Reference no: EM133962206
Engineering Mathematics Assignment - Mathematical Methods and Statistical Techniques
Vocational Scenario or Context You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. She has asked you to undertake a series of such evaluations. Get reliable and affordable assignment help today!
Task 1
The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula;
P = V2/R
Since you are new to the company your new Line Manager is unsure of your capabilities, and has asked you to use the dimensions of P and V to determine the dimensions of R.
A guitar string, made by your Musical Instruments division, has mass (m), length (??) and tension (F). It is proposed by one of your junior colleagues that a formula for the period of vibration (t) of the string might be;
t = 2Π√(m3l/F)
Use dimensional analysis to show your colleague that this formula is incorrect.
An analogue-to-digital converter (ADC), manufactured by your Signals division, takes 20 voltage samples of a ramp waveform, measured in mV, as follows... 2, 4, 6, 8, 10 ...40
Your Test colleague has asked you to assist by using a formula to calculate the sum of these 20 voltage samples.
A digital chip, made by your Microelectronics division, counts continuously in the sequence: 1024, 2048, 4096, 8192, ...You have been asked to use a formula to calculate the 9th count of the chip.
A series electrical circuit which you are testing features a capacitor (C) charging via a resistor (R) and a DC supply voltage (Vs). The voltage across the capacitor (Vc) may be described by the equation...
where t represents time. vc = vs(1 - e-t/RC)
Assuming that Vc is 1V after a time of 4 seconds, determine the approximate value of the capacitor.
Task 2
Two of the six bolts exceed the diameter.
More than two of the six bolts exceed the diameter.
Your components division manufactures capacitors, and the mean capacitance of 400 capacitors you have selected is 100µF, with a standard deviation of 7µF. If the capacitances are normally distributed, determine the number of capacitors likely to have values between 90µF and 110µF.
Note: Use the z-table given in Appendix A when answering part c.
A colleague, who is a Fuels engineer, is testing the effects of an experimental fuel additive for petrol engines which your company is developing. She adds the same sample amount of additive to 100 full petrol tanks for the same model of car and records the number of miles per gallon (mpg) for each car after being driven around a test track at a constant speed, until the fuel runs out. She knows that such testing undertaken without the additive produces a mean mpg figure of 44. Collecting results with the additive, she notices that the mean mpg figure is 48 with a sample standard deviation of 13 mpg.
By interpreting the results of the testing, show whether you agree, or not, with her hypothesis that the fuel additive has influenced the number of miles per gallon for the cars.
Draw by hand, or use suitable software, to produce a graphic, suitable for a non-technical company executive, which represents the results of your analysis.