Some Questions, Some Problems for Under Graduate Students in Some Branches of Engineering

 

Some Questions, Some Problems for Under Graduate Students in Some Branches of Engineering

This post is only for current or to be Civil Engineering / Mechanical Engineering / Aerospace Engineering professionals. They are definitely not for those who use their degree in engineering merely as a box to be ticked in their applications for an IT job.

The questions, however, are not limited to this branch of engineering; indeed, if one were to explore the powers of critical thinking of students, then such strait jacketing is most inappropriate. Critical thinking must be accompanied by fleet-footedness of the brain–jump here, there, everywhere in search of the answers or solutions in everything learned in high school onwards.

In my limited experience in teaching I found that a majority of the students leave whatever they have learned in high school at the gates of the school. There is a need to put a finger on why students do this. My idea is that the excessive pressures of the examinations drain any enthusiasm/love students may have for what they learn. The goal makes them forget the path they traversed. For those students who sit for competitive examinations for engineering UG entrance, what is learned lasts only till those examinations are over, and their fate is sealed–they are in or out. Fortunately for me, it was not so for me, five decades ago.

It is no more than about 10% of students in a class who respond to any question that has any bearing on their high school subjects. This is pathetic. Of course, they do not forget what they learned in elementary school–what is two plus two, for example. Then why the change in the students’ attitude about high school topics? Anyone cares to respond?

With that introduction, I now lay out the smorgasbord of questions. Dig in, if you care to.

1.      If while standing, one faces a mirror with her right arm akimbo, the image in the mirror has the left arm akimbo. This is the well known effect of “lateral inversion”. Of course, with respect to the head and feet, such an inversion does not take place. Explain the difference.

2.      Two reservoirs are connected by a 10 km long pipe, through a pump. The water levels in the reservoirs have an elevation difference of 15 m when the pump motors are not running and all the valves are open. Find out the minimum power in terms of head (in meters of water column) the pump needs to begin pumping water (even at an infinitesimally small rate) from the lower to the upper reservoir.

3.      If two points ‘A’ and ‘B’ are given and also only a compass (with a pencil attached), would you be able to locate point ‘C’ such that all the three points lie in a straight line and distances, ‘AB’ and ‘BC’ are equal. Explain how you would do it if you can, and explain the logic inherent in the process.

4.      Train ‘A’ runs from Chennai Egmore to Trichy at 45 kmph, uniform speed from start to end, and a bird perched on the tip of the engine starts to fly at the same time along the railway line at 58 kmph. Exactly one hour later, another train starts from Trichy Junction towards Chennai Egmore on the same track–again, with uniform speed from start to end– at 52 kmph. The distance, along the railway line between the two stations is 349.2 km. The bird flies to-and-fro repeatedly between the two trains at 58 kmph throughout its flying till the engines clash and the bird dies. How long did the bird fly in this journey before meeting death?

5.      You are rowing a boat upstream. The river flows at 5 kmph. Your speed against the current is 7.083 kmph, under your maximum effort. You lose your hat on the water; yet, only after forty five minutes you realize it is missing. How long does it take for you to row back (at your maximum effort) to reach your floating hat?

6.      You look at the licence plate number of a car that reads (only numerals) 9845. Out of fancy you reverse it to get 5489. You divide the four digit number into two, two-digit numbers, like 9845 is 98 and 45. Likewise, 5489 gives 54 and 89. Take the pair of numbers from the first four digit number, and subtract the latter from the former. You get 45 – 98 = – 53. For the altered four digit number, the same operation gives, 89 – 54 = 35. Find the permutation of the four digits such a way that you get ‘0’ in both the cases. You are to work out the solution through high school algebra, and not by trial and error.

7.       

8	1	6
3	5	7
4	9	2

 

The above is the almost trivial Magic Square you have perhaps been teased about by your schoolmates. You can tease them back, if you can figure out the logic behind the nine numbers aligning themselves as they have done here. That is the question.

8.      Two patterns, marked ‘L’ and ‘R’, are shown. The task is to trace the patterns on the following conditions: i. Pencil on paper (or a stylus on the screen, or any such facility) shall not lose contact with the surface on which the pattern is drawn; ii. No line shall be re-traced, that is, no going over a traced line again.

The true puzzle comes now. Are you able to successfully draw both the patterns? At least one? If either one of them cannot be drawn give a logical reason for this inability. Check that this reason is invalid for the pattern that you could draw.

9.      Give a physical reason for the difference between γ_sub and γ_sat of a soil. You shall not invoke any equations.

10.  While we say Load-Deflection diagrams or Stress-Strain curves, giving prominence to the load or stress as the case maybe, we ALWAYS draw deflection on the horizontal axis, which per convention is the independent parameter and the vertical axis is the dependent. Should we change it? If no, state why not?

11.  A beaker is filled to the rim with an ice cube floating in it. The part of the ice cube is above the level of water. Over time, the ice cube melts. Will the melt water overflow the beaker?

12.  If in trying to find the focal length of a bi-convex lens using the optical bench, would we get an image of the object (say a candle) if we blocked a small circular area around the bench axis on the lens? Realize that when we draw the schematics of the experiment, we use a ray parallel to the axis of the lens, and another one through the centre point of the lens. This ray will be blocked.

13.  Explain what happens physically within a soil mass when quick sand condition occurs in it.

14.  How can we determine whether a given truss is internally statically determinate or not without using any equations? Whatever procedure you may use, explain why it is valid.

15.  If you are sitting in the front passenger seat of a car, and the driver takes a sharp right turn (small radius turn at high speed), will you be pushed towards the door of the car or towards the inside? Explain your answer.

16.  An explorer starts off from a point, treks 20 km south, takes a left turn and treks for another 20 km east. At the end of this 40 km trek so far, he takes some rest and starts off on another leg, due north, for 20 km.  He thinks he needs to take another 40 km trek to reach his starting point where he had left his camping stuff. Yet, at the end of the trek till this point (three legs), he sees his camping equipment where he left off. How could this have been?

I have made it a point to ask at least three or four questions out of the above in every class I have taught, as relevant to the subject taught. About 10% of the students evince keen interest, and get this, they are very satisfied when they get the answer and only a little bit less so, even when I give them the answer. This is a moment of great happiness to this erstwhile teacher!

Raghuram Ekambaram