at rest on a frictionless,
horizontal surface, is connected to a spring of
force constant 706 N/m. If the block moves a distance 1 cm to the
right after the bullet passed through it, find
the speed v at which the bullet emerges from
the block.
Answer in units of m/s

(part 2 of 2)
Find the magnitude of the energy lost in the
collision.
Answer in units of J

Explanation / Answer

first finding velocity of block just after the collision
(1/2)*8*v2 = (1/2)*706*0.012

so we get v=0.09394m/s

now conservation of linear momentum along horizontal direction we get

0.006*500 = 8*0.09394 + 0.006*u

we get u=374.74667m/s

now magnitude of energy lost in collision = (1/2)*0.006*5002 - (1/2)*8*0.093942 - (1/2)*0.006*374.746672

= 328.6595 J

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