A $11\mathrm{.}5-$gram bullet is fired into a block of wood. The velocity of the bullet right before it hits the block is $257\frac{m}{s}$ to the right. The block is attached to a spring that has a spring constant of $205\frac{N}{m}.$ The bullet and the block undergo a perfectly inelastic collision. The block and bullet continue to move together after the collision, compressing the spring by $35\mathrm{.}0$ cm before the bullet$-$block system momentarily comes to a stop. Assuming that the surface on which the block is initially resting is frictionless and horizontal, determine the mass of the wooden block.