Wednesday, February 25, 2009

The centre of gravity of a collection of masses is the point where all the weight of the object can be considered to be concentrated.
from: http://theory.uwinnipeg.ca/physics/rot/node4.html

The centre of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. The centre of mass is a function only of the positions and masses of the particles that comprise the system. In the case of a rigid body, the position of its centre of mass is fixed in relation to the object (but not necessarily in contact with it). In the case of a loose distribution of masses in free space, such as, say, shot from a shotgun, the position of the centre of mass is a point in space among them that may not correspond to the position of any individual mass. In the context of an entirely uniform gravitational field, the center of mass is often called the centre of gravity — the point where gravity can be said to act.
from: Wikipedia

Centre of Gravity vs Centre of Mass.
In a uniform gravitational field the centre of gravity is identical to the centre of mass , a term preferred by physicists. The two do not always coincide, however. For example, the Moon's centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform sphere), but its centre of gravity is slightly displaced toward the Earth because of the stronger gravitational force on the Moon’s near side.
from: http://www.britannica.com

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Saturday, February 21, 2009

Archimedes
This was given on the day I was absent.
But I did research anyway.

According to Wikipedia:
Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.
Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. AD 530 by Isidore of Miletus, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

Watch the videos to get a deeper understanding. I recommend the first and last one.

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Monday, February 16, 2009

Astronauts' outer space poo area.
Buzz Aldrin became the first man to poo on the moon in 1969. He collected his waste in a bag, but because of zero gravity, the contents would often escape during the disposal process and fly around the shuttle. To curb this issue, astronauts ate very little fiber to prevent them from pooing very often. Modern astronaut toilets work like a vacuum cleaner. In order to use the toilet the astronauts must strap themselves to the toilet seat and then turn on a powerful fan. A suction hole then slides open and the poo is sucked away to be stored, and then disposed.
from http://www.vincecorvelli.com/poo.htm.

watch this video of how to poo in space.

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Principle of moments.
The principle of moments means for a body in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments about the same point.
from: http://www.fearofphysics.com/w.php?define=principle%20of%20moments.

and from TutorVista.com,
If a body is in equilibrium under the action of a number of forces, then the algebraic sum of the moments of the forces about any point is equal to zero. In other words, the sum of the clockwise moments equals sum of the anticlockwise moments when the body is in equilibrium.







Clockwise moments equal to anti-clockwise moments.
In the figure above,
sum of clockwise moments = sum of anti-clockwise moments
(50 x 40) + (100 x 20) + (60 x 10) = (30 x 20) + (100 x 40)

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Sunday, February 15, 2009

Terminal velocity.
According to Wikipedia:

A free falling object achieves its terminal velocity when the downward force of gravity (F_g) equals the upward force of drag (F_d). This causes the net force on the object to be zero, resulting in an acceleration of zero. Mathematically an object asymptotically approaches and can never reach its terminal velocity.

As the object accelerates (usually downwards due to gravity), the drag force acting on the object increases. At a particular speed, the drag force produced will equal the object's weight (mg). Eventually, it plummets at a constant speed called terminal velocity (also called settling velocity). Terminal velocity varies directly with the ratio of drag to weight. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity. An object moving downward with greater than terminal velocity (for example because it was affected by a downward force or it fell from a thinner part of the atmosphere or it changed shape) will slow until it reaches terminal velocity.

e.g. Based on wind resistance, for example, the terminal velocity of a skydiver in a free-fall position with a semi-closed parachute is about 195 km/h (120 mph or 55 m/s). This velocity is the asymptotic limiting value of the acceleration process, since the effective forces on the body more and more closely balance each other as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on. Higher speeds can be attained if the skydiver pulls in his limbs. In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s) which is also the terminal velocity of the peregrine falcon diving down on its prey. And the same terminal velocity is reached for a typical 150 grain bullet travelling in the downward vertical direction — when it is returning to earth having been fired upwards, or perhaps just dropped from a tower — according to a 1920 U.S. Army Ordnance study.

Competition speed skydivers fly in the head down position reaching even higher speeds. The current world record is 614 mph (988 km/h) by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.

An object falling toward the surface of the Earth will fall 9.81 meters per second faster every second (an acceleration of 9.81 m/s²). The reason an object reaches a terminal velocity is that the drag force resisting motion is directly proportional to the square of its speed. At low speeds, the drag is much less than the gravitational force and so the object accelerates. As it accelerates, the drag increases, until it equals the weight. Drag also depends on the projected area. This is why things with a large projected area, such as parachutes, have a lower terminal velocity than small objects such as cannon balls.

Mathematically, terminal velocity, without considering the buoyancy effects, is given by

where

V_t = terminal velocity,

m = mass of the falling object,

g = gravitational acceleration,

C_d = drag coefficient,

ρ = density of the fluid through which the object is falling, and

A = projected area of the object.

On Earth, the terminal velocity of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area.

For objects falling through the atmosphere, air density increases with decreasing altitude, ca. 1% per 80 m (see barometric formula). Therefore, for every 160 m of falling, the terminal velocity decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal velocity.

And according to The Physics Zone:

Terminal velocity is the velocity at which the driving forces are cancelled out by the resistive forces. Terminal velocity depends a great deal upon the shape of the object that is facing the direction it is moving. Once an object has reached terminal velocity, the object is not accelerating (a=0), therefore it is not speeding up or slowing down. It is a constant velocity unless the driving forces or the resistive forces change. Typically, Terminal Velocity is only a possibility when you are dealing with fluid friction as opposed to contact friction like static or kinetic friction.

Driving Forces are forces that try to cause motion: In the case of falling it would be gravity (weight). In the case of a car it would be the force from the engine (through the friction on tires). Sometimes an object can have multiple driving forces. (ie. an airplane in a dive, has the engine pushing it down at the same time gravity is pulling it down).

Resistive Forces are the forces that try to resist motion. The force of fluid friction (from a liquid or gas) plays the main role in creating terminal velocity.

Fluid Friction differs from contact friction because the amount of fluid friction depends on how fast the object is moving through the fluid. The greater the speed, the greater the friction. This can be felt if you are in a pool of water. Trying to walk from one side of the pool to the other is much easier than trying to run. That's because the faster you move, the harder the fluid pushes against you. When you examine contact friction you find that speed has no effect on the amount of kinetic friction.

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Question!



















If a force of 1 N acts on the box, causing it to move, and after that a force of 1 N acts on it while it is in motion, will the box stop immediately?

Answer: No. The box will slow down first, then stop. In order to stop the box immediately, the force that acts on it while it is in motion has to be stronger than 1 N. (refer to the law of inertia)

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Monday, February 9, 2009

Quicksand
Quicksand is basically just ordinary sand that has been so saturated with water that the friction between sand particles is reduced. The resulting sand is a mushy mixture of sand and water that can no longer support any weight. If you step into quicksand, it won't suck you down. However, your movements will cause you to dig yourself deeper into it.

how to get out of quicksand?
watch this video:

1. Drop everything. Because your body is less dense than quicksand, you can't fully sink unless you panic and struggle too much (which will cause the sand to further liquefy) or you're weighed down by something heavy. If you step into quicksand and you're wearing a backpack or carrying something heavy, immediately take off your backpack or drop what you're carrying. If it's possible to get out of your shoes, do so; shoes, especially those with flat, inflexible soles (many boots, for example) create suction as you try to pull them out of quicksand. If you know ahead of time that you are highly likely to encounter quicksand, change out of your boots and either go barefoot or wear shoes that you can pull your feet out of easily.
2. Relax. Quicksand usually isn't more than a couple feet deep, but if you do happen to come across a particularly deep spot, you could very well sink quite quickly down to your waist or chest. If you panic you can sink further, but if you relax, your body's buoyancy will cause you to float.
3. Breathe deeply. Not only will deep breathing help you remain calm, it will also make you more buoyant. Keep as much air in your lungs as possible. It is impossible to "go under" if your lungs are full of air.
4. Get on your back. If you sink up to your hips or higher, bend backward. The more you spread out your weight, the harder it will be to sink. Float on your back while you slowly and carefully extricate your legs. Once your legs are free you can inch yourself to safety by using your arms to slowly and smoothly propel yourself. If you are very near the edge of the quicksand, you can roll to hard ground.
5. Take your time. If you're stuck in quicksand, frantic movements will only hurt your cause. Whatever you do, do it slowly. Slow movements will prevent you from agitating the quicksand—the vibrations caused by rapid movements can turn otherwise relatively firm ground into more quicksand. More importantly, quicksand can react unpredictably to your movements, and if you move slowly you can more easily stop an adverse reaction and, by doing so, avoid getting yourself stuck deeper. You're going to need to be patient; depending on how much quicksand is around you, it could take several minutes or even hours to slowly, methodically get yourself out.
6. Get plenty of rest. Other than panic, exhaustion is your worst enemy. Since it can take a long time to get yourself out of quicksand, be sure to take breaks and just float on your back if you feel your muscles getting tired. If you're in a dangerous tidal zone, however, you may be in a race against time (see warning below).
7. Use a stick (optional). A stick is not necessary to extricate yourself from quicksand, but it can be helpful if you have one.
   
   
   • As soon as you feel your ankles sink, lay the pole on the surface of the quicksand horizontally behind you.
   • Flop onto your back on top of the pole. After a minute or two, you will achieve balance in the quicksand, and you'll stop sinking.
   • Work the pole towards a new position, under your hips. The pole will prevent your hips from sinking, so you can slowly pull one leg free, then the other.
   • Stay flat on your back with your arms and legs fully touching the quicksand and use the pole as a guide. Inch sideways along the pole to firm ground.

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Sunday, February 8, 2009

Newton's Three Laws of Motion
from http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion / http://hyperphysics.phy-astr.gsu.edu/hbase/Newt.html :
The first law is the law of inertia. Newton's first law states that if the vector sum of all forces (also known as the net force) acting on an object is zero, then the state of motion of the object does not change.

• An object that is not moving will not move until a net force acts upon it. - The energy from the force will cause the object to move.
  
• An object that is moving will not change its velocity (accelerate) until a net force acts upon it. - Moving objects will always eventually stop moving. This is because friction (a force; see post on forces) is acting on the object. Without friction, moving objects would never stop moving or even slow down.

The second law is that the change of the momentum of a body is proportional to the impulse impressed on the body and happens along the straight line on which that impulse is impressed.
This means the force is proportional to the acceleration of the body and the second law can be represented by the formula F = ma.

















The third law is for every action there is an equal and opposite reaction.

A mind-map of Newton's laws of motion:

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Friday, February 6, 2009

Greenwich Meridian Time(GMT)
learnt from http://wwp.greenwichmeantime.com:
GMT has been in Greenwich, England since 1884. GMT is called Greenwich Meridian Time because it is measured from the Greenwich Meridian Line at the Royal Observatory in Greenwich. Greenwich is where all time zones are measured.
The Greenwich Meridian (/Prime Meridian/Longitude Zero degrees) marks the starting point of every time zone in the world. GMT is also known as Greenwich Mean Time because GMT is the mean (average) time that the earth takes to rotate from noon-to-noon.
GMT is World Time and the basis of every world time zone which sets the time of day and is at the center of the time zone map. GMT sets current time or official time around the globe. Most time changes are measured by GMT. Although GMT has been replaced by atomic time (UTC) it is still widely regarded as the correct time for every international time zone.
GMT is also known as Zulu Time.
* good place for you to set your clocks right - http://wwp.greenwichmeantime.com/info/current-time.htm and one that automatically checks your computer clock - http://wwp.greenwichmeantime.com/gmt-timestamp.htm

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Tuesday, February 3, 2009

Weight = Mass x Gravitational acceleration (W=mg)

Weight.
Weight is measured in newtons [N].
example of instrument that measures weight: spring balance

Mass.
Mass is measured in kilograms [kg].
example of instrument that measures mass: beam balance

Gravitational acceleration
Gravitational acceleration is measured in meters per square second [m/s(squared)] or newtons per kilogram [N/kg].
*measuring gravitational acceleration (N/kg)
[N] = [kg]G
G = [N]/[kg]
= [N/kg]
= N/kg
example:
G = 20N/2kg
= 10 N/kg

gravity...
on earth = 10 N/kg - secondary school
= 9.81 N/kg - JC
= 9.817 N/kg - industry
on moon = 1.6 N/kg
weight...
on earth = 40(kg) x 10(N/kg)
= 400N
on moon = 40(kg) x 1.6(N/kg)
= 64N

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Density is mass per unit volume.
mass = 0.5kg
= 0.5 x 1000
= 500g
density = 500/10
= 50 g/cm cube

* Why is salt water denser than pure water?
In pure water, the water molecules are spread around in the water. But when salt is dissolved into water, the salt molecules are actually shoved in between the water molecules, making the molecules very tightly packed and thus making the liquid denser.

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Monday, February 2, 2009

Question!
If the density of the liquid is A g/cm cube and the density of the object is also A g/cm cube, when the object is placed inside the liquid, will it float, sink or just stay suspended in the middle?

Ans:
It would stay suspended in the middle. If the object is of a lower density than the liquid, it will float. If it is of a higher density than the liquid, it will sink. So if both densities are the same, the object will stay in the middle of the liquid.

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