Mathcad Assessed Worksheet

PH15720 MathCAD Assessed Worksheet

This assignment forms the marked portion of the mathCAD section of your PH15720 module.

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

The questions in section A 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. Questions in Section B 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. Where the reference tables give the specific gravity of a material, you may take this to be in gm/cm3.

Your completed worksheet should be emailed as an attachment to before 17:00 on Tues 2nd December 2008. 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.

Part A: Portfolio Examples.

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)

Calculate the volume and surface area of a sphere of radius 3 cm. The formulae you will need are:

/ and /

The specific gravity of gold (Gold) is 19.32 gm/cm3. This can be found in the resource centre.

Calculate the mass of the 3 cm radius gold sphere. Display your answer in kg and also in lb.

Example 1 from example sheet 3. (Motion under constant acceleration)

The equations of motion for bodies moving under constant acceleration are as follows:

Where the terms have the following meanings:

s / Distance travelled
u / Initial Velocity
v / Final Velocity
a / Acceleration
t / Time Elapsed

These equations will need to be translated to make them specific to the following problem.

According to manufacturers data a Ford RS Cosworth should accelerate from 0 to 60mph in 6.2 sec. Using the formulae above calculate the following:

The final velocity in m/s (vRS60)

The average acceleration (aRS60) over this period in [m/s2]

The distance travelled (sRS60) whilst accelerating [in m]

The mass of the car, complete with driver and fuel is approximately 1300kg.
Calculate the kinetic energy of the car (keCar) at the end of the acceleration period [J]

Use the formula:
The brakes are applied and the car stops in 1.8 sec.
Calculate the average power dissipated in the brakes during braking [W]

Example sheet 5 (Current against voltage plot & resistor calculation)

Various voltages are applied across the resistor and the resultant current measured.

The Applied voltage and measured current and shown below:

(Note that these values are different from those in the lecture slide)

Vapplied / Imeasured
(Volts) / (ma)
0 / 0
0.5 / 0.465
1 / 0.923
1.5 / 1.387
2 / 1.869
2.5 / 2.337
3 / 2.811
3.5 / 3.287
4 / 3.747
4.5 / 4.177

Create an input table to hold the values taken from the experiment.
Separate the readings into two vectors, one to hold the applied voltages and the other to hold the measured currents. At the same time multiply the bare numbers by appropriate units.
Insert an X-Y plot and drag it to a reasonable size.

In the X-Axis placeholder type the name of the vector holding the applied voltages.
In the Y-Axis placeholder, type the name of the vector holding the measured currents.
Since the graph is of a set of discrete readings, rather than a continuous curve, format the trace to plot points show by circles.

Use the slope function to calculate the slope of the best straight line fit through the points.
This slope is the slope of IMeasured vs VApplied, so the resistance is given by its reciprocal. Calculate and display the resistance

Create a function, ITheory(vv), which gives the theoretical current for an applied voltage vv.
Having created the function, test it at a couple of applied voltages and compare the results with the experimental data.
Plot the theoretical and experimental data on the same graph.

Part B: Experimental Data Handling

Problem B1 – Volume and Surface Area.

As part of a high temperature physics experiment, it is proposed to levitate a sphere of graphite in a gas jet and heat it up by means of a powerful laser. If the sphere is 1.9mm in diameter calculate its volume, surface area and mass.

You will need to find the density (or specific gravity) of graphite from the reference tables within the MathCAD help system.

The door of a cobalt irradiation facility is a cylindrical plug of lead, 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 385mm in diameter, the inner face is 270mm in diameter and the door is 200mm thick.

The specific gravity (density) of lead is given in the reference tables within mathCAD under the heading ‘Properties of Metals’.

/ The volume of the door piece may be calculated by either calculating the volume of a cone complete with ‘point’ and then subtracting the volume of the ‘point’, or by knowing that such a shape is called a “Frustum of Right Circular Cone’.
The reference tables may help.

Problem B2 – Expansion coefficient of air column

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

The temperatures are recorded in K

Temp
(K) / Length of column
(cm)
293 / 7.1
302 / 7.3
311 / 7.5
323 / 7.8
332 / 8
341 / 8.2
357 / 8.6
369 / 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 () and the length of the column l0, at zero K temperature.

The length and temperature are connected by the following formula:

which canbe re-arrangedto give:

You will need to determine l0 first from the intercept and then divide the slope of the graph by this in order to get a value for .

Create a function lcolumn(t)giving the predicted length of the column at any temperature, t.

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.

Problem B3 – Moore’s Law

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 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.

1971 / 2,250
1972 / 2,500
1974 / 5,000
1978 / 29,000
1982 / 120,000
1985 / 275,000
1989 / 1,180,000
1993 / 3,100,000
1997 / 7,500,000
1999 / 24,000,000
2000 / 42,000,000

Create a data table and populate it with the data from the above table. Extract two appropriately named vectors from the data.
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.

Note:

In a relationship defined by Y= Aektthe ‘doubling time’ is defined as ln(2)/k