2 blocks collide, 5% energy loss. 2 answers, which correct?

[Ocata]

Homework Statement

The question I have is not how to arrive at the correct values of final velocity, but once I have the values of final velocity, how do I know which velocities (which are computed from a quadratic equation) are correct?

Two blocks, block A and Block B, are traveling to the right.

Before collision:

Block A is 4kg at 10m/s
Block B is 2kg at 5m/s

After collision:

Block A is 4kg at vf = ?
Block B is 2kg at Vf = ?

Energy loss is .05

Homework Equations

mvi + MVi = mvf + MVf

1/2mvf^2 + 1/2MVf^2 = .95[1/2mvi^2 + 1/2MVi^2]

The Attempt at a Solution

mvi + MVi = mvf + MVf ==> Vf = 25 - 2vf

1/2mvf^2 + 1/2MVf^2 = .95[1/2mvi^2 + 1/2MVi^2] ==> 4vf^2 + 2Vf^2 = 427.54vf^2 + 2(25 - 2vf) = 427.5 ==> 12vf^2 - 200vf + 822.5 = 0

Quadratic Formula ==> vf = 9.28m/s and 7.38m/s

then,
Vf = 25 - 2(9.28) = 6.44m/s and Vf = 25 - 2(7.38) = 10.24m/s

So the possible answers are:

[vf = 9.28m/s Vf = 6.44m/s] or [vf = 7.38m/s Vf = 10.24]


Given the energy loss of .05, how could I know which set of final velocities are correct? I don't think I can just rationalize it because in either case, the faster, heavier block A slows down upon colliding with the lighter, slower block B. And Block B speeds up upon being struck by the faster, heavier block A. What I mean is, in both final answers, Block A is slowing down and Block B is speeding up.

Is there a computation that will determine which set of velocities are correct?

 

[PeroK]

So the possible answers are:

[vf = 9.28m/s Vf = 6.44m/s] or [vf = 7.38m/s Vf = 10.24]

Is there a computation that will determine which set of velocities are correct?

In the first case the larger block is moving faster than the smaller block after the collision. Do you think this is possible?

 

[Ocata]

Makes perfect sense PeroK. The larger block must be moving slower that the smaller block after collision because the larger block is behind the smaller block. It can't physically pass the smaller block. I was simply looking at the numbers in a scalar sense and not considering the bigger picture.

Thank you.

 

[PeroK]

Makes perfect sense PeroK. The larger block must be moving slower that the smaller block after collision because the larger block is behind the smaller block. It can't physically pass the smaller block. I was simply looking at the numbers in a scalar sense and not considering the bigger picture.

Thank you.

If you solve the problem with no energy loss, you'll find one solution is where the blocks miss each other and continue with their original velocities. The first case is, therefore, a variation of this with the 5% energy loss.

 

[Ocata]

Thanks PeroK