Cold Fusion

Cold Fusion

In 1989, an experiment performed at the University of Utah by Pons and Fleischmann's which claimed to have demonstrated fusion. The experiment was essentially an electrolysis cell, consisting of Platinum and Palladium electrodes placed in heavy-water (D2O). When the experiment was performed, it was found that the more heat was produced than can could be accounted for by chemical processes alone. Pons and Fleischmann concluded that the excess heating must be nuclear in origin.

The experiment hinges on the accuracy of the calorimetry used to determine the heating. More accurate calorimeters were tried and the heating effect was found to be significant. Other researchers found it difficult to reproduce the results so, after an initial media frenzy, the claims were widely dismissed.

Despite the general lack of acceptance by the mainstream scientific community, research continues by a few. In 2004, the Department of Energy peer reviewed the experimental evidence for cold fusion. It concluded that:

"The experimental data shows evidence of: the existence of a physical effect that produces heat in metal deuterides".

"The production of 42He in amounts commensurate with a 21H + 21H -> 42He reaction mechanism, a physical effect that results in the emission of energetic particles."

"The underlying process that produce these results are not manifestly evident from experiment. The scientific questions posed by these experiments are both worthy and capable of resolution by a dedicated program of scientific research".

Distances and Magnitudes

Distances and Magnitudes

Distances

In the words of Douglas Adams, the author of The Hitch-Hiker's Guide to the Galaxy:
Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

The distances involved in the universe are so vast that we must introduce some new units.
The Astronomical Unit A.U.

The most practical units we can use are related to the distance from the Sun to the Earth. This is the A.U. or Astronomical Unit. 1 Astronomical Unit = 149 598 000 km

The Parsec


How to calculate the parsec

Parallax is the apparent shift in the nearest stars due to the motion of the Earth around the Sun. The method of parallax gives rise to a natural distance unit that astronomers call the parsec (which we shall abbreviate as pc). The parsec is defined to be the distance at which a star would have a parallax angle p equal to one second of arc.





parsec in trigonometric terms.

Taking the unit is the parsec. This is defined as

1 Parsec = 3.08568025 × 1016 m. also used are kpc =1000 pc and Mpc =1 million pc
Light Year

The light year is the distance travelled by light in one year. All electromagnetic waves travel at a speed of x 299,792,458 ms-1 and an average year being 365.25 days. One light year is 299,792,458 x 108ms-1 x (365.25 x 24 x 60 x 60) s =

9.46073 x 1015 m. or 9.46073 x 1012 km.

With our new measuring sticks we can give a few examples of the scale of the universe.

The distance from the Earth to the nearest star after our Sun is 4.42 ly.

The Milky Way Galaxy is about 150,000 light-years across

The andromeda galaxy is 2.3 million light-years away.

The edge of the observable universe is 46.5 Giga light years away.

Moments and Couples

Moments and Couples

The moment of a Force or Torque

The moment of a force is the perdendicular force F acting at a distance, d and causes an object to rotate.

The moment of a force, also known as the torque T is defined as the force F acting at a perpendicular distance d.

T = F d(1)

Figure 1. The moment of a force.

The dimension of moment is [M L² T^-2] which is the same as energy, however there is no direct relationship between the two. The SI unit of a moment is the Newton meter (Nm).

A special case of moments is where two anti-parallel forces separated by a distance d cause an object to rotate. This is known as a couple.

Couples

If two opposite moments act to cause an object to rotate, such as when your two hand are at the 'quarter-past-three' position on a car steering wheel, it is called a couple. The moment of a couple is called the torque. It is quite often said of engines and applys to the ability of the engine to turn the wheels, or wrongly by Jeremy Clarkson from 'Top Gear' as in, "This engine has a lot of torques."

Figure 2. A couple.

The torque is a psuedo-vector quantity. That is, it has magnitude and it has a direction that is projected perpendicular to the plane of the vectors F and r. The direction of the vector from the plane follows a right-handed corkscrew rule or equivalently the right-hand screw rule.

Torque is a psuedo-vector quanitity with the direction given by the right-hand screw rule.

The magnitude of the torque of a couple can be found by finding the net torque from clockwise and anti clockwise moments acting on an arbitrary point of rotation.

T =F(x + d)

T =F x
Equating, F x +F d = F x.
Net Torque. T = F d

Newton's Laws of Motion

Newton's Laws of Motion

Newton's First Law  

"A body in motion remains in motion unless it is acted on by an external force. If the body is at rest it remains at rest". 

Newton's first law may seem counter intuitive to our everyday experience. If we move an object by pushing it, it will move and then come to a halt. To keep it moving at the same speed a force must be applied. However, most objects are slowed to a halt by friction or air-resistance. Newton's first law gives rise to the idea of inertia. It takes a large force to start to move an object with a large mass and it also takes a large force to stop it moving. A moving object has a reluctance to stop moving and a stationary object has a reluctance to move.

An external force is a force that is applied to the object. There may be other forces inside the object, for example, there are forces produced by the motion of the atoms that make up the object but on average, they cancel each other out and so do not effect the motion of the object.

Newton's first law applies in inertial reference frames, i.e. when the frame of reference is stationary or moving with constant velocity. It does not apply when the frame of reference is accelerating. Strictly speaking, the Earth is accelerating because it is rotating as well as orbiting the Sun, however the effect of this is small enough to consider the Earth as an inertial reference frame.

Newton's Second Law

"The force, F on an object is equal to the rate of change of momentum, p, with time". 

In mathematical terms.

F = dpdt(1)

Or since p = mv, then

dpdt = d dt (mv) = m dvdt + vdmdt   (using the product rule)

For constant mass, dm/dt = 0 is zero therefore,

F= mdvdt

We recognise dv/dt as the acceleration, a and so an alternative form of Newton's 2nd law is

F = ma(2)

and since, a = dvdt = d²rdt²

F = md²rdt²(3)

For this relationship to be true, we must measure the force F in Newtons [N], the mass m in kilograms and the acceleration in ms^-2 otherwise there will be a constant of proportionality will have a value other than 1.

The force in Newton's 2nd law refers to the resultant force. If there are many forces acting on an object, it is the vector sum of those forces is the force that produces any acceleration.

∑F_ext = ma(4)

Newton's Third Law of Motion

"Newton's third law applies to pairs of bodies. If a body A exerts a force on a body B, then body B exerts an equal and opposite force on body A". 

Newton's third law reminds us that forces occur in equal and opposite pairs.

There are many examples of Newton's third law all around us. Every object that is on the floor or on top of another object is exerting a weight force toward the center of the Earth. If the object is stationary, then whatever the object is on top of is exerting an equal force in the opposite direction.

A rocket is also a good example of Newton's third law, it works by accelerating a mass in the form of hot gases, which produces a force. This produces an equal and opposite fore that pushes the rocket in the opposite direction.

The Importance of Newton's Laws

Newton's laws are extremely important not just in mechanics but in the whole of physics. When trying to understand a physical process, we often understand it by looking at the forces acting and working out the equations of motion. This is true of the motion of the planets to the flow of electrons in an electric or magnetic field.

Applications of Induction

Applications of Induction

AC Generator

The ac generator uses Faraday's laws of induction, it consists of a coil of wire rotating a magnetic field. As the coil rotates it cuts the magnetic flux generating an EMF, the EMF produced is given by Faraday's law. The angle is changing at the angular frequency ω. Therefore at a given moment in time the angle between the normal to the area and the magnetic field lines will be ωt. Therefore the flux linkage, φN will be BAN cos(ωt). Differentiating cos(ωt) function with respect to time gives -ω sin(ωt). Therefore, the EMF is given by

 

An AC Generator

The electrons flow first in one direction and then, in the other. The generator produces an alternating current. One advantage that AC has over DC is that it can easily be "stepped up" or "stepped down" with a transformer. In other words, a transformer can take a low-voltage current and make it a high-voltage current, and vice versa. Power is the product of voltage × current (P =VI). For a given amount of power, a low voltage requires a higher current and a higher voltage requires a lower current. Since metal conducting wires have a certain resistance, some power will be wasted as heat in the wires. This power loss is given by P = I²R. Thus, if the overall transmitted power is the same, and given the constraints of practical conductor sizes, low-voltage, high-current transmissions will suffer a much greater power loss than high-voltage, low-current ones. This holds whether DC or AC is used. However, it was very difficult to transform DC power to a high-voltage, low-current form efficiently, whereas with AC this can be done with a simple and efficient transformer.

Transformers

Another application for electromagnetic induction is the transformer. Transformers are used to either increase or decrease the magnitude of an alternating current. The structure of a transformer consists of two coils, called the primary and the secondary, linked by an iron core which is used to concentrate the magnetic field. When an alternating current is applied to the primary, it generates a magnetic field in the iron core the changing magnetic field induces an EMF in secondary coil. Depending on the ratio of turns in the primary coil to the secondary determines whether the transformer is a step-up or step-down.

Schematic diagram of a transformer

Spherical Convex Mirrors

Introduction of Spherical Convex Mirrors

Convex mirrors are also curved mirrors but the silvered surface bulges outward instead of inward as with the concave spherical mirror. As with all mirrors, the angle of incidence of a ray of light is equal to the angle of reflection with respect to a normal on the surface. On a curved surface the normal changes with the curvature.

Therefore, the light rays will diverge from the object. If the rays of light are extrapolated back to the point where they converge, this will be the point where the image is formed.

For reflections off a convex mirror, the image is virtual and upright.

Reflection off a convex spherical mirror

Use of Convex Mirrors

Convex mirrors are often used in car wing-mirrors because they have a greater field of view than a similar plane mirror. However the greater field of view is at the expense of making objects seem further away than they are in reality. Hence the expression seen etched on to the mirrors, 'Objects in Mirror are Closer than they Appear'. Concave mirrors are also used as security mirrors as they enable the viewer to see over a greater region of space.

Battery Operation

Battery Operation

Why does this produce electricity? The flow of current can be understood as the flow of ions from the more reactice metal to the less reactive metal. The ions moving from one electrode to the other creates an electrical charge which is neutralised by the flow of electrons across the wire.

Before considering the reaction of two metals, consider what happens when we place a single metal electrode in an electrolyte. Some of the metal atoms in the electrolyte go into solution as ions while the remaining electrons create a negative charge on the metal. The separation of ions and electrons leads to a separation of charge. However, this build up of charge cannot continue indefinitely because as the negative charge builds up in the metal it becomes increasingly difficult for positive metal ions to go into solution. A similar build up in positive charge in the electrolyte also prevents the build up of charge. This degree of charge build up depends on the metal and represents the work required to separate electrons from the ions. This is known as the electro neutrality principle

Similarly, if a copper strip is placed in an aquaous Copper(II)Sulfate solution the copper will also lose ions. These reactions are often written as Cu | Cu⁺² this is the half-cell reaction.

The tendancy for Zinc to lose ions is greater than that of Copper. When the two cells are joined together (using a copper wire to connect the electrodes and porous barrier that allows the ions to pass known as a salt-bridge connect the elecrolytes, the build up of electrons on the zinc will flow to through the wire onto the copper.

The copper ions in the electrolyte gain electrons and become copper atoms.

Thus the reaction can be written,

Zn | Zn²⁺ | | Cu²⁺ | Cu