Transcript Conservation of Energy

What is kung fu if not physics?
How is it done?
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Speed…
Strength…
Accuracy…
Focus…
• You need enough force to break the board
(and avoid breaking your hand!)
We can consider…
• Force…
• Momentum…
• Energy…
• We’ll start by considering energy
How much energy do we need?
• Convert GPE to KE! (GPE = mgh)
• Drop different masses from different
heights – when does the wood break?
• Does it matter which way round the wood
is?
• Watch your toes!
Finding your hand speed
• Use the datalogger to measure the speed
of your hand in a downward strike
• At which point is your hand moving
fastest?
Finding the mass of your hand
• To estimate the mass of your hand use data
about the masses of different parts of the human
body, from a biomechanics paper (Zatsiorsky,
Selujanov, 'The mass and inertia characteristics
of the main segments of the human body'.
Biomechanics YIII-B.) pp. 1151-1159, (1983)).
Body part as% of total body mass
• Head=6.68 Trunk=42.57 Upper Arm=2.55
Forearm=1.38 Hand=0.56 Thigh=14.78
Calf=4.81 Foot=1.29
What’s the maximum KE of your
hand?
• Conservation of energy:
• KE of my hand before the break equals the energy that goes into
breaking the board (called the deformation energy) and kinetic
energy of the hand and the board after the strike
• Where M= the mass of my hand and forearm, Vo = velocity of hand
at point of impact, m = the mass of board, V = velocity of hand and
board after impact.
• The above equation assumes that the hand and the board travel at
the same speed immediately after the impact.
The law of conservation of momentum says the momentum of the hand
before the impact is equal to the momentum of the board and the hand
after the impact.
Rearrange equation 1) in terms of deformation energy:
Rearrange equation 2) in terms of V:
Put them both together:
To give a formula to find the deformation energy!
How much energy do we need?
• For the amount of energy needed to break
the wood use a value from a physics
paper (Wilk, McNair, Feld, 'The Physics of Karate',
American Journal of Physics 51, 783-790 (1983)).
• The value is 5.3 ± 2.8 J
• The ± 2.8 J bit means that the value is
accurate within 2.8 Joules, so the energy
needed to break the wood could be as
much as 8.1 J.
Can it be done (theoretically?)
• Use the formula derived earlier to
calculate the deformation energy of the
wood
• How does this compare to your maximum
hand KE?
• SHOULD physics let you break the wood?
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The need for speed
From what Chris tells me, the most important thing is to make sure my arm is moving at the
maximum possible speed when it hits the board. This seems kind of obvious, but what worries me
is this: I've tried pushing down on the wood as hard as I can and I can't break it, so why will I be
able to break it just because my hand is moving?
Luckily, Chris's advice does make sense from a physics point of view. It's all about Force. A force
is a push or a pull that can speed something up, slow something down or change its direction.
When I move my hand very quickly for a strike, the wood (which is rigid) must exert a force on my
hand to slow it down. Because the wood is brittle and does not bend or compress very much, it
has to do this very quickly. To slow my hand down in a fraction of a second means there is a very
large deceleration and a very large force acting on my hand. (this is because of Newton's second
law of motion) The maximum force the wood can exert on my hand depends on the strength of its
fibres. If the force required to stop my hand is larger than the strength of the wood, the wood will
break.
There are two cases where it would not be so easy to break something. One is if the material is
elastic and can bend or compress, such as a piece of rubber. In this case, the rubber would
stretch and slow my hand down gradually over several seconds, which would require a smaller
force. The rubber would not break and my hand would bounce off! The other example is less
pleasant. If the material is very strong, although the force required to stop my hand is high, the
material will be strong enough to produce it. The hand will stop abruptly and would hurt for a very
long time. So I'm not going to try to break concrete slabs just yet!
• Point of focus
Technique: Chris's advice is to pretend that the target is beyond
where it actually is.
Explanation: This is related to the need for speed. Beginners
naturally slow down as they reach the target, to avoid hurting their
hand. If I do this I could end up hurting my hand even more, as I
might not have enough force to break the wood. All my downwards
momentum would be absorbed by the wood as it bends slightly, and
then directed back at my hand as the wood springs back to its
original position. Ouch!
• Use of body mass
Technique: Chris puts more of his body mass into the strike by
snapping with his hips and moving his whole body downwards as he
strikes.
Explanation: Kinetic energy is proportional to mass, so the more
mass I can put into my strike, the greater my force will be.
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Striking Surface
Technique: Chris turns his hand upwards just before the point of impact.
Explanation: I think that one of the advantages of this is that it's best to hit the wood
with the smallest possible surface area of my hand. This will maximise the amount of
energy per unit surface area that I transfer to the board. I don't need to put energy
into the whole board, just enough energy into a small area, so that the wood fibres in
that part of the board shatter.
What I've written so far are just theories about how the block breaking works. To
confirm what's really going on I need to do some experiments. The most important
thing to test, for the sake of my own safety, is whether it's possible for me to break
these boards. To test this I'm going to measure the speed of my arm as I practice the
strike. I can then work out if my strike generates enough energy to break the board.
For the amount of energy needed to break the wood I'm using a value from a physics
paper (Wilk, McNair, Feld, 'The Physics of Karate', American Journal of Physics 51,
783-790 (1983)). The value is 5.3 ± 2.8 J (J stands for Joules, a unit of energy). The
± 2.8 J bit means that the value is accurate within 2.8 Joules, so the energy needed
to break the wood could be as much as 8.1 J. I've made sure that the piece of wood
I'm breaking is the same type and size as the wood that the measurements were
taken from. Now I need to work out how much energy I can put into the wood with my
strike…
• Newton's Second Law of Motion
Newton's second law of motion says that the acceleration of an
object is dependent upon two variables: the net force acting on the
object and the mass of the object.
The greater the force, the greater the acceleration, and vice-versa. If
you double the force, then you double the amount of acceleration.
At the same time, the more mass something has, the harder it is to
accelerate. To accelerate a 4kg and a 2kg mass by the same
amount, I have to apply twice as much force to the 4kg mass.
The second law is expressed mathematically as a=F/m, where a is
acceleration, F is net force, and m is mass. It's more commonly
rewritten as F=ma (which means the same thing). To get F=ma you
multiply both sides of a=F/m by 'm' (remember: when rearranging
equations, you always have to do the same thing to both sides).
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Conservation of Energy
An alternative way of thinking about the strike is in terms of energy. Energy is a
measure of how much work something can do. Work is done when a force causes an
object to move. One form of energy is kinetic energy: the energy something has due
to its motion. The equation for the kinetic energy of my hand is:
Where m stands for the mass of my hand, and v stands for it's speed.
Energy is always conserved. This means that the kinetic energy of my hand just
before the impact is equal to the sum of the energy used up in breaking the block
(called the deformation energy) and the kinetic energy of the block fragments and my
hand after the collision. Some of the energy is also lost as heat energy (the wood and
my hand heat up slightly), and sound (the sound of the wood as it cracks).
The more kinetic energy my hand has, the more energy I'll be able to put into
breaking the block. Because kinetic energy is proportional to the square of the speed,
it makes sense for me to maximise my hand's speed.