An inelastic collision and an explosion are for all intents and purpose polar opposites. One begins with two or more objects that unite to form a single object. The other begins as a single object that breaks into two or more pieces. Explosions are typically violent and occur so quickly that analyzing them is difficult / messy. However, an explosion scenario occurs everytime someone throws an object providing us with the means to see why momentum cannot represent mechanical energy.

**The Astronaut Wrench Experiment**

This experiment can easily be replicated exactly as stated here and is representative of what occurs during any explosion but in a far more controlled manner.

Newton’s 3rd Law is often quoted as, “For every action there is an equal and opposite reaction.” This tells us that force acts in two directions at the same time; push on something and that something pushes back with equal force. This is particularly evident in space where the effects of gravity and other factors cannot obscure one of Newton’s most remarkable discoveries.

If
an astronaut during a spacewalk throws a wrench, both he and it accelerate away
from one another. Neither the wrench nor the astronaut experiences force
unless the other one does as well; **time** is therefore the
defining factor when it comes to force. If the astronaut is more massive
than the wrench, the wrench will accelerate more quickly. Newton’s 2nd Law,
usually written as *F**=m***a**,
explains this. Because both accelerate for the same amount of time, the less
massive wrench will windup moving faster than the more massive astronaut.
Consequently, the wrench moves a greater distance than the astronaut. And
in case there is any question, distances would be measured begining from the
point the astronaut was holding the wrench.

With the Work Energy Theorem deemed a fact, the wrench will wind up with more kinetic energy than the astronaut; this is not viewed as a problem but it should be. Both the astronaut and wrench receive identical actions for the same amount of time and yet one has more mechanical energy than the other. This could be thought of as a violation of Newton’s 3rd Law even though that Law was developed specifically for motion, not energy as it is understood today.

In this simple experiment we also find the reason that
momentum, the product of mass and velocity, cannot represent mechanical energy.
When we take the momentum of the astronaut and add that to the wrench’s
momentum, the mathematical result is always zero. Before the experiment, neither
is moving and thus neither has mechanical energy nor momenta. Using the idea
that the mass of the astronaut is 100*m* with the wrench having a mass of
*m*, consider what happens after throwing the wrench. The wrench achieves
velocity ** v** moving to the right while the astronaut
retreats in the opposite direction. Since his mass is one hundred times as
great, the magnitude of his velocity will be 1/100

The wrench moves to the right and has momentum while the astronaut moves to the left and also has momentum. Their respective momenta is exactly the same but when added together, the result is zero — no net momenta. Mathematically, this is as follows.

Arrows were placed above the variables ** v**
to indicate direction; we could have just as easily used a plus sign (+), if you
like, indicating movement to the right as positive with a minus sign (-) for
movement to the left. In any event, the sum is as shown — zero. This tells us
that none of the biological energy used by the astronaut manifests as mechanical energy

Interestingly, if we were to use the product of mass and
speed (*ms*) to describe mechanical energy, an entirely different result
occurs. And in that case, the amount of biological *energy* the
astronaut converted into mechanical would be positive. In that case, the
*ms* of the wrench added to the *ms* (*100m x s/100 = ms*)
of the astronaut would equal *2ms *(*ms +ms*), not zero.
Moreover, if he used a greater amount of biological energy so that the wrench
traveled at a faster speed, the amount of mechanical energy would be greater
just as it should be.

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