A rifle bullet of mass 10 grams is shot into a block of mass 1.99 kg that is ini

Question

A rifle bullet of mass 10 grams is shot into a block of mass 1.99 kg that is initially at rest on a frictionless horizontal surface and is attached to a spring of force constant k = 1800 N/m. The bullet remains embedded in the block, and the maximum compression of the spring after impact is 5 cm. Find the velocity of the bullet-block system just after impact, which occurs very quickly. Find the initial speed speed of the bullet Find the magnitude and direction of the impulse exerted by the spring on the bullet-block system during the 5 cm compression.

Explanation / Answer

(A) Applying energy conservation after the collision,

PEi + KEi = PEf + KEf

0 + m v^2 / 2 = k x^2 /2 + 0

(1.99 + 0.010) v^2 /2 = 1800 (0.05^2) / 2

v^2 = 2.25

v = 1.5 m/s ........Ans

(B) Applying momentum conservation for the collision,

(0.010)v0 + (1.99 x 0) = (1.99 + 0.010) (1.5)

v0 = 300 m/s

(C) Impulse = change in momentum

= m (vf - vi)

= 2 (0 - 1.5)

= -3 kg m/s

magnitude = 3 kg m/s

Direction = to the left

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