(a) 1.49 m/s
The conservation of momentum states that the total initial momentum is equal to the total final momentum:
where
m = 0.016 kg is the mass of the bullet
is the initial velocity of the bullet
M = 3 kg is the mass of the block
is the initial velocity of the block
v = ? is the final velocity of the block and the bullet
Solving the equation for v, we find
(b) Before: 627.2 J, after: 3.3 J
The initial kinetic energy is (it is just the one of the bullet, since the block is at rest):
The final kinetic energy is the kinetic energy of the bullet+block system after the collision:
(c) The Energy Principle isn't valid for an inelastic collision.
In fact, during an inelastic collision, the total momentum of the system is conserved, while the total kinetic energy is not: this means that part of the kinetic energy of the system is losted in the collision. The principle of conservation of energy, however, is still valid: in fact, the energy has not been simply lost, but it has been converted into other forms of energy (thermal energy).