A 2 kg block with initial velocity +2m/s collides with a stationary 6 kg block with initial velocity 0m/s on a frictionless surface. After the collision, the 2 kg block is moving at –1 m/s and the 6kg block is moving to the right at +1 m/s.

Show that the total momentum is conserved in this collision
is the collision elastic or inelastic ?

Initial momentum: 2*2=4

final momentum: 6(1)+2(-2)=4

initial KE=1/2 (2)2^2=4j
final KE=1/2( 2(-1)^2+6(1)^2 )more energy? not elastic, some internal force added energy.

To show that the total momentum is conserved in the collision, we need to calculate the initial and final momenta of the system and compare them.

1. Calculate the initial momentum:
The initial momentum of an object can be calculated by multiplying its mass with its initial velocity.

For the 2 kg block:
Initial momentum = mass * velocity = 2 kg * 2 m/s = 4 kg m/s

For the 6 kg block:
Initial momentum = mass * velocity = 6 kg * 0 m/s = 0 kg m/s

Total initial momentum = initial momentum of 2 kg block + initial momentum of 6 kg block
= 4 kg m/s + 0 kg m/s
= 4 kg m/s

2. Calculate the final momentum:
The final momentum of an object can be calculated by multiplying its mass with its final velocity.

For the 2 kg block:
Final momentum = mass * velocity = 2 kg * (-1 m/s) = -2 kg m/s

For the 6 kg block:
Final momentum = mass * velocity = 6 kg * 1 m/s = 6 kg m/s

Total final momentum = final momentum of 2 kg block + final momentum of 6 kg block
= -2 kg m/s + 6 kg m/s
= 4 kg m/s

3. Compare the initial and final momenta:
The total initial momentum was 4 kg m/s, and the total final momentum is also 4 kg m/s. Since the total momentum before and after the collision is the same, we can conclude that the total momentum is conserved in this collision.

Now let's determine if the collision is elastic or inelastic.

An elastic collision is one where both momentum and kinetic energy are conserved. In an inelastic collision, only momentum is conserved, but kinetic energy is not.

To determine if the collision is elastic or inelastic, we need to compare the initial and final kinetic energies.

Calculate the initial and final kinetic energies:

For the 2 kg block:
Initial kinetic energy = (1/2) * mass * (velocity)^2 = (1/2) * 2 kg * (2 m/s)^2 = 4 J
Final kinetic energy = (1/2) * mass * (velocity)^2 = (1/2) * 2 kg * (-1 m/s)^2 = 1 J

For the 6 kg block:
Initial kinetic energy = (1/2) * mass * (velocity)^2 = (1/2) * 6 kg * (0 m/s)^2 = 0 J
Final kinetic energy = (1/2) * mass * (velocity)^2 = (1/2) * 6 kg * (1 m/s)^2 = 3 J

Since the total initial kinetic energy is 4 J and the total final kinetic energy is 4 J, we can conclude that the collision is elastic.