# A SMASHING TIME (The physics behind breaking)

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As a fifth degree black belt and International Instructor/Examiner I had been considering this issue about force applied when breaking boards for a while and although I recognise that the Encyclopaedia of Taekwon-Do outlines a theory of power it doesn’t specifically deal with the science behind that power when breaking boards. So I decided when teaching a year ten science class (I am medical scientist involved in Respiratory research but did a few years as a high school science teacher) to incorporate the theory into a unit on force. What follows are my findings.

The basic premise that should be considered are Newtons laws and in particular his first and second laws.

The first law states:   “A body will not change its state of rest or motion unless it is made too by a force acting on it”.

Or in plain language “you need to push or pull something to start it moving or you need to pull or push against something to slow it down once it is moving”.

The second law states: ” the rate of change in momentum is proportional to the force applied and acts in the direction of the force”.

What does this mean in plain language? Here I must be a little more specific .

We need to understand what the term momentum means. It is basically the product of the “mass” (which we may think of as weight) and the “velocity” (which is speed in a certain direction).  So momentum is the weight multiplied by the speed.  (i.e. mass x velocity = momentum (symbolised by P)

So getting back to Newtons second law.

If we consider this in terms of someone breaking a board, the change in momentum is:

The amount of momentum the person has just before they hit the target – the amount of momentum they have when they hit the board and come to a stop.

So: the rate of change in momentum is determined by, the weight they apply multiplied by the speed at which the striking tool is travelling immediately before it hits the target (i.e. its momentum whilst moving) minus its momentum after it hits the board (which is zero because the striking tool has stopped) divided by how long it takes to stop.

Since the weight of objects does not change (unless we eat bucket loads of ice cream very quickly whilst moving or leave the earth and move into space or a very high altitude) we can say that the amount of push or pull (i.e. the force) applied to stop a moving object determines how quickly it is slowed down (or speeds up).

So if it is slowed down quickly the force must be larger than if it is slowed down more slowly. (We know this whenever we foot our foot on the brake pedal in our car. If we push it down hard (more force) we stop quickly, if we push it gently (less force) we slow down more slowly ).

In mathematical terms ( and using the correct type of units ) this is shown as

Force = mass (m) ( final velocity (v) – initial velocity (u))                                                                            Time taken to stop

Note also that: final velocity – initial velocity   = acceleration(a)                                                                      time taken

so F = ma

This is easier to see if we put numbers in

If we have a hand which weighs 1 Kg (i.e. mass “m” ), and it is  travelling at 30 km/hr (initial velocity “u” ) as it strikes a board (therefore the final velocity is 0 km/hr)

and the hand takes ¼  second (t) (0.25sec)to break the board

then we see that:

Force = 1kg (weight of hand) ( 0km/hr – 30 km/hr

0.25sec

Force = 1 x (-30)

0.25

Force = -30                  = -120 Newtons

0.25

The force is negative because it acts in the opposite direction to the movement of the hand.

So a force of 120 Newtons has been applied the board.

If however the board does not break because the board moves with the hand as it strikes the board , the force is reduced because the time the force is applied is greater. For example if the force was applied to the board for one second we can see that the force applied would be 30 Newtons.

i.e.

Force = -30

1

force = – 30 Newtons

But this 30 newtons would have been applied for 1 second not ¼ second.

Our experience tells us this, for example when we hold focus mitts. If we hold the mitt firmly as the hand or foot strikes, the force is transferred quickly and feels hard whereas if we let the mitt move with the strike (thereby increasing the time it takes to transfer the force) it reduces the “hardness” of the strike.

Summarising this:

This means the Force will be large if the time taken to smash the board is small and the change in momentum is great  (that is the hand is moving very fast initially and stops very quickly as the brick smashes) but a smaller force will be produced if the hand transfers the force more slowly because the board moves with the hand as it strikes it. The other factor of course is the amount of weight that is applied when smashing the board. If this is large the force will be greater, if it is less the force will be less. We cannot of course change the weight of the persons’ hand but we can change the amount of body weight we apply as we strike. If we put more of our body into the swing then of course we are applying more weight or mass. I believe this is how the International Taekwon-Do Federation principle of using a sine wave motion works by applying more of our body to the technique as we strike the object thus increasing the force.

From this explanation it becomes clear why we need to use a good board holder or very stable people to hold our boards when breaking.

I would not claim that this is the definitive explanation of force and board breaking since there are other factors such as the angle of the strike on the board and the size of the attacking tool, it is merely my interpretation of the situation regarding the impulsive force applied in board breaking.

Master Steven Weston VIIth dan has been practicing Taekwon-Do for over 35 years and has recently moved to Korea to work with the ITF HQ Korea team. He has just retired from his profession as a medical scientist at the University of Tasmania and will now focus entirely on his contribution to the world of Taekwon-Do

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