Since the block does not move significantly during the collision, the elastic and gravitational potential energies do not change. Thus, Eis the energy that is transferred. The ratio is E/E0= (6.94 J)/(563 J) = 0.0123 or 1.23%. 69. (a) Assume the bullet becomes embedded and moves with the block before the block moves a significant distance. Then the momentum of the bullet-block system is conserved during the collision. Let mbe the mass of the bullet, Mbe the mass of the block,v0be the initial speed of the bullet, and vbe the final speed of the block and bullet. Conservation of momentum yields mv0= (m+ M)v, so =+=0.0501500.050+ 4.0=1.85. 0vmvmMkgm / skgkgm/safafWhen the block is in its initial position the spring and gravitational forces balance, so the spring is elongated by Mg/k. After the collision, however, the block oscillates with simple harmonic motion about the point where the spring and gravitational forces balance with the bullet embedded. At this point the spring is elongated a distance A=+Mmgkaf/,somewhat different from the initial elongation. Mechanical energy is conserved during
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.