A 9.40 10-3 kg bullet is fired horizontally into a 2.40-kg wooden block attached

Question

A 9.40 10-3 kg bullet is fired horizontally into a 2.40-kg wooden block attached to one end of a massless, horizontal spring (k = 855 N/m). The other end of the spring is fixed in place, and the spring is unstrained initially. The block rests on a horizontal, frictionless surface. The bullet strikes the block perpendicularly and quickly comes to a halt within it. As a result of this completely inelastic collision, the spring is compressed along its axis and causes the block/bullet to oscillate with an amplitude of 0.200 m. What is the speed of the bullet?

_______m/s

Explanation / Answer

from conservation of momentum

m1u1+m2u2 = (m1+m2)v

here u2 = 0

v = m1u1/(m1+m2)

w = sqrt(k/m) = sqrt(855/2.4094) = 18.84 rad/sec

maximum velocity is = Aw = 0.2*18.84 = 3.768 m/sec

u1 = (m1+m2)v/m1

u1 = 2.4094*3.768/0.0094 = 965.8 m/sec

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