Math-LO4
Posted: Wed Mar 09, 2022 9:20 am
Math-LO4
Scenario: As an electrical and electronic engineer you always encounter equations, problems and data that need to be analysed in order to understand the results in a practical way. You are working as an engineer and you have completed many tasks in a job that you were asked to carry out. A report must be prepared for you senior in order to analyse the results that you have obtained in your experiments. You must analyse the results carefully using methodologies that you have learnt in engineering maths. Your report must be clear and presented in a professional way as this will have a major impact on how well you impress your superiors and obtain the promotion that you have been working for a long time. All the tasks must be finalised on time and the analysis must be thorough and convincing.
LO4: Examine how differential and integral calculus can be used to solve engineering problems. 1 R1 R 1 dR1 + a- If two resistors with resistances R1 and R2 are connected in parallel as shown in the figure below, their electrical behaviour is equivalent to a resistor of resistance R such that R2 If R1 changes with time at a rate r = and R2 is constant, express the rate of change of the resistance of R in terms of R1 and R2. b- If an object with a speed v giving by the equation v (t) = 1 + 4t + 3 t2 where t is the time taken to move per minute, what is the travelled distance during the third minute? dR dt dR1 dt dt C- A wire of mild steel has a radius of 0.5 mm and a length of 3 m. If the young modulus Y = 2.1 x 1011 N/m3 and the wire is stretched by a force of 40 N determine: 1- The longitudinal stress 2- The longitudinal strain 3- The elongation d- If the switch 'S' is at position '1' sufficiently long enough before it is moved to position 2 and after this it is kept in position 2 as shown in the figure below determine: 1- Values of the instantaneous inductor voltage vi and the instantaneous current through the inductor iz 2- Values of the inductor voltage v, and the current through the inductor i just after the switch changes 3- The rate of change of i, at t = 0
S(switch) 1092 I 1 10A t=0 10Ω 10Ω mor L4H = e- If the equation y = x3 – 6 x2 + 9x Find the stationary points of the curve and determine whether these points are maxima or minima and prove this.
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LO4: Examine how differential and integral calculus can be used to solve engineering problems. 1 R1 R 1 dR1 + a- If two resistors with resistances R1 and R2 are connected in parallel as shown in the figure below, their electrical behaviour is equivalent to a resistor of resistance R such that R2 If R1 changes with time at a rate r = and R2 is constant, express the rate of change of the resistance of R in terms of R1 and R2. b- If an object with a speed v giving by the equation v (t) = 1 + 4t + 3 t2 where t is the time taken to move per minute, what is the travelled distance during the third minute? dR dt dR1 dt dt C- A wire of mild steel has a radius of 0.5 mm and a length of 3 m. If the young modulus Y = 2.1 x 1011 N/m3 and the wire is stretched by a force of 40 N determine: 1- The longitudinal stress 2- The longitudinal strain 3- The elongation d- If the switch 'S' is at position '1' sufficiently long enough before it is moved to position 2 and after this it is kept in position 2 as shown in the figure below determine: 1- Values of the instantaneous inductor voltage vi and the instantaneous current through the inductor iz 2- Values of the inductor voltage v, and the current through the inductor i just after the switch changes 3- The rate of change of i, at t = 0
S(switch) 1092 I 1 10A t=0 10Ω 10Ω mor L4H = e- If the equation y = x3 – 6 x2 + 9x Find the stationary points of the curve and determine whether these points are maxima or minima and prove this.