This assignment forms the marked portion of the mathCAD section of your PH15010 module.

Create a mathCAD worksheet to hold the answers to all of the questions.

Some of the questions are ones that you should have already solved as part of the weekly worksheets, copy and paste the answers for these from the files you already have. Other questions will require starting from scratch.

All formulae and numerical constants required to answer the questions are either contained within this sheet or may be found in the mathCAD resource center.

Your completed worksheet should be emailed as an attachment
to dpl@aber.ac.uk before 23:59 on Friday 13^{th}
December 2002. If you have difficulty sending files as attachments, please
contact me before that date.

Marks will be given for correctness of answers, proper use of mathCAD facilities, appropriate comments and explanations, layout of the sheet and style.

Copy and paste the following sections from the files you have created whilst working through the course worksheets.

- Example 3 from example sheet 2. (More volume and surface area calculations)
- Example 1 from example sheet 3. (Motion under constant acceleration)
- Example sheet 5 (Current against voltage plot & resistor calculation)
- Example sheet 7 page 3 (Vec3DA…)
- Example sheet 7 page 7 (Matrix solutions to simultaneous equations [all 3])

__Problem 1 – Volume and Surface Area.__

a)

As part of a high temperature physics experiment, it is proposed to levitate a sphere of graphite in an air jet and heat it up by means of a powerful laser. If the sphere is 2mm in diameter calculate its volume, surface area and mass.

b)

The door of a cobalt irradiation facility is a cylindrical plug, looking much like a cone with its point cut off. When the cobalt source is in use it is swung into place protecting users from harmful radiation.

The door is shown below, calculate its mass. The outer face of the door is 380mm in diameter, the inner face is 270mm in diameter and the door is 200mm thick.

You may assume that the specific gravity of water is 1.00
gm/cm^{3}

The following table gives the length (in cm) of a column of air a different temperatures.

The temperatures are recorded in K above 0C

Temp Above 0C (K) |
Length of column (cm) |

23 |
7.1 |

32 |
7.3 |

41 |
7.5 |

53 |
7.8 |

62 |
8 |

71 |
8.2 |

87 |
8.6 |

99 |
8.9 |

Enter the readings as an input table and then create from it two vectors with suitable names and units to hold the sets of readings.

Plot the values of length obtained against temperature on a graph. Format these as points.

Calculate the coefficient of expansion (a) and the length of the column l_{0},
given that the length and temperature are connected by the following formula:

_{}

You may need to re-arrange this formula in order to use it.

Create a function giving the predicted length of the column at any temperature.

Plot the function of predicted lengths on another graph together with the experimental points.

The accuracy of the ruler for measuring the length of the column is ±0.1cm. Add error bars to the graph.

In 1965 Gordon Moore, the founder of Intel, proposed that the complexity and component count of silicon integrated circuits would double every 18 months. This prediction has turned out to be startlingly accurate and has driven the electronic revolution we see around us.

The following data file is taken from Intel’s web site and contains two columns of data. The first column has the year of introduction of various processors and the second has the number of transistors in each of these processors.

http://users.aber.ac.uk/dpl/ph15010/handouts/Transistors.txt

Copy the file into your own filestore.

Create a file read component to read in the data file and split it into two appropriately named vectors.

Create a plot showing the number of transistors on a chip over the years 1970 to 2000. Use a logarithmic scale to show how this approximates to a straight line.

By taking logarithms and performing regression analysis, show how close to the target doubling time of 18 months Intel’s engineers were able to achieve over the 3 decades from 1970 to 2000.

Create a function Moore(y) which will predict the number of transistors on a chip for any given year.

Create a plot showing how this function compares with the experimental data.