Collision Problem - A gain of kinetic energy?

[eurekameh]

In Fig. 9-64, block A (mass 1.1 kg) slides into block B (mass 2.9 kg), along a frictionless surface. The directions of velocities before and after the collision are indicated; the corresponding speeds are vAi = 5.6 m/s, vBi = 2.2 m/s, and vBf = 4.9 m/s. What is velocity vAf (including sign, where positive denotes motion to the right)?

I believe that this collision is inelastic and not elastic, because kinetic energy is lost to other forms of energy, correct? And so momentum is conserved, kinetic energy is not?

I conserved momentum and found the final velocity of block A. However, when I calculated the kinetic energy before and after the collision, I found that the kinetic energy after the collision is greater than the kinetic energy before the collision. How is this possible?

Edit: No external forces are present.

 

[eczeno]

can you show us the work you did.

 

[eurekameh]

Momentum before = Momentum after
(1.1)(5.6) + (2.9)(2.2) = (1.1)(vAf) + (2.9)(4.9)
I found vAf.
But when I calculated the kinetic energy before and after the collision, I got an increase in kinetic energy, as in : kinetic energy before collision < kinetic energy after collision.

Kinetic energy before collision:
(1/2)(1.1)(5.6)^2 + (1/2)(2.9)(2.2)^2 = 24.3 J.

Kinetic energy after collision, using vAf = -1.52, found when conserving momentum:
(1/2)(1.1)(-1.52)^2 + (1/2)(2.9)(4.9)^2 = 36.1 J.

My question is this: Is it possible to have an increase in kinetic energy when there are no apparent external forces acting on the system of the two colliding blocks? Or are my calculations faulty? Or is the problem itself faulty?
Thanks for the responses.

 

[eczeno]

well, we seem to have an impossible situation here. and in fact we do. if you look at the change in KE of B, it is bigger than the whole of A's KE coming in. this is impossible. these numbers do not correspond to a possible physical situation.

 

[rwisz]

I can confirm that this is indeed an inelastic collision, as kinetic energy is lost to other forms of energy such as heat and sound. Momentum is conserved in all collisions, but kinetic energy is not necessarily conserved.

In this specific scenario, the gain of kinetic energy after the collision is due to the conversion of potential energy into kinetic energy. Block A had a higher initial velocity and thus had more potential energy before the collision. This potential energy is converted into kinetic energy, resulting in a higher final velocity for block A.

It is important to note that the calculation of kinetic energy only takes into account the velocity and mass of the objects involved. It does not consider any external forces, such as gravity or friction, which may have an impact on the final kinetic energy. In this case, the absence of external forces may have contributed to the higher final kinetic energy.

In conclusion, while kinetic energy may not be conserved in this collision, momentum is still conserved and the increase in kinetic energy can be explained by the conversion of potential energy.