## Wednesday, March 16, 2011

### PARALLEL CIRCUITS

Not all the current goes through every load. There is at least one fork or branch in the circuit. In the diagram below, the current, ITOT, that leaves the source is split. Some current, I1, goes through R1 and the rest, I2
goes through R2 . The sum of the currents I1 and I2 equals the total current ITOT.
In parallel circuits current is split at least one junction.

Unlike the series circuit, adding more branches reduces resistance and increases current. This is easy to understand: Suppose a large city developed on both banks of a river and there was only one bridge across the river. If the bridge was narrow, a traffic jam would probably develop at least during rush hour. One way to reduce the resistance to traffic flow would be to build another bridge. With more bridges across the river, more traffic flows. With more branches in the circuit more current can flow, and the less resistance there is to current flow.

The voltage supplied to each branch is the same as the voltage supplied to the source. A branch with low resistance carries more current than a branch with high resistance.

In summary, for parallel circuits,
ITOT = I1 + I2 + . . . .
VTOT = V1 = V2 = . . . .
1/(REFF) = 1/(R1) + 1/(R2) + . . .

PROBLEMS

4. In the diagram of a parallel circuit above, suppose R1 and R2 were light bulbs. If the light bulb at R2 burned out, what would happen to the brightness of the light bulb at R1?
5. Two resistors, 2.0 ohm and 3.0 ohm, are connected in parallel with a 12 V battery. Calculate: (a) the effective resistance of the circuit; (b) the current leaving the battery; (c) the current through each resistor; (d) the voltage drop across each resistor.
6. In the following diagram the three resistances each represent identical light bulbs. Describe what happens to the brightness of the other light bulbs when one of them goes out.
A complex circuit consists of parallel loads in series with at least one other load.

7. Sketch a diagram showing a complete circuit involving only a dry cell, one wire, and a flashlight bulb.

### SERIES CIRCUITS

In series circuits, all current goes through every load; there are no forks or branches in the circuit. So, the current, I1, through resistor, R1, and the current, I2, through resistor R2 are the same and equal to the current, I, of the circuit.
In series circuits the same current flows through all circuit components.

Just like pinching two places in the same hose results in less flow then pinching in only one place, the resistances of resistors in series add to give the total resistance of the circuit.

In accordance with the Law of Conservation of energy, the voltage drops across each resistor (the energy used by each resistor) add up to the voltage (energy) supplied by the source.

In summary, for series circuits,
ITOT = I1 = I2 = . . . .
RTOT = R1 + R2 + . . . .
VTOT = V1 + V2 + . . . .

PROBLEMS

2. In the diagram of a series circuit above, suppose R1 and R2 were light bulbs. If the light bulb at R2 burned out, what would happen to the brightness of the light bulb at R1?
3. Two resistors, 2.0 ohm and 3.0 ohm, are connected in series with a 12 V battery. Calculate: (a) the total resistance of the circuit; (b) the current leaving the battery; (c) the current through each resistor; (d) the voltage drop across each resistor.

### OHM'S LAW

The simplest electric circuit contains a source of electric energy such as a dry cell or wall outlet, a load such as a light bulb or fan, and conductors such as wires to provide a path for electric current to flow. The resistor, a load that converts electric energy to heat, will be used in all diagrams to represent the load. A dry cell will be used to represent the energy source.

When water flows through a hose friction between the water and the impedes the flow. Pinching the hose further adds more friction and reduces the flow more. Water pressure is what is needed to keep the water moving. The more pressure, the more water flows, the more friction, the less water flow.

As current flows through the conductor, the atomic structure of the conductor provides resistance to current flow in much the same way a hose impedes water flow. The more energy the source provides, the more current flows. With more resistance, less current flows. Unlike a water hose, an electric circuit has to make a complete circle from the source through the load(s) and back to the source again or no current will flow.

Resistance, R, is measured in ohms; current, I, (the amount of charge that flows with time) is measured in amperes (A), and the energy provided per coulomb of charge provided by the source is measured in volts (V). All resistance will be attributed to the load(s); the resistance of the conductors and the internal resistance of the power source will be considered negligible.

The relationship between these quantities is given by Ohm's Law:
V = IR

PROBLEMS

1. A 12 V battery causes 2.0 A of current to flow through a light bulb. What is the resistance of the bulb?

## Tuesday, March 15, 2011

### Nucear Decay

Nuclear Fission

http://library.thinkquest.org/17940/texts/fission/fission.html

Nuclear Fusion

http://library.thinkquest.org/17940/texts/fission/fission.html

## Saturday, March 12, 2011

### Waves

1. A guitar string of length, L, is fixed at both ends. Which of the following wavelengths for standing waves is not possible on this string?
a. L/2 b. 2L/3 c. L d. 2L e. 4L

2. Pipe A is 30.0 cm long and is closed at one end, open at the other. Pipe B is open at both ends. How long will pipe B have to be to have the same fundamental frequency as pipe A?

3. Two speakers receive the same 256 Hz signal from an amplifier. When one speaker is placed directly behind the other, what is the smallest distance between them that produces destructive interference at any point front of them? (speed of sound = 342 m/s)

4. Signal m is 6.8 dB louder than signal w. What is the ratio of the sound intensity of signal m to signal w?

5. A rock is dropped from a cliff is heard striking the ground 3.4s later. If the speed of sound is 340 m/s, how high is the cliff?

6. Why is the loudness directly proportional to the logarithm of intensity?

7. The noise from a grinder in a factory is 32000 times more powerful than the noise from a dishwasher. By how many decibels is the factory noise greater than the dishwasher noise?

8. Pat stands between two high walls, at a point one-third the distance between the walls. Pat fires a starter pistol, and hears one echo one-tenth of a second after the first echo. If the speed of sound is 340 m/s, how far apart are the walls?

9. A loud sound is 90 dB. When the sound is reduced to 5% of its original intensity, what is the decibel level?

### Particle Accelerators

What is a particle accelerator and why do we use them?

Just after the Big Bang, the universe was a rapidly expanding ball of fundamental particles. As the universe expanded, it cooled and the particles decayed, changing into other fundamental particles. These particles then joined together and gradually formed the matter that we see around us today.

In particle accelerators we smash beams of particles together in head-on collisions that are energetic enough to turn the clock back to just after the Big Bang. The more energetic the collisions, the more likely we are to make fundamental particles appear again. Once we've produced fundamental particles we can study their behaviour to find out why the universe is made the way it is.
What does a particle accelerator look like?

The biggest particle accelerator in the world is at CERN, the centre for particle physics research, just outside Geneva in Switzerland.

Above ground, you wouldn’t know anything about it, but if you were to go 100m underground, you’d find yourself in a circular tunnel, about the size of a London underground tube tunnel. This is where the Large Hadron Collider (LHC), the world’s most powerful particle accelerator is being built.

The LHC tunnel runs for about the same distance as the London Underground Circle Line – 27km in a ring underneath the French/Swiss border. If you were inside the accelerator tunnel you would see a tube which runs continuously in either direction. This tube is the "beam pipe" - so-called because inside here, two beams of particles fly round the tunnel. The beams are accelerated to very high energies by magnets surrounding the beam pipe. These make sure that the two particle beams circulate in opposite directions without crashing into each other. When the beams of particles reach their final top energy, the magnets alter their path and bring them into collision at pre-determined points around the accelerator ring.

By this time the particle beams are travelling so close to the speed of light that they collide forty million times a second. Inside each collision we have a snapshot of the fundamental particles that last existed billionths of a second after the Big Bang. Now all we have to do is build gigantic particle detectors at each collision point to try and work out exactl

### Particle Physics

Particle physics – science doesn’t get much bigger or more exciting than this.

It involves the biggest, most complicated experiments in the history of science, with the fastest computers, the coldest temperatures and the strongest magnets on Earth.

Particle physics re-creates the universe just after the Big Bang and hopes to answer the questions that humans have been asking for eternity; “Where do we come from?” “What are we made of?”

So what exactly is particle physics? Find out, from atoms and particles to accelerators and detectors in our introductory pages.

You can link direct to the biggest particle physics experiments around the world and visit our news section to see what goes on in particle physics in the UK and worldwide.

Atoms and Particles
So what is particle physics?

Particle physics is a journey into the heart of matter.

Everything in the universe, from stars and planets, to you and the chair that you're sitting on, is made from the same basic building blocks - particles of matter.
Some particles were last seen only billionths of a second after the Big Bang. Others form most of the matter around us today.

Particle physics studies these very small building block particles and works out how they interact to make the universe look and behave the way it does.

We see that atoms consist of a nucleus, ten thousand times smaller than the atom, surrounded by a cloud of electrons. The nucleus is a collection of particles called protons and neutrons. And inside protons and neutrons we find particles called quarks. Quarks are so small that we haven't yet been able to measure how big they are - we just know that they are at least ten thousand times smaller than the nucleus. They are so small that we treat them like mathematical pinpoints in our theories.

Zooming down in scale from a person to a fundamental particle like a quark or an electron is like shrinking the diameter of the whole earth to the size of a 5p coin. And then shrinking the 5p by the same amount again. This is what we mean by really small.
How do we do particle physics?

We recreate the conditions just after the Big Bang, when particles roamed freely through the Universe. We do this with powerful particle accelerators which accelerate particles close to the speed of light and smash them together. Particle physicists then look at what happens in the high energy collisions.

Particle physics is a bit like trying to find out how a watch works by bashing together two very expensive Swiss watches and then learning to rebuild them from all the bits of glass, cogs and springs. In place of Swiss watches we use particles so small that you could fit about ten thousand million of them across a watch face, and despite their tiny size, the collisions between these particles have as much energy as a large aeroplane taking off!

### Thermal Energy

1. When the temperature inside a particular house is 24 °C and the temperature outside is -10 °C, 28100 J of heat leaks out of the house.. What increase in the entropy of the universe does this heat loss produce?

2. Concrete slabs 14 m long (20ºC) are subjected to temperature variations from -30ºC to +50 ºC. How wide should the expansion cracks be (at 20 ºC)?

3. A car is consuming 10 kg of gasoline per hour with an efficiency of 25%. If gasoline releases 46,000 J/gram of heat, what is the average horsepower output of the engine? (1 hp = 746 W).

4. A vertical cylinder containing a gas is closed at the bottom and sealed by a movable frictionless piston at the top end. A block is placed on the piston. The combined mass of the block and piston is 102 kg. When 2140 J is added to the system, the internal energy of the gas increases by 1580 J. What distance does the block rise?

5. A house is heated to a constant 25 oC while the outside temperature is -30 oC. What is the rate of heat loss through a closed sealed single-pane window having an area=6 m2, thickness=1.75 cm, and thermal conductivity=0.80 J/(s*m*C). If the glass was replaced with styrofoam (thermal conductivity =0.010 J/(s*m*C)), how much less heat would be lost in one day?

6. A cylinder contains 0.250 mol of ideal gas at 27.0 C. A constant pressure of 1.00 atm is maintained by a frictionless piston. If the gas is heated to 127.0 C:

a. How much work is done by the gas in this process?

b.On what is this work done?

c. What is the change in internal energy of the gas?

d. How much heat was supplied to the gas?

7. The air outside a 30 cm. thick wall (area=15 m2) is 0 degrees Celsius and and 22.3 degrees celsius on the other side. If the thermal conductivity of the wall is .8 how much heat is conducted by the wall in 1 hour?

8. What is the R value for a 1.4 cm thick layer of a.) glass (Kg. =.80) b.) plywood? (Kp=.085 W/K *m)

9. By how much has the internal energy of a 2.2 Kg. block of ice change when it melts to water at 0 degree celsius? Neglect the small change in volume.

10. Find the change in internal energy of 2.3 mol of argon gas (number of freedom, i = 3) and the work it does when it is heated from -45 degrees to 90 degrees celsius at

a.) constant volume

b.) constant pressure.

11. A body at 37 degrees Celsius is emitting energy at the rate of approximately 105 W. At what rate is the entropy changing?

12. Steam is injected into an engine at 600 degrees Celsius and exhausts at 70 degrees Celsius What is the highest efficiency possible of this engine?

13. A 100 W light bulb is left on for 30 days. If electricity is generated with 30% efficiency, how much energy is released to the environment?

14. An engine with a Carnot efficiency of 20 percent operates between a high temperature T1 and a low temperature T2 = 47 0C. What is the high temperature?

15. A glass sphere (10 cm radius) is heated from 20ºC to 100ºC. What is its percent increase in volume?

16. A 0.519 g lead pellet traveling at 118 m/s is stopped by a boulder. Neglecting any heat lost by the pellet, what is the temperature change of the pellet? The specific heat of lead is 0.0305 kcal/kg*ºC.

17. A brass ring with an inside diameter 17 cm at 56 ºC is heated, slipped over an aluminum rod with an outside diameter 17.01 cm at 56 ºC and allowed to cool. At what temperature may this combination be separated? (coefficients of linear expansion: brass = 1.9X10-5 ºC-1 ; aluminum = 2.4X10-5 ºC-1)

18. A layer of ice is 1.012 m wide, 1.505 m long and 7.622 mm thick. The ice, originally at –1.000 °C, receives solar radiation at 300 W / m2, and is converted to liquid water at 5.000 °C How much time does this process take?

19. At standard pressure, what would the temperature of water molecules be if they had a root mean square (rms) velocity of 5.87 m/s?

20. A particular alloy has a melting point of 1298 K and a tensile strength of 2.026 x 105 kPa. It is used to construct a 50.00L tank that contains 4.000 kg of helium at room temperature. If it is slowly heated, will it melt first or explode?

21. A vertical cylinder with an inside diameter of 121.0mm and a 88.3g piston on top contains 1.000 liter of helium gas. While 0.0900g of hydrogen gas are injected into the cylinder, the cylinder and its contents maintain a temperature of 25.00 Celsius and a pressure of 1.000atm. What is the maximum distance the piston will travel? Why will it not travel this far?

22. If a 150-lb person lowers their center of mass 0.5 m by squatting to pick up a penny, and the cost of a 300-(food)calorie donut is \$1, is it worth the effort to pick up a penny?

23. An 87g glass containing 214g of water, and the surrounding air, are at 5.0 ºC. What will be the final temperature of the glass-water system after 7.0g of water condenses onto the glass, and if there is negligible heat exchange between the system and the surroundings?

24. The timing of a clock is controlled by a brass pendulum. The pendulum has a period of 0.5520s at 20ºC. How long will the clock take to loose one minute at 35ºC?

25. After 2.0 kg of mercury gained 2.52 X 104 J of heat energy, its final temperature was 130 ºC. What was its initial temperature?

26. A Carnot refrigerator cools 5.00 kg of water at 20.0ºC to ice at -15.0ºC. The room temperature is 25.0ºC.
a. How much heat must be removed from the water?
b. How much work is put into the refrigerator?
c. What is the coefficient of performance of the refrigerator?
heat capacities: water 4.186 kJ/kg*K ice 2.05 kJ/kg*K
latent heat water 333.5 kJ/kg

27. The density of an ideal gas at 0ºC and atmospheric pressure is 0 = 0.179 kg/m3. What density would the gas have if temperature is then raised to 103ºC, at constant pressure?

28. A sealed window is made of two 0.50 cm thick glass panes and a 1.0 cm thick layer of air in between. Determine the rate of energy transfer through 1.5 m2 of the window when the surface temperature inside is 20.5 ºC outside is 0.0 ºC.

29. A volume of 2.2 m3 of air at 1.2 atm and 323ºC ("state 1") is subjected to the following sequence:
(i) isothermal compression from state 1 through a volumetric compression ratio of 45 (rv) to state 2
(ii) isobaric expansion from state 2 back to the initial volume thus reaching state 3
(iii) isochoric cooling from state 3 back to the original pressure to return to state 1.

For this sequence of processes, sketch a fully annotated p-V diagram & determine:
(i) the mass of air present
(ii) the maximum pressure in the cycle
(iii) the maximum temperature in the cycle
(iv) the total heat transfer in the isobaric expansion
(v) the net work done in the cycle.

Assume for air: R = 0.287 kJ/kg K
Cp = 1.005 kJ/kg K.

30. How long it will take a 350 W immersion heater to heat 250 mL of water from 20 ºC to 50 ºC?

31. What will be the final temperature of a system consisting of a 150-g aluminum cup containing 820 g of water at 12.0º and a 270-g block of copper at 300ºC?

32. A laborer does 1.30*105 J of work and losses 0.110 kg of water due to perspiration. What is the laborer's change in internal energy? Latent heat of evaporation of water is 2.42*106 J/kg.

33. A plant generates 1.3 GW of electricity while operating at 79% of its maximum theoretical (Carnot) efficiency between temperatures of 660ºC and 370ºC. How much waste heat is discharged per hour?

34. 1.0 kg of water at 40ºC is mixed with 1.0 kg of ice at -20ºC in a thermally isolated container. How much ice remains when thermal equilibrium is reached?

35. For an isolated system, how many 30.0 g ice cubes (originally at 0ºC) are required to cool 200 liters of water from 25ºC to 16ºC? The density of water is 1000 kg/m3, the specific heat of water is 1.0 cal/gºC, the specific heat of ice is 0.5 cal/gºC, and the latent heat of fusion of water is 80 cal/g.

36. How much energy is required to raise the temperature of 5 kilograms of coal from 20ºC to 220ºC?

37. A hole in a steel plate has a 0.99970cm diameter at 300ºC. To what temperature must the plate be heated for the hole to have a diameter of 1.00000 cm?

38. What mass of storage rock cools from 65 oC to 22 oC while losing 5 x107 cal of heat? (Specific heat of rocks is 0.21 cal/g-oC)

## Sunday, March 6, 2011

EXAMPLE 1

The radioactivity of milk in one sample was 1750 Bq/L due to iodine-131 with half-life 8.04 days. For comparison, find the activity of milk due to potassium. Assume that one liter of milk contains 1.60 g of potassium, of which 0.0117% is the isotope 40K with half-life 1.28X109 yr.
Calculation of Activity

A = [(ln 2)/T]

where ln 2 = 0.693, and T is the half-life in seconds.

One kilogram of a pure radioactive isotope with half-life T[sec] has activity A[Bq/kg]

The unit of activity is Becquerel (1 Bq = 1 decay/sec)

T = (1.28 x 109 yr)( 31,557,600 s/y) = 4.039 x 1016 s

A = [0.693/4.039 x 1016][ 6.0221415×1026 / 40] = 2.583 ×108 Bq/kg

A = [2.583 ×108 Bq/kg][0.00160 * 0.0117/100 kg/L] = 48.35 Bq/L

## Thursday, March 3, 2011

### Ocillations-Q's

Q1) Calculate the period and frequency of an oscillation that has an angular frequency of 26 rads-1.

Q2) A cosinusoidal oscillation has a maximum amplitude of 3 and an angular frequency of 3 rads-1. What is the amplitude at a time of 20 s?

Q3) A harmonic wave B has a phase difference of -3π/2 with respect to a harmonic wave A. Sketch and label the two waves.

### Ocillations

Oscillations occur when a system is disturbed from a position of stable equilibrium. This displacement from equilibrium changes periodically over time. Thus, Oscillations are said to be periodic, and display periodic motion. Oscillations are very common in everyday life with familiar examples being the motion of a clock pendulum or the vibrations of strings on musical instruments. Oscillations are also important in many mechanical systems in the real world such as a car suspension. It is thus very important to be able to study and understand these mechanical systems in order to control them in critical situations.

Notice that for a system to be oscillating, the shape of the displacement - time graph does not matter. The only Property that matters is that the motion is periodic.

Basic properties of Oscillating Systems

It is important for us to understand the basic properties of oscillating systems if we are going to be able to understand the system as a whole. The first of these properties we must understand is the Amplitude of the oscillation. The amplitude of the oscillation is the parameter that varies with time and this resides on the y-axis of the oscillation graphs. In figure 1, the amplitude of the oscillation is the displacement of the object from its equilibrium position - however this is not always the case. In other systems, such as electric fields, the amplitude of the oscillation is the intensity of the electric field as it is the intensity that varies with time.

Another important property of an oscillation system is the Time Period (T) of the oscillation. The time period of the oscillation is simply the time taken for the oscillation to repeat itself. That is, it is the time between successive oscillations of the system (see figure 2). The other basic property of an oscillating system is the frequency, which is closely related to the time period. As we know, one complete oscillation of the system is defined by the time period, T and is known as 1 cycle. The frequency of the oscillating system is simply the amount of cycles that happen in 1 second. So,
Formula

The units of frequency are cycles per second which are given the name Hertz (Hz).

Further Properties of Oscillating Systems

Angular Frequency

The Angular Frequency of a system is the rotational analogue to frequency. It is given the symbol ω and is measured in radians per second (rads-1). It is defined by the equation
Formula ω = 2#/T

but, f = 1/T

and so is related to frequency by ω = 2#f

Phase

The Phase of an oscillation is the amount the oscillation lags behind, or leads in front of a reference oscillation. For example, take a sine oscillation of maximum amplitude, A, and angular frequency, ω, and also a cosine oscillation of maximum amplitude, A, and angular frequency, ω .

Now, we can take the sine wave to be our reference oscillation. It can be seen from the diagram that the cosine wave lags behind the sine wave by π/2 (1/4 of a wavelength). So, we can say that the two waves are out of phase by π/2 or that there is a phase difference of π/2. Oscillations can have phase differences of any multiple of π. However, if they have a phase difference of either 0 or 2π they are said to be in phase.

Harmonic Oscillations

Harmonic oscillations are just oscillations that are made up of sine and cosine varying waves. They make up the largest group of oscillations that exist. Any oscillation that varies with a sine or cosine function, or both, is said to be a harmonic oscillator. For a harmonic cosine oscillator, with maximum amplitude, A, and angular frequency, ω, the amplitude at anytime is given by y= A cos ωt. Similarly, for a harmonic sine oscillator, with maximum amplitude, A, and angular frequency, ω, the amplitude at anytime is given by y= A sin ωt.