False News Report?

The only thing fishy in here is the irony displayed in the picture.

It is reported that two identical - meaning of equal mass and shape - are both seen to travel at a certain speed toward each other - specifically 1 m/s - and then after the collision their speed has doubled.

We can treat this carts-system as a closed, isolated system (meaning no net external force acts on the carts). Thus, we can apply the Law of Conservation of Momentum:

$m_1v_1 + m_2v_2 = m_1v'_1 + m_2v'_2$

Since $m_1=m_2,$

$m(1m/s)+m(-1m/s)=m(2m/s)+m(-2m/s)$

$\boxed{0=0}$

The law is checked, and nothing is violated. Now the question is, where did the extra energy come from? The total kinetic energy of the system certainly increased. Did we violate the Law of Conservation of Energy?

No. The law states that the total amount of energy must be conserved, not just one type. Here, we could have had a super-elastic collision, where some form of the carts' mechanical energy (such as internal electric or chemical) could have been transformed to kinetic. For example, the carts could have gunpowder on them, and upon collision trigger an explosion. In a closed, isolated system, energy may find its way around, but not momentum.

Momentum is always conserved.

(Can you find the condition for elastic collision in which both momentum and kinetic energies are conserved? To find out, try the following simulations:

WileyPlus

higheredbcs

(Note: elasticities $>1$ are called super-elastic - that is, the total kinetic energy of the system increases from the collision due to some release of internal mechanical energy. And as you've guessed, $0=$ completely inelastic.)

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