Answer:
0.372 kg
Explanation:
The collision between the bullet and the block is inelastic, so only the total momentum of the system is conserved. So we can write:
(1)
where
is the mass of the bullet
is the initial velocity of the bullet
is the mass of the block
is the velocity at which the bullet and the block travels after the collision
We also know that the block is attached to a spring, and that the surface over which the block slides after the collision is frictionless. This means that the energy is conserved: so, the total kinetic energy of the block+bullet system just after the collision will entirely convert into elastic potential energy of the spring when the system comes to rest. So we can write
(2)
where
k = 205 N/m is the spring constant
x = 35.0 cm = 0.35 m is the compression of the spring
From eq(1) we get
And substituting into eq(2), we can solve to find the mass of the block: