A modulus of strength is a way of measuring the characteristic strength of materials independent of its size. For example, a 4" thick piece of wood may be stronger than an 1/16" thick piece of iron. This is because of the thickness. The intrinsic strength of iron is much higher than wood. So for the same thickness, the iron would have the greater strength. The modulus is usually expressed as force/area or some such normalizing method. Bone has a much stronger strength/area than either concrete or wood.
What is the modulus of rupture of of bone compared to concrete and how does this help explain why a Karate blow can fracture concrete blocks?
The modulus of rupture characterizes the force/area that is necessary to rupture the material If bone has a larger modulus of rupture than concrete, it can shatter concrete of a similar area without shattering itself. If the bone had a modulus that was 10x larger than material X, then the bone can shatter a piece of that material up to 10X it's area.
Why can a Karate blow shatter concrete when the athlete cannot break the concrete block by pushing or pulling on it with the same muscles as were used to accelerate the Karate blow?
By pushing or pulling, the hand can only apply the limited force of the muscle. In the Karate blow, the hand stores up the energy supplied by the muscles and then releases it very sharply so that a MUCH larger force is created... thereby permitting the user to shatter boards and concrete blocks.
Archery
A bow and arrow combination is not completely efficient. If an archer does 70J of work to cock the bow and the .015kg arrow is shot off with a speed of 140mi/hr. How much energy does the arrow have? Where does the rest of the energy go? If the arrow were to be fired with 100% absorbtion of the energy, how fast would the arrow go?
The arrow would have an energy of K = 1/2 mv^2 = 1/2 (.015)*(61)^2 = 28J
In this case, the archer has done 70J of work to cock the bow.
The 70-28 = 42j of energy is absorbed by the bow and the string. A bow and arrow with only 40% efficiency is not very good.
If the arrow were to get 100% of the energy, the velocity would be:
v^2= 2K/m . v=sqrt(2K/m) =sqrt(2*70/.015) =97m/s = 222 mi/hr.
You can see that the invention of efficient bows permitted arrows to be shot with the ability to penetrate armour!!
Aristotle Aristotle commented upon the necessities to produce motion in his treatise on Progressionn of Animals. Give some examples of applications of his stated principles in your own experiences.
In the principle stated in PoS, the animal must makes its change of position by pressing agains that which is beneath it;..... Examples are if you press with a spiked shoe on a firm track, you will propel yourself very well. Similar tries at pressing against loose sand will produce less motion. Pressing against very slippery ice may produce almost no motion. In the limit of a perfectly slippery surface, no motion is possible.
propulsion
Efficiency of sculling by the method of figure 8 at the stern vs oars transverse to the boat. How is the efficiency determined? Where does the lost energy go? Way of measuring efficiency of propulsion. Perfect efficiency would be if you did 100J of work and this work were to produce 100J of work in propelling the boat. [Recall that for the archery case, the energy obtained by the arrow is always less than the work done by the archer... even for the best bows and strings. Some energy always slips away to the bow and string.] In the case of boat propulsion, you want a maximum energy of the sculler to go into boat propulsion and not much of it should go to flexing the rigging and oars, etc.. in some inelastic way. In the case of sculling, this is like running on loose sand... a lot of the energy goes into moving the sand around. In the case of rowing, lots of the energy goes into moving the water around.
The most efficient stroke is one in which a minimum of energy is delivered to the water and the maximum is delivered to moving the boat. Imagine poling a boat by pushing with a pole on the bottom of a shallow river. In the ideal situation, the pole doesn't slip and ALL of the work by the punter goes into boat propulsion. The stern sculling stroke used in Chinese boats delivers a much smaller energy to the water than transverse oars for the same propulsion. This has to do with the principle of LIFT rather than resistive force [which we will discuss more later.]
Efficiency of sailing. Why isn't a sheet on a couple of poles as efficient as a fully battened sail for courses such as reaching and close hauled? Does it make a difference when sailing down wind?
-------------- For sailing downwind, the force on the sail is purely produced by resistive forces so that shape doesn't matter. The spinnaker sail used by yachts going downwind act like a parachute.
For reaching or sailing close hauled, the lift force is paramount. The lift force is like the force produced on an airplane wing. It depends on making the air flow on the surface in a smooth way and making it change it's direction. A good aerodynamic shape is necessary. [an airplane wing is an example of a good aerodynamic shape. A poor shape will produce some directional change but mostly it would make the air into turbulent vortices that have energy but no coherent direction. [A poor shape might be one that has a very large camber and is misaligned relative to the airflow. Another poor shape would be one that has many bumps and protrusions that would cause turbulence.]
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Horsemanship
Describe a few actions which made a horseman on a saddle with stirrups much more effective than a horseman without stirrups.
In the middle ages, a method of warfare was to charge using lances or to use sabres. To use these weapons effectively, the upper body must be held to the horse effectively. The saddle/stirrup combination carried this out and still gave the option of bailing out in case of falling or other reasons.