A SMASHING TIME (The physics behind breaking)

 

By Steve Weston,

IV degree Senior Instructor, Southern ITF Taekwon-Do. Hobart, Tasmania, Australia.

e-mail southernitftaekwondo@bigpond.com

 

As a fourth degree black belt and International Instructor/Examiner I have been considering this issue about force applied when breaking a brick or board for a while. So I decided when teaching a year ten science class (I am a medical scientist and more recently a high school science teacher) to incorporate the theory into a unit on force. This is what my investigations revealed. The basic premise that should be considered is Newtons laws and in particular his first and second laws.

 

The first law states that 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)

So getting back to Newtons second law.

The change in momentum is the amount of momentum it has just before it hits the target minus the amount of momentum it has when it comes to a stop.  So the rate of change in momentum is determined by its weight and the speed at which it is travelling before it hits the target divided by how long it takes to stop. Since the weight of objects does not change (unless we eat bucketloads 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.

 

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 ( final velocity (v) – initial velocity (u))

                                                                                    Time taken to stop

 

                                                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) 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 used to break 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 does not slow down as fast by smashing the brick. 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.