# University entrance examinations. Industrial Technology

This test is designed to answer FOUR of the following six questions. Each exercise is worth 2.5 points. If you answer more than one exercise, only the first four will be assessed.

As this is not an official exam, you can do the whole test and it will not affect the final mark.

Previous considerations of the test.

• Exercise 1: when the answers are checked it is shown whether the answer is correct or incorrect (green if it is correct and red if it is not).
• In all the other exercises, the incorrect answer is followed by a display showing the correct answer and, in most cases, the steps to follow to get there.
• As an extra, I have added a help to the user in the sections I thought necessary. This is an automatic calculation that may help you to understand the calculations done.
• Plus, there is a step by step solution in some cases (in which the algerbra is not that clear to express by words) through JavaScript using MathJax.

Plus, there is an HTML coded calculator, in case you need to do some calculations.

#### Exercise 1

Indicate the correct answer to each question. If you do not indicate the answers, the questions will be considered unanswered.

[In each question you can only choose ONE answer. Question well answered: 0.5 points; question incorrectly answered: -0.16 points; question not answered: 0 points.]

Question 1

A mountain hut wants to install photovoltaic panels to provide a maximum consumption during the winter of 150 kWh per month. Determine the surface area of the panels required assuming a radiation density of 700 W/m2 during the winter months, a solar gain of 4 hours a day for 30 days a month and an efficiency of the installation of 8%.

a) 6,696 m2
b) 1,94 m2
c) 44,8 m2
d) 22,32 m2

Question 2

A person on a skateboard goes down a 30m long slope with a slope of 5°. He starts from the rest and does not take the brake at any time. The mass of the person and the skateboard is 82 kg. How fast will the skate go at the end of the descent if all the losses are neglected?

a) 7,161 m/s
b) 5,424 m/s
c) 24,26 m/s
d) 51,28 m/s

Question 3

If you have a 12 H7/g6 adjustment, the tolerance of the hole is (180) µm and the tolerance g6 of the shaft is (-6-17) µm, thus it can be stated that:

a) The maximum clearance is 24 µm
b) The minimum clearance is 17 µm
c) The maximum clearance is 17 µm
d) In this adjustement there cannot be any interference.

Question 4

The Ti-6Al-4V titanium alloy is used in the manufacture of malleable prostheses. It contains 4.5% vanadium (V), 6.5% aluminium (Al) and the rest is titanium (Ti). In obtaining this alloy, how much aluminium is needed to combine it with 20 kg of titanium?

a) 1,3 kg
b) 1,461 kg
c) 1,011 kg
d) 14,61 kg

Question 5

A university residence wants to reduce its annual electricity consumption, which currently stands at 41 MWh. To do this, it wants to replace the lighting with low-consumption lighting and use presence detectors in common areas. It is estimated that the saving in electricity consumption will be 12 %. If the company indicates that its electricity mix is 360 g of CO2/(kWh), how much annual CO2 emissions savings will the residence achieve?

a) 12,99 tones of CO2
b) 14,76 tones of CO2
c) 1,771 tones of CO2
d) 17,71 tones of CO2

#### Exercise 2

The aim is to design the circuit that controls a fire alarm. The alarm must be triggered when the fire alarm goes off, or when two or more of these three conditions are met: a temperature limit has been exceeded, there is smoke in the room, and/or the temperature has risen sharply. Answer the following questions using the following status variables:

 alarm: \begin{align} a=\begin{cases}1: active \\ 0: not active \end{cases}; \end{align} push button: \begin{align} p=\begin{cases}1: pressed \\ 0: not pressed \end{cases}; \end{align} smoke: \begin{align} f=\begin{cases}1: detected \\ 0: not detected \end{cases}; \end{align} temperature: \begin{align} t=\begin{cases}1: if&t\geqq 58ºC \\ 0: if&t\lt 58ºC\end{cases}; \end{align} temperature increment: \begin{align} t=\begin{cases}1: if&t\geqq 8ºC/min \\ 0: if&t\lt 8ºC/min\end{cases}; \end{align}

a) Write the system's truth table. [1 point]
 p f l t a 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1

 p f l t a 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1

 p f l t a 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1

 p f l t a 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1

b) Determine the logical function between these variables and, if necessary, simplify it. [1 point]
$$a={p}{l}+{f}{t}+{l}$$

$$a={p}\bar{lt}+{pl}+{fl}$$

$$a={p}+{lt}+{ft}+{fl}$$

$$a={p}+{ft}+{t}{l}+lf$$

Karnaugh Map

c) Draw the equivalent logical gates diagram. [0,5 points]

#### Exercise 3

The following table shows the values recorded in a tensile test with a test piece of length L0 = 125mm and diameter d=8mm.

 Deformation ε Tension σ [MPa] 0 1·10-3 2·10-3 3·10-3 4·10-3 0,02 0,05 0,1 0 69 138 207 276 300 290 257

a) Draw the tension-deformation diagram. [0,5 points]
Curve 1
Curve 2
Curve 3
Curve 4

b) Calculate the elasticity module E of the material. [0,5 points]
43 GPa
89 GPa
136 GPa
69 GPa

Help
 Enter σe GPa Enter ε The elasticity module E of the material is GPa Comment:

c) Determine the force F that must be applied to subject the pipe to a tension σF=200MPa. What increase in length ΔL will the pipe undergo? [1 point]
10,05 kN and 362,3 · 10-3mm
15,05 kN and 362,3 · 10-3cm
1,050 kN and 362,3 · 10-3m
10,50 kN and 362,3 · 10-3dm

Help
 Enter σF kPa Enter the diameter d m The force F that must be applied to subject the pipe is kN Comment:
Help
 Enter σf MPa Enter E MPa Enter L0 mm The increase in length ΔL the pipe undergo is mm Comment:

d) If the pipe is subjected to a tension of 300 MPa, will it recover its initial length? [0,5 points]
If the pipe is subjected to 300 MPa it will recover the initial length because this stress is below the elastic limit of the material.
If the pipe is subjected to 300 MPa it will not recover the initial length because this stress is below the elastic limit of the material.
If the pipe is subjected to 300 MPa it will recover the initial length because this stress is above the elastic limit of the material.
If the pipe is subjected to 300 MPa it will not recover the initial length because this stress is above the elastic limit of the material.

#### Exercise 4

The firefighters use a fire-fighting fan that eliminates smoke and removes large volumes of air. The fan blades have a diameter of d = 420 mm and the air is blown out at a rate of q = 33660 m3/h. The fan is driven by a four-cycle motor of power Pmot = 3,58kW rotating at n =3600 min-1. The fuel is diesel with a calorific value pc= 44,8 MJ/kg and density ρgasoil = 0,85 kg/L, and the engine has a consumption c = 1,4 L/h. The diesel emissions factor is FE = 2,87 kg CO2/L. Determine:

a) Power consumed Pcons by the engine. [1 point]
12,14 kW
18,92 kW
21,18 kW
14,81 kW

Help
 Enter c L/h Enter ρgasoil kg/L Enter pc kJ/kg Power consumed by the engine is kW Comment:

b) Engine performance η. [0,5 points]
26,80 %
15,76 %
22,35 %
24,17 %

Help
 Enter Pmot kW Enter Pcons kW The engine performance is % Comment:

c) The speed of the tip of the blade of the helix. [0,5 points]
320 000 km/s
285 km/h
320 km/h
255 km/h

Help
 Enter n min-1 Enter d m The speed of the tip of the blade of the helix is km/h Comment:

d) The greenhouse gas emissions (CO2) mCO2 that it will emit in t = 20 min of operation. [0,5 points]
3,200 kg CO2
1,339 kg CO2
0,955 kg CO2
2,550 kg CO2

Help
 Enter c L/h Enter FE kg CO2/L Enter t1 s The mCO2 is kg Comment:

#### Exercise 5

The figure shows a folding garage door of length 2L. To open and close it, its highest point P is guided horizontally, to which a force F is applied. The centre of inertia of the door is at its midpoint and the vertical displacement of this point is forced by a guide. All friction is considered negligible.

a) Draw the diagram of the door. [0,5 points]

b) Find the expression of the coordinate h as a function of x. [0,5 points]
h = √(L2+x2)
h = √(L2-x2)
h = √(L2/x2)
h = 1+√(L2+x2)

The door is held in repose in a generic position x. Determine, as a function of x:

c) The F force that must be used to keep the door open. [1 point]
F = mgh (L2+x2)-1/2 N
F = mgx h N
F = mgx (L2-x2)-1/2 N
F = mgx h-1/2 N

d) The normal forces in each of the guides. [0.5 point]
NG = mgx and NP = mg
NG = mgx/h2 and NP = mgx
NG = F and NP = mg
NG = mgx/h and NP = mgx

#### Exercise 6

The municipal public lighting system of a town consists of n=308 light points, which are on, on average, t = 11 hours a day. Each light point uses a high pressure sodium vapour pump (VSAP) with a power of 100W. The tariff set by the electricity company sets an electricity cost of celectr = 0,1370 €/(kWh). In addition, the City Council has to assume an annual cost associated with the maintenance of this system cmant= 14,000 €.

Determine:

a) The annual money that the City Council pays to the electricity company cHPVSP. (Hint: calculate the energy consumption of the public lighting VSAP first!) [1 point]
16,941 €
21,220 €
27,527 €
14,925 €

Help
 Enter PVSAP W Enter celec €/(kWh) Enter n light points Enter time h per day The annual money that the City Council pays to the electricity company is € Comment:

The city council wants to replace all the lighting points with new ones that will use LED technology bulbs with a power of Pled = 36W. Each light has a unit cost of €500 (including the bulb). The cost of the installation of the new lighting is estimated at cinst = 43,000€. In this installation the maintenance cost can be neglected. Determine:

b) The money that the City Council would save annually csave. (Hint: Calculate the new electricity consumption Eled) [1 point]
21,058€
23,759€
22,621€
24,842€

Help
 Enter PLED W Enter PVSAP W Enter EVSAP kWh Enter celectr €/(kWh) The money that the City Council would save annually is € Comment:

c) The total cost of the investment cinv. How many years Δt will it take to recover the investment made? [0.5 points]
157,000€ and it would be recovered in 7 years
157,000€ and it would be recovered in 8 years
197,000€ and it would be recovered in 8 years
197,000€ and it would be recovered in 7 years

Help
 Enter n light points Enter clight € Enter csave € The total cost of the investment is € The time that it take to recover the investment made is years. Comment: