(a) Only momentum conservation
In order to find the speed of the ball, momentum conservation is enough. In fact, we have the following equation:
where
m is the mass of the baseball
u is the initial velocity of the baseball
M is the mass of the brick
U is the initial velocity of the brick
v is the final velocity of the baseball
V is the final velocity of the brick
In this problem we already know the value of: m, u, M, U, and V. Therefore, there is only one unknown value, v: so this equation is enough to find its value.
(b) 12.1 m/s
Using the equation of conservation of momentum written in the previous part:
where we have:
m = 0.144 kg
u = +28.0 m/s (forward)
M = 5.25 kg
U = 0
V = +1.1 m/s (forward)
We can solve the equation to find v, the velocity of the ball:
And the sign indicates that the ball bounces backward, so the speed is 12.1 m/s.
(c) 56.4 J, 13.7 J
The total mechanical energy before the collision is just equal to the kinetic energy of the baseball, since the brick is at rest; so:
The total mechanical energy after the collision instead is equal to the sum of the kinetic energies of the ball and the brick after the collision:
(d)
A collision is:
- elastic when the total mechanical energy is conserved before and after the collision
- inelastic when the total mechanical energy is NOT conserved before and after the collision
In this problem we have:
- Energy before the collision: 56.4 J
- Energy after the collision: 13.7 J
Since energy is not conserved, this is an inelastic collision.
(e) No
As shown in part (c) and (d), the kinetic energy of the system is not conserved. This is due to the fact that in inelastic collisions (such as this one), there are some internal/frictional forces that act on the system, and that cause the dissipation of part of the initial energy of the system. This energy is not destroyed (since energy cannot be created or destroyed), but it is simply converted into other forms of energy (mainly heat and sound).