A few days ago, some students asked what would happen when an unstoppable force meets an immovable object. It was an innocent question, but one that caused the whole class to stop work and ponder on the answer. Since the class was supposed to cover a whole different topic on physics (thermal transfer),  I decided to answer the question, under the condition that we had to finish the topic before going through the physics behind the force and the object.

The question is: how many kilograms are there in an Instagram? In a stricter sense, what is the equivalent mass, in kilograms, of an image sent to Instagram?

The Situation

An object is immovable. Something that is unstoppable comes along. What happens when they meet?

This is actually a common metaphor used in the English language, where two large entities collide in an epic showdown. But aside from common usage, this is also a common question in introductory Physics courses in university.

So what would happen, theoretically, when this does happen?

The Physics

For simplicity, let\’s call the unstoppable force the Ball, and the immovable object the Wall.

The Ball is unstoppable. This means two things. First, it is moving. Second, it cannot stop. In physics terms: The Ball is always in a state of constant velocity, and will never experience a reduction in its velocity. It will never experience deceleration.

When acceleration is being considered, then force must also be accounted for. Newton\’s second law of motion guarantees it.

Let\’s take a closer look at this. If the ball has any finite value for its mass, any force can make it accelerate. Hence, anything with a finite mass cannot be the unstoppable ball. This then leads us to the conclusion that the ball has to have an infinite mass.

Now, let\’s look at the Wall. Since it does not move, its velocity (relative to us observing it) is always zero. Again, using some physics terms:  The Wall is always in a state of zero velocity, and will never experience an increase in its velocity. It will never experience acceleration.

Let\’s analyse the Wall. If it had a finite mass, it would accelerate when a force is applied. It\’s almost just like the ball. So we can get to the same conclusion that the Wall has infinite mass.

Many physical laws will have to broken to get infinite mass. However, since we are simplifying everything by ignoring other laws of physics, let\’s make the Wall and the Ball collide.

Since the two entities cannot accelerate, nothing should happen when they collide. And by \”nothing\”, we do mean it. The Ball does not decelerate, so it passes through the Wall. But the Wall does not accelerate in any way (including breaking down), so it must stay whole and unmoving. This means that there should be no interaction between the Wall and the Ball.

A bit anticlimactic, but what can we expect? The whole problem breaks every law of physics that we know.

A Possible Way Out

Since the Wall and the Ball passing right through each other is not too realistic, it\’s time to approach this another way.

Immovable is simple enough. The Wall cannot move at all. However, just because the ball is unstoppable does not mean it cannot be deflected. In other words, the problem is not clear as to the Ball has a constant speed or a constant velocity.

If the Ball has a constant speed, then it is still unstoppable, but can still be deflected. The end result now would be that the Wall still does not move, but the Ball is moving one way and then the other.

This time, another law of physics is broken: The law of conservation of momentum. Essentially another form of Newton\’s third law of motion, this is now the final blow to the scenario.

In Summary

The scenario of an unstoppable force and an immovable object is not only physically impossible, but mathematically nonsense (a paradox). If both exist, nothing else does, and we would not be here to discuss this problem.

I know most of this would be unsatisfying, but don\’t worry. You\’re not alone, as I am still wondering about the Wall-and-Ball situation even after I have finished writing this article. You have to admit though, that was a good topic to discuss. 🙂