Is This a Case of Inelastic Collision?

[jemerlia]

Homework Statement

Two wooden blocks of mass 8 kg and 4 kg respectively approach
each other from opposite directions on a smooth level surface at a
relative speed of 16 m s^1 . After a head-on collision they separate
at a relative speed of 6 m s^1 . The initial velocity of the 8 kg block
was 7 m s -1 North. Find the velocity of
(a) the 4 kg block immediately before the impact;
(b) the 8 kg block immediately after the impact;
(c) the 4 kg block immediately after the impact.

Homework Equations

f=ma
F x delta T= delta P

For an elastic collision
va-vb = -(va'-vb')

The Attempt at a Solution

Part (a) is straightforward

Part (b) appears awkward because the collision seems inelastic because
the relative velocity after impact is different in magnitude to that before
impact and doesn't follow the relationship:
va-vb = -(va'-vb')

Am I correct in assuming the collision to be inelastic?
How does one approach a solution to problem (b)?

Help and guidance gratefully received.

 

[Doc Al]

Am I correct in assuming the collision to be inelastic?

Yes.

How does one approach a solution to problem (b)?

By making full use of the given information (the relative velocity after the collision) and applicable conservation laws (what's conserved?).

 

[nlightner]

I would first confirm that the collision is indeed inelastic. In an inelastic collision, kinetic energy is not conserved and the objects involved stick together or deform upon impact. This is different from an elastic collision where kinetic energy is conserved and the objects bounce off each other with no deformation.

Once I have confirmed that the collision is inelastic, I would approach the problem by using the concept of conservation of momentum. In an inelastic collision, although kinetic energy is not conserved, momentum is still conserved. This means that the total momentum before the collision is equal to the total momentum after the collision.

For part (b), I would use the equation F x delta T= delta P to calculate the change in momentum of the 8 kg block. Since the initial velocity of the 8 kg block was given, I can use the mass and velocity to calculate its initial momentum. Then, using the relative speed after the collision, I can calculate the final momentum of the 8 kg block. The difference between the two will give me the change in momentum. From there, I can use the mass and the change in momentum to calculate the final velocity of the 8 kg block after the collision.

For part (c), I would use the same approach as part (b) but with the 4 kg block instead. I would use the change in momentum of the 8 kg block as the initial momentum of the 4 kg block and solve for its final velocity.

Overall, I would also consider the possibility of friction or external forces acting on the blocks during the collision, which may affect the final velocities. I would also double check my calculations and assumptions to ensure accuracy in my answers.