A 5.0 kg block moving east with speed of 6 kg m/s collides head on with another 8.0 kg block moving west with speed of 4 m/s. After the collision the 5.0 kg block was moving west with speed of 5 m/ s while the 8.0 kg block was moving east.

a) What is the speed of the 8.0 kg block after the collision?
b) Determine whether the collision was elastic or inelastic?

To solve this problem, we can use the principle of conservation of momentum and the concept of elastic and inelastic collisions.

a) To determine the speed of the 8.0 kg block after the collision, we can first find the initial momentum and final momentum of the system.

Momentum (p) is calculated by multiplying mass (m) and velocity (v).

The initial momentum of the system is the sum of the individual momenta of the two blocks before the collision:

Initial momentum = (mass of the 5.0 kg block * velocity of the 5.0 kg block) + (mass of the 8.0 kg block * velocity of the 8.0 kg block)

Initial momentum = (5.0 kg * 6 m/s) + (8.0 kg * (-4 m/s))
= 30 kg m/s - 32 kg m/s
= -2 kg m/s

The final momentum of the system is the sum of the individual momenta of the two blocks after the collision:

Final momentum = (mass of the 5.0 kg block * velocity of the 5.0 kg block) + (mass of the 8.0 kg block * velocity of the 8.0 kg block)

Final momentum = (5.0 kg * (-5 m/s)) + (8.0 kg * v) [let v be the velocity of the 8.0 kg block after the collision]

Final momentum = -25 kg m/s + 8v kg m/s
= (-25 + 8v) kg m/s

According to the principle of conservation of momentum, the initial momentum and the final momentum of a system must be equal in the absence of external forces.

Therefore, we can equate the initial momentum to the final momentum:

-2 kg m/s = (-25 + 8v) kg m/s

Simplifying the equation, we have:

8v = -2 + 25
8v = 23
v = 23/8
v ≈ 2.88 m/s

b) To determine whether the collision is elastic or inelastic, we need to consider whether kinetic energy is conserved.

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, only momentum is conserved, and kinetic energy may be lost to other forms (such as heat or sound).

To check if kinetic energy is conserved, we can calculate the initial kinetic energy and the final kinetic energy of the system.

The initial kinetic energy of the system is the sum of the individual kinetic energies of the two blocks before the collision:

Initial kinetic energy = 0.5 * (mass of the 5.0 kg block) * (velocity of the 5.0 kg block)^2 + 0.5 * (mass of the 8.0 kg block) * (velocity of the 8.0 kg block)^2

Initial kinetic energy = 0.5 * 5.0 kg * (6 m/s)^2 + 0.5 * 8.0 kg * (-4 m/s)^2
= 90 J + 64 J
= 154 J

The final kinetic energy of the system is the sum of the individual kinetic energies of the two blocks after the collision:

Final kinetic energy = 0.5 * (mass of the 5.0 kg block) * (velocity of the 5.0 kg block)^2 + 0.5 * (mass of the 8.0 kg block) * (velocity of the 8.0 kg block)^2

Final kinetic energy = 0.5 * 5.0 kg * (-5 m/s)^2 + 0.5 * 8.0 kg * (2.88 m/s)^2
= 62.5 J + 66.048 J
≈ 128 J

Comparing the initial kinetic energy (154 J) and the final kinetic energy (128 J), we can see that the kinetic energy is not conserved. Therefore, the collision is inelastic.

To summarize:
a) The speed of the 8.0 kg block after the collision is approximately 2.88 m/s.
b) The collision is inelastic.