Momentum conserved, but extra Kinetic energy?

Question

In a situation where a bigger mass hits a smaller mass, momentum is conserved. M(bigger)V(smaller) -> M(smaller)V(bigger)

So when they collide, because of the 2nd object's smaller mass, it will have a bigger velocity.

But when we look at the kinetic energy:

1/2 M(bigger) V^2(smaller) < 1/2 M(smaller) V^2 (bigger)

Becoz Ek is proportional to the mass, but proportion to the sqaured of the velocity, that means the smaller object will now have an Ek greater than the Ek the bigger object had.

Where does this energy come from??

Answer 1

Ive been out of this type of stuff for quite some time, but there can be no more nor less energy than initially.  As energy really cannot just be created nor destroyed.   The equation seems to be incorrect.  

Answer 2

That cannot happen.  The smaller object cannot gain more kinetic energy than the big object loses.  It&#039;s impossible.

You&#039;re writing the formulation of conservation of momentum incorrectly.  The correct way to write it is this:

p initial = p final

(m1 * v1 + m2 * v2) initial = (m1 * v1 + m2 * v2) final

m1i * v1i + m2i * v2i = m1f * v1f + m2f * v2f

Answer 3

are you subtracting energy? it is all addition. if you  find the velocity of each mass and calculate the energy, they cannot be subtracted. the guy above me wrote out the math. the &quot;+&quot; is inside the &quot;()&quot;. do your math in the proper order of operations.

Answer 4

Is there any potential energy at the beginning of the scenario? If so, some of the potential energy may have just been converted to kinetic energy.  If not, there&#039;s probably a calculation error somewhere.  Energy can be lost in the form of sound, etc., but you can&#039;t have more energy at the end of a scenario than you had at the beginning.

Answer 5

That energy came from the bigger mass.  The bigger mass will have a smaller velocity after the collision, therefore less energy than before the collision.  That reduction in energy of the big mass went into the smaller mass.  The total energy of the system is not changed.

EDIT:

You said  &quot;smaller object will now have an Ek greater than the Ek the bigger object had.&quot;, not more than the bigger one has.  I thought of an example to show this.  Imagine a slow moving large mass moving to the left, and we aim a small mass at high velocity toward it moving to the right.  If we select the right velocities, the small mass can stop the large one.  Now the initial energy of the system was E = Es + El, the sum of the energies of the large and small mass.  After the collision, the large mass has zero energy, so all of the system&#039;s energy is in the small mass, which is Es + El, definitely larger than the large mass&#039; original energy El.  The large mass transferred all of its energy to the small mass.