• Question: What would happen if an immovable object got hit by an unstoppable moving object?

    Asked by mustumar to Chris, Dave, David, Fiona, Jack on 25 Jun 2013.
    • Photo: Dave Farmer

      Dave Farmer answered on 25 Jun 2013:


      You’d find out which one of those descriptions was true, they couldn’t both be!

      Most likely though, there’d be a lot of kinetic energy dissipated as heat very quickly, i.e. an explosion.

      Dave

    • Photo: David Freeborn

      David Freeborn answered on 25 Jun 2013:


      Hi mustumar,

      Good question. They sometimes ask this in philosophy entrance interviews at University, though I’m yet to see it in a science one!

      I guess it depends what you mean. One answer is that they cannot both exist. If there exists such thing as an immovable object, then there can’t be such thing as an unstoppable force. If there exists such thing as an unstoppable force, then there can’t be such thing as an immovable object.

      A better question: What would happen if an infinitely heavy object got hit by an infinitely powerful force.

      We can answer that using Newton’s equation F=ma and some maths. Forces create an acceleration, and we know that a=F/m. So what if both F and m are infinite?

      It depends on the type of infinity. Infinity in mathematics is just a limit, not a real number, and it has to be a limit of some equation.

      Suppose the mass is the limit of 1/x as x becomes very small and tends towards zero. Then the mass would tend towards infinity as x becomes smaller and smaller.

      Suppose the force is the limit of 1/(x^2) as x becomes very small and tends towards zero. Then the force would tend towards infinity as x becomes smaller and smaller.

      The acceleration would then be the limit of a = F/m = (1/x^2)/(1/x) as x becomes smaller and smaller. If you do the maths, you realise that means that
      a = 1/x as x becomes smaller and smaller. So as x tends to zero, the acceleration tends to infinity. The infinitely heavy object would have infinite acceleration and would shoot off in the direction of the force! (In the process, it would destroy the Universe!!!)

      What if they were the other way round?
      Suppose the mass is the limit of 1/(x^2) as x becomes very small and tends towards zero. Then the mass would tend towards infinity as x becomes smaller and smaller.

      Suppose the force is the limit of 1/(x) as x becomes very small and tends towards zero. Then the force would tend towards infinity as x becomes smaller and smaller.

      The acceleration would then be the limit of a = F/m = (1/x)/(1/x^2) as x becomes smaller and smaller. If you do the maths, you realise that means that
      a=x, as x becomes very small and approaches zero. So the acceleration would be zero, when x reaches zero.

      The infinitely heavy object wouldn’t move. (But an infinitely heavy object would still destroy it’s universe with its gravity).

      That’s how you take limits in physics. It’s a very, very useful skill.

      But the short answer is, the Universe gets destroyed either way!

Comments