Question

A bullet of mass m is fired by a rifle that communicates an impulse to it. When leaving the rifle the bullet is embedded in a fixed block to ground, long fan as necessary so that the bullet cannot completely cross said block. The resistance force offered by the block to penetration is:

a) constant and of value fr = c

b) proportional to the advance of the bullet inside the wooden block fr = c * x. calculate in both cases the penetration of the bullet in the block and the relationship between the two

Answer 1

case 1
Fr = C

Fr (x1) = 0.5 m v^2

x1 = 0.5 mv^2/C

case 2

Fr = Cx

energy spent = integral f.dx =integral cxdx = cx^2/2

cx^2/2 = 0.5 mv^2

x2 = sqrt ( mv^2/c)

x1/x2 =[ 0.5 mv^2/c]sqrt( c/mv^2)

= 0.5 sqrt ( mv^2/c)