The Edu Zeal ®: Physics

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Sunday, 20 January 2013

Torricelli's (Roger's) law

Torricelli's (Roger's) law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an opening to the height of fluid above the opening.

Torricelli's law states that the speed of efflux, v, of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e. $v = \sqrt{2gh}$ , where g is the acceleration due to gravity (9.8 N/kg). This last expression comes from equating the kinetic energy gained, $\frac{1}{2}mv^2$ , with the potential energy lost, mgh , and solving for v.

Friday, 18 January 2013

Magnetism

Magnetism is a force of attraction or replusion that acts at a distance. It is due to a magnetic field, which is caused by moving electrically charged particles or is inherent in magnetic objects such as a magnet.
A magnet is an object that exhibits a strong magnetic field and will attract materials like iron to it. Magnets have two poles, called the north (N) and south (S) poles. Two magnets will be attacted by their opposite poles, and each will repel the like pole of the other magnet. Magnetism has many uses in modern life.
Questions you may have include:

What is a magnetic field?
What is a magnetic force?
What is the relationship between magnetism and electricity?

This lesson will answer those questions.

Useful tool: Metric-English Conversion

Magnetic field

A magnetic field consists of imaginary lines of flux coming from moving or spinning electrically charged particles. Examples include the spin of a proton and the motion of electrons through a wire in an electric circuit.
What a magnetic field actually consists of is somewhat of a mystery, but we do know it is a special property of space.

Magnetic field or lines of flux of a moving charged particle

Names of poles

The lines of magnetic flux flow from one end of the object to the other. By convention, we call one end of a magnetic object the N or North-seeking pole and the other the S or South-seeking pole, as related to the Earth's North and South magnetic poles. The magnetic flux is defined as moving from N to S.

Magnets

Although individual particles such as electrons can have magnetic fields, larger objects such as a piece of iron can also have a magnetic field, as a sum of the fields of its particles. If a larger object exhibits a sufficiently great magnetic field, it is called a magnet.

Magnetic force

The magnetic field of an object can create a magnetic force on other objects with magnetic fields. That force is what we call magnetism.
When a magnetic field is applied to a moving electric charge, such as a moving proton or the electrical current in a wire, the force on the charge is called a Lorentz force.

Attraction

When two magnets or magnetic objects are close to each other, there is a force that attracts the poles together.

Force attracts N to S

Magnets also strongly attract ferromagnetic materials such as iron, nickel and cobalt.

Repulsion

When two magnetic objects have like poles facing each other, the magnetic force pushes them apart.

Force pushes magnetic objects apart

Magnets can also weakly repel diamagnetic materials.

Magnetic and electric fields

The magnetic and electric fields are both similar and different. They are also inter-related.

Electric charges and magnetism similar

Just as the positive (+) and negative (−) electrical charges attract each other, the N and S poles of a magnet attract each other.
In electricity like charges repel, and in magnetism like poles repel.

Electric charges and magnetism different

The magnetic field is a dipole field. That means that every magnet must have two poles.
On the other hand, a positive (+) or negative (−) electrical charge can stand alone. Electrical charges are called monopoles, since they can exist without the opposite charge.

Summary

Magnetism is a force that acts at a distance and is caused by a magnetic field. The magnetic force strongly attracts an opposite pole of another magnet and repels a like pole. The magnetic field is both similar and different than an electric field.

Surface Tension

Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in the floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects (e.g. water striders) to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids.
Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.
In materials science, surface tension is used for either surface stress or surface free energy.

Causes

Diagram of the forces on molecules of a liquid

Surface tension prevents the paper clip from submerging.

The cohesive forces among liquid molecules are responsible for the phenomenon of surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure and forces liquid surfaces to contract to the minimal area.
Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.
Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.
As a result of surface area minimization, a surface will assume the smoothest shape it can (mathematical proof that "smooth" shapes minimize surface area relies on use of the Euler–Lagrange equation). Since any curvature in the surface shape results in greater area, a higher energy will also result. Consequently the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

Effects of surface tension

Water

Several effects of surface tension can be seen with ordinary water:
A. Beading of rain water on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.
B. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.
C. Flotation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area.
D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its physics are the same.
E. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

A. Water beading on a leaf
B. Water dripping from a tap
C. Water striders stay atop the liquid because of surface tension
D. Lava lamp with interaction between dissimilar liquids; water and liquid wax
E. Photo showing the "tears of wine" phenomenon.

Surfactants

Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.

Emulsions are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Basic physics

Two definitions

Diagram shows, in cross-section, a needle floating on the surface of water. Its weight, F_w, depresses the surface, and is balanced by the surface tension forces on either side, F_s, which are each parallel to the water's surface at the points where it contacts the needle. Notice that the horizontal components of the two F_s arrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up to balance F_w.

Surface tension, represented by the symbol γ is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2 $\scriptstyle\gamma$ L (the factor of 2 is because the soap film has two sides, hence two surfaces). Surface tension is therefore measured in forces per unit length. Its SI unit is newton per meter but the cgs unit of dyne per cm is also used. One dyn/cm corresponds to 0.001 N/m.
An equivalent definition, one that is useful in thermodynamics, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, $\scriptstyle\gamma$ δA, is needed.This work is stored as potential energy. Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm². Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume.
The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.

Surface curvature and pressure

Surface tension forces acting on a tiny (differential) patch of surface. δθ_x and δθ_y indicate the amount of bend over the dimensions of the patch. Balancing the tension forces with pressure leads to the Young–Laplace equation

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation:

$\Delta p\ =\ \gamma \left( \frac{1}{R_x} + \frac{1}{R_y} \right)$

where:

Δp is the pressure difference.
$\scriptstyle\gamma$ is surface tension.
R_x and R_y are radii of curvature in each of the axes that are parallel to the surface.

The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalisation).
Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a water strider's feet make on the surface of a pond).
The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

Δp for water drops of different radii at STP
Droplet radius	1 mm	0.1 mm	1 μm	10 nm
Δp (atm)	0.0014	0.0144	1.436	143.6

Liquid surface

Minimal surface

To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds
The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles

Main article: Contact angle

The surface of any liquid is an interface between that liquid and some other medium The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater than) its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.

Forces at contact point shown for contact angle greater than 90° (left) and less than 90° (right)

Where the two surfaces meet, they form a contact angle, $\scriptstyle \theta$ , which is the angle the tangent to the surface makes with the solid surface. The diagram to the right shows two examples. Tension forces are shown for the liquid-air interface, the liquid-solid interface, and the solid-air interface. The example on the left is where the difference between the liquid-solid and solid-air surface tension, $\scriptstyle \gamma_{\mathrm{ls}} - \gamma_{\mathrm{sa}}$ , is less than the liquid-air surface tension, $\scriptstyle \gamma_{\mathrm{la}}$ , but is nevertheless positive, that is

$\gamma_{\mathrm{la}}\ >\ \gamma_{\mathrm{ls}} - \gamma_{\mathrm{sa}}\ >\ 0$

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of $\scriptstyle f_\mathrm{la}$ is canceled by the adhesive force, $\scriptstyle f_\mathrm{A}$ .

$f_\mathrm{A}\ =\ f_\mathrm{la} \sin \theta$

The more telling balance of forces, though, is in the vertical direction. The vertical component of $\scriptstyle f_\mathrm{la}$ must exactly cancel the force, $\scriptstyle f_\mathrm{ls}$ .

$f_\mathrm{ls} - f_\mathrm{sa}\ =\ -f_\mathrm{la} \cos \theta$

Liquid

Solid

Contact angle

water

soda-lime glass

lead glass

fused quartz

0°

paraffin wax

107°

silver

90°

methyl iodide

soda-lime glass

29°

lead glass

30°

fused quartz

33°

mercury

soda-lime glass

140°

Some liquid-solid contact angles

Since the forces are in direct proportion to their respective surface tensions, we also have

$\gamma_\mathrm{ls} - \gamma_\mathrm{sa}\ =\ -\gamma_\mathrm{la} \cos \theta$

where

$\scriptstyle \gamma_\mathrm{ls}$ is the liquid-solid surface tension,
$\scriptstyle \gamma_\mathrm{la}$ is the liquid-air surface tension,
$\scriptstyle \gamma_\mathrm{sa}$ is the solid-air surface tension,
$\scriptstyle \theta$ is the contact angle, where a concave meniscus has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.

This means that although the difference between the liquid-solid and solid-air surface tension, $\scriptstyle \gamma_\mathrm{ls} - \gamma_\mathrm{sa}$ , is difficult to measure directly, it can be inferred from the liquid-air surface tension, $\scriptstyle \gamma_\mathrm{la}$ , and the equilibrium contact angle, $\scriptstyle \theta$ , which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).
This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid-solid/solid-air surface tension difference must be negative:

$\gamma_\mathrm{la}\ >\ 0\ >\ \gamma_\mathrm{ls} - \gamma_\mathrm{sa}$

Special contact angles

Observe that in the special case of a water-silver interface where the contact angle is equal to 90°, the liquid-solid/solid-air surface tension difference is exactly zero.
Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this. Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.

$\gamma_{\mathrm{la}}\ =\ \gamma_{\mathrm{ls}} - \gamma_\mathrm{sa}\ >\ 0\qquad \theta\ =\ 180^\circ$

Statistical Mechanics

Overview

The essential problem in statistical thermodynamics is to calculate the distribution of a given amount of energy E over N identical systems. The goal of statistical thermodynamics is to understand and to interpret the measurable macroscopic properties of materials in terms of the properties of their constituent particles and the interactions between them. This is done by connecting thermodynamic functions to quantum-mechanical equations. Two central quantities in statistical thermodynamics are the Boltzmann factor and the partition function.
Statistical mechanics or statistical thermodynamic is a branch of physics that applies probability theory, which contains mathematical tools for dealing with large populations, to the study of the thermodynamic behavior of systems composed of a large number of particles. Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life, thereby explaining thermodynamics as a result of the classical and quantum-mechanical descriptions of statistics and mechanics at the microscopic level.
Statistical mechanics provides a molecular-level interpretation of macroscopic thermodynamic quantities such as work, heat, free energy, and entropy. It enables the thermodynamic properties of bulk materials to be related to the spectroscopic data of individual molecules. This ability to make macroscopic predictions based on microscopic properties is the main advantage of statistical mechanics over classical thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.
Statistical mechanics was initiated in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.Boltzmann's original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, thermal equilibrium, the equation of state of gases, and similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist and physical chemist J. Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish physicist James Clerk Maxwell in 1871. "Probabilistic mechanics" might today seem a more appropriate term, but "statistical mechanics" is firmly entrenched.

WATCH THIS VIDEO FOR MORE INFO

Collisions

Overview

Collision is short duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this . Collisions involve forces (there is a change in velocity). The magnitude of the velocity difference at impact is called the closing speed. All collisions conserve momentum. What distinguishes different types of collisions is whether they also conserve kinetic energy.Line of impact - It is the line which is common normal for surfaces are closest or in contact during impact. This is the line along which internal force of collision acts during impact and Newton's coefficient of restitution is defined only along this line.
Specifically, collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes also called a plastic collision.
A “perfectly-inelastic” collision (also called a "perfectly-plastic" collision) is a limiting case of inelastic collision in which the two bodies stick together after impact.
The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly-inelastic collision has a coefficient of restitution of zero.

Types of collisions

There are two types of collisions between two bodies - 1) Head on collisions or one-dimensional collisions - where the velocity of each body just before impact is along the line of impact, and 2) Non-head on collisions, oblique collisions or two-dimensional collisions - where the velocity of each body just before impact is not along the line of impact.
According to the coefficient of restitution, there are two special cases of any collision as written below:
1)A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to internal energy and other forms of energy, so no large scale impacts are perfectly elastic. However, some problems are sufficiently close to perfectly elastic that they can be approximated as such. In this case, the coefficient of restitution equals to one.
2)An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Momentum is conserved in inelastic collisions (as it is for elastic collisions), but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. In this case, coefficient of restitution does not equal to one. In any type of collision there is a phase when for a moment colliding bodies have same velocity along line of impact then kinetic energy of bodies reduces to its minimum during this phase and may be called as maximum deformation phase for which momentarily coefficient of restitution become one.
Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.
Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions.

Analytical vs. numerical approaches towards resolving collisions

Relatively few problems involving collisions can be solved analytically; the remainder require numerical methods. An important problem in simulating collisions is determining whether two objects have in fact collided. This problem is called collision detection.

Examples of collisions that can be solved analytically

Billiards

Collisions play an important role in cue sports. Because the collisions between billiard balls are nearly elastic, and the balls roll on a surface that produces low rolling friction, their behavior is often used to illustrate Newton's laws of motion. After a zero-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This is an important fact that professional billiards players take into account,^[1] although it assumes the ball is moving frictionlessly across the table rather than rolling with friction. Consider an elastic collision in 2 dimensions of any 2 masses m₁ and m₂, with respective initial velocities u₁ and u₂ = 0, and final velocities V₁ and V₂. Conservation of momentum gives m₁u₁ = m₁V₁+ m₂V₂. Conservation of energy for an elastic collision gives (1/2)m₁|u₁|² = (1/2)m₁|V₁|² + (1/2)m₂|V₂|². Now consider the case m₁ = m₂: we obtain u₁=V₁+V₂ and |u₁|² = |V₁|²+|V₂|². Taking the dot product of each side of the former equation with itself, |u₁|² = u₁•u₁ = |V₁|²+|V₂|²+2V₁•V₂. Comparing this with the latter equation gives V₁•V₂ = 0, so they are perpendicular unless V₁ is the zero vector (which occurs if and only if the collision is head-on).

Perfectly inelastic collision

In a perfectly inelastic collision, i.e., a zero coefficient of restitution, the colliding particles stick together. It is necessary to consider conservation of momentum:

$m_a \mathbf u_a + m_b \mathbf u_b = \left( m_a + m_b \right) \mathbf v \,$

where v is the final velocity, which is hence given by

$\mathbf v=\frac{m_a \mathbf u_a + m_b \mathbf u_b}{m_a + m_b}$

The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a center of momentum frame with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is. With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a projectile, or a rocket applying thrust (compare the derivation of the Tsiolkovsky rocket equation).

Examples of collisions analyzed numerically

Animal locomotion

Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in prosthetics is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a force platform (sometimes called a "force plate") as well as detailed kinematic and dynamic (sometimes termed kinetic) analysis.

Collisions used as a experimental tool

Collisions can be used as an experimental technique to study material properties of objects and other physical phenomena.

Space exploration

An object may deliberately be made to crash-land on another celestial body, to do measurements and send them to Earth before being destroyed, or to allow instruments elsewhere to observe the effect. See e.g.:

During Apollo 13, Apollo 14, Apollo 15, Apollo 16 and Apollo 17, the S-IVB (the rocket's third stage) was crashed into the Moon in order to perform seismic measurement used for characterizing the lunar core.
Deep Impact
SMART-1 - European Space Agency satellite
Moon impact probe - ISRO probe

Mathematical description of molecular collisions

Let the linear, angular and internal momenta of a molecule be given by the set of r variables { p_i }. The state of a molecule may then be described by the range δw_i = δp₁δp₂δp₃ ... δp_r. There are many such ranges corresponding to different states; a specific state may be denoted by the index i. Two molecules undergoing a collision can thus be denoted by (i, j) (Such an ordered pair is sometimes known as a constellation.) It is convenient to suppose that two molecules exert a negligible effect on each other unless their centre of gravities approach within a critical distance b. A collision therefore begins when the respective centres of gravity arrive at this critical distance, and is completed when they again reach this critical distance on their way apart. Under this model, a collision is completely described by the matrix $\begin{pmatrix}i&j\\k&l\end{pmatrix}$ , which refers to the constellation (i, j) before the collision, and the (in general different) constellation (k, l) after the collision. This notation is convenient in proving Boltzmann's H-theorem of statistical mechanics.

Attack by means of a deliberate collision

Types of attack by means of a deliberate collision include:

with the body: unarmed striking, punching, kicking, martial arts, pugilism
striking directly with a weapon, such as a sword, club or axe
ramming with an object or vehicle, e.g.:
- a car deliberately crashing into a building to break into it
- a battering ram, medieval weapon used for breaking down large doors, also a modern version is used by police forces during raids

An attacking collision with a distant object can be achieved by throwing or launching a projectile.

Hover Around It

Sunday, 20 January 2013

Torricelli's (Roger's) law

Friday, 18 January 2013

Magnetism

Magnetic field

Names of poles

Magnets

Magnetic force

Attraction

Repulsion

Magnetic and electric fields

Electric charges and magnetism similar

Electric charges and magnetism different

Summary

Surface Tension

Causes

Effects of surface tension

Water

Surfactants

Basic physics

Two definitions

Surface curvature and pressure

Liquid surface

Contact angles

Special contact angles

Statistical Mechanics

Overview

Collisions

Overview

Types of collisions

Analytical vs. numerical approaches towards resolving collisions

Examples of collisions that can be solved analytically

Billiards

Perfectly inelastic collision

Examples of collisions analyzed numerically

Animal locomotion

Collisions used as a experimental tool

Space exploration

Mathematical description of molecular collisions

Attack by means of a deliberate collision