QUESTION 1 (10 Marks) A negative temperature coefficient thermistor, RT, is used as part of a voltage divider, as shown in the figure. The resistance of the thermistor is given in the table and the fixed resistance, R1, is 500 ?. FILE: REVISION: PAGE OF DRAWN BY: TITLE METR3100 Voltage divider 1 1 Peter Jacobs Vout R1 RT 1 2 B1 Vzero Temperature (?C) RT (?) -20 3311 -15 2607 -10 2070 -5 1656 0 1335 5 1083 10 885 15 727 20 601 25 500 30 418 35 352 40 298 45 253 (a) If the battery supplies 5 V, plot the output voltage of the divider as a function of temperature. (b) Plot, also, the line of best fit given that the device is to be used as a domestic thermometer about the nominal temperature of 25?C. (c) Determine the maximum linearity error. (d) A microcontroller is to be used to digitize the output voltage from the divider with its built-in 12-bit analogue-to-digital converter. Assume that the 5 V battery used for the voltage divider also provides the reference voltage for the converter. At 25?C, what temperature change corresponds to 1 LSB of the analogue-to-digital converter. (e) What is the expected digital count for a temperature of 30?C. Page 2 of 5 Semester Two Final Examinations, 2017 ENGG7601 Experimental Design QUESTION 2 (10 Marks) In a school-room experiment, a cart rolls down an incline of slope ?, as shown in the figure. The goal of the experiment is to measure the acceleration, a, of the cart by timing the passage of the cart at the two photocells, each connected to a timer. If the cart has length l and takes time t1 to pass the first photocell, it’s speed there is v1 = l/t1. Assume that this average speed is effectively the instantaneous speed at the photocell. The speed at photocell 2 is determined the same way, to give v2 = l/t2. If the distance between the photocells is s, then the relation between the velocities is v 2 2 = v 2 1 + 2 a s Use this relation and the following data to determine the acceleration of the cart and the uncertainty in your estimate of acceleration. l = 5.00 ± 0.05 cm s = 100.0 ± 0.2 cm t1 = 0.054 ± 0.001 s t2 = 0.031 ± 0.001 s Identify which measurement contributed most to the uncertainty in the acceleration estimate. Page 3 of 5 Semester Two Final Examinations, 2017 ENGG7601 Experimental Design QUESTION 3 (20 Marks) A sacrificial buffer to stop a train at the end of a platform is designed in the form of a plastically deforming cylinder of 200 mm diameter, 1000 mm long, as shown in the figure below. It is designed to stop a train of 100 tonnes mass (105 kg) travelling at a speed of 2 m/s within a distance of 200 mm. The buffer is designed to give a uniform rate of deceleration. U,m/s Train, M1 x L Buffer The behaviour of the buffer under impact is believed to be characterised by the following variables: Quantity Symbol Units impact velocity U m/s elapsed time for train to stop after impact t s mass of impactor (train) M1 kg initial undeformed length of buffer L m yield stress of buffer material E Pa distance by which buffer is compressed x m deceleration of train (assumed constant) a m/s2 (a) Identify appropriate dimensionless parameters to study the problem. (b) A 100-to-1 scaled experiment is to be performed to validate the design. That is, the buffer in the scaled experiment will be geometrically identical to the full-size design, but a factor of 0.01 on linear dimensions. The experiment will be performed at the same impact speed (2 m/s) and using the same buffer material properties as for the full size product. Find the appropriate setting of the adjustable variables to give similarity with the full-scale design, with all dimensionless parameters being conserved. (c) What will the deceleration of the scaled model be? Note that it is assumed to be constant during buffer deformation. (d) What force will have to be transmitted through the buffer in the full scale design? (e) As a result of the experimental testing, it is decided that this force is too great to be transmitted directly to the platform and, in a modified design, the sacrificial buffer is to be mounted on an inertial mass M2, sitting on a gravel bed. See the following Page 4 of 5 Semester Two Final Examinations, 2017 ENGG7601 Experimental Design figure. The inertial mass slides on impact and a constant frictional force of F = µM2g is generated by the gravel bed, whilst the mass is in motion. Identify the new dimensionless parameters which must be considered. U,m/s Train, M1 x L Buffer Inertial Mass M2 x2 F (f) It is decided to do a full factorial experimental program on a scale model of the improved design with all factors fixed except for the impact velocity of the train, U, and the inertial mass, M2, which will each be allowed 3 levels of variation. How many treatment conditions will be needed? Sketch a table with a suitable testing sequence.