Prof. Dr. Abdurrahman Tanyolaç'ın Özgün Sınav Sorularına Örnekler:

 

·           The arms of a two-fluid manometer is attached to the bottom and upper parts of the pipe (at the same location) that brings Kızılırmak water to Ankara. The heavy fluid in manometer is mercury (ρ=13600 kg/m³) and light one is water (ρ =1000 kg/m³). Daily 300 000 m³ is pumped through the pipeline and while water flows no difference in the manometer arms is observed. If there is no flow, the difference is 15 cm. Calculate the average velocity of the water in the pipe in m/s when pumps are on.   

 

·         The project involves the simulation of a cockroach jumping pathway that accidentally dropped from the aspirator unit onto the center of a hot plate of a hamburger parlor. Due to hot plate temperature (220^oC) the bug jumps randomly anywhere being incapable of sensing the environment with its antenna. Being exposed to unusual temperature, the structure of its legs/feet limits the number of jumps. If it passes over the border of the hotplate then it survives with fried legs but if it cannot then it becomes a part of the food to be served!  You are expected to come up with a program which simulates the random track of the bug and determines whether it survives. Then the program applies the simulation to 1000 bugs to have statistical values of average survival percent and average escape time of the survivors. Refer to your textbook and other java sources for the use of randomize function of Java.

 

·           A guy once bought a flat in Eryaman-Ankara with a price of 30,000 USD in 1991 and sold it for 60,000 USD in the year 2008 (after 17 years). Meantime he got a constant net rent income of 200 USD per month, which he immediately deposited into a monthly savings account. Considering a constant annual interest rate of 4% (for monthly deposits, please have 1/12 of this value), deduce whether the guy made a fruitful investment or not using the present values of the year 2008.

·           A true observation. In some universities abroad (in less developed countries), instructors collect a special fee of 25 USD from each student taking the course. The instructors claim that there are really underpaid even below the poverty line i.e. the paycheck of a professor is 100 USD maximum while at least 500 USD per month is a must for making a living in that country. As a poor student you are expected to turn in this “fine” at the end of semester before the announcement of the final grades. If you do not pay then you fail from that course no matter how hard you work and how well you perform. However, if you pay, you get a straight “A” from the course regardless of your success in exams and attendance. Evaluate this case in terms of human survival, bribery, and professional ethics. Name the ethic codes violated, if any.

 

·           A couple, both professors, work at the university and can save together a fixed amount of 2000 TL per month. If there are 27 years for their retirement and annual interest rate is 7.95 % after tax, calculate the value of their savings at the time of retirement as of today. Is the total savings enough for a car and a house when they get old?  To find monthly interest rate, divide the annual value by 12.

 

·           A sweet and smart kindergarten girl ask you why the top of the mountains is colder than the seaside while the summit of the mountain is closer to the sun, which is really hot. Her very own experience taught her the fact that if one gets closer to the hot object it gets hotter (she touched the stove once!). Explain her the answer as the way she can understand.

 

·           The guys A and B are good old buddies and are fanatic drivers of Ford Focus Sedan manual gear (100 HP, gasoline engine). They both drive 10,000 kms per year but have different philosophies of renewing cars. The guy A buys the car, uses 2 years and sells it while buying a new one of the same kind with the idea that second hand selling price of a 2 year old car is still high. The guy B, buys the car, uses 8 full years then sells it and buys a new one with the idea that the car is tough to stand 8 years (or 80000 kms) without any major problem or cost and keeping it 8 years saves a lot of money. Annual cost of the car maintenance is constant up to 100,000 kms as the annual traffic insurance. After 3 years of exemption for a new car, one has to renew DMV check-up license every 2 years which costs 250 TL fixed for last 8 years. The guys A and B bought cars in the year 2000 and they came along to year 2008. Assuming a fixed interest rate of 8% per annum and taking the below new and second hand prices of the cars into account, deduce which guy is really saving money. (Hint: make all your calculations with respect to the year 2008).

·           In distinguished universities, a regular course assessment is made both on instructor and student side at the end of the semester. Just like in our university, the student is expected to fill in a questionnaire about the course comprising 20-25 questions. The dean of the faculty considers these results together with academic achievement of the faculty member to decide on his/her salary.  At X University, the instructor A, who is incapable to teach but good in research, prefers to be a popular, student friendly instructor, and does not require any homework and project in his course. Moreover, he always highlights the topics where he will ask in exams and exam questions are very similar to problems solved in the class. Naturally, the success is almost 100% and in return, students grant him almost 100% in every aspect for course evaluation. Although he is really a terrible instructor, he turns out to be the most many making guy in the department due to excellent teaching and research activities. Evaluate this case in terms of professional ethics and name the ethic codes violated, if any

 

·           In ancient times, as narrated in tales, the king of the country used to be selected by “the fortune bird”. After the funeral of the late king, all people gathered together in the city agora and they let the fortune bird fly and wait until it lands on someone’s head. If the bird lands on the same head repeatedly 3 times, then that lucky guy becomes the king. Propose 3 creative and realistic ideas to assure to become the king. The fortune bird is an ordinary bird of natural instincts.

 

·           Almost three centuries ago, a beautiful and genius French princess discovered that kinetic energy of a body is proportional to square of its linear velocity, not to the velocity itself as most physicist believed at that time. As you learned in this course, the drag force acting on a moving body is proportional to square of its linear velocity and we defined the work as the force times the distance traveled. Making use of the formula below, prove that the following statements are true and be a prince/princess yourself right a way! (Although time is a little late today for the discovery)

a)    The ratio of brake distances of a car is proportional to the ratio of squares of corresponding linear velocities, i.e. if you stop after 40 m with a solid brake when traveling at 100 km/h, then with the same car you stop after 10 m when traveling at 50 km/h. (Excerpt: Draw slowly or you can’t STOP!)

b)     The ratio of fuel consumption at two different velocities for the same car is proportional to the ratio of squares of corresponding velocities, i.e. your car consumes 4 times more gasoline if you double the speed (Excerpt: Drive at an economic speed, i.e. at 80 km/h engaged to 5^th gear at 2000 rpm, see the miracle in mph! Plus you can enjoy watching scenery)

 

Formula: KE=0.5*M*(V)²       W= F*D        F_d= 0.5*C_d*(V)²*Ar*_p

 

Here KE is kinetic energy, M is the mass of the car, V is the velocity of the car, W is work done after the brake till complete stop, D is the brake distance, F_d is the drag force of the air acting on the moving car, C_d  isris the drag coefficient,  the density of the air and A_p is the cross section of the car perpendicular to the direction of movement. Assume road is uniform and the brake is solid. Please bear in mind that for a particular car M, C_d, A_p and  are r constant.