Question 3:

a)The number of equilateral triangles nT that fit to build the star and the perimeter of the carved fish pT in this case. of the carved fish pT in this case. [0.5 points]

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b) The number of lozenges nR that fit to build the star and the perimeter of the fishes carved pR in this case. [0.5 points]

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c) The perimeter cut pE if the star is built by cutting the outer profile directly. [0.5 points]

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d) The surface area of wood needed to build the star, and the cost cT, cR and cE of each of the three options above. Which is the most economical option? [1 point]

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a) The mechanical power P_{càrrega} required to raise the load. [0,5 punts]

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b) The power P_m and torque Γ_m at the engine output shaft. [1 point]

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c) The intensity I consumed by the electric motor. [0,5 points]

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d) The total power dissipated P_{diss} by the motor-reducer set. [0,5 points]

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The aluminium plate in the figure, of thickness e = 5 mm, is hinged to the ground at point O. To keep it in repose, a steel cable is used which is fixed at point A and which has the direction shown in the figure. The cable has a circular section with a diameter of d = 2 mm. The density of the aluminium is ρaluminium = 2 710 kg/m3 and the elastic modulus of the steel is Eacer = 207 GPa.

a) Draw the full-costs diagram of the plate. [0,5 punts].

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b) The mass m of the plaque. [0,5 punts].

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c) The force T that makes the cable, and the horizontal forces F_h and vertical F_v at point O. [1 point ]

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d) The normal stress σ of the cable and its unit length ε. If the elastic limit of the steel is σe,acer = 350 MPa, does the cable become permanently deformed? [0,5 point ]

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An outdoor beacon consists of fifteen LEDs connected as shown in the circuit in the figure. The voltage drop of each LED is ULED = 3.4 V. To regulate the illumination, the beacon can be powered with n = 3 or 4 batteries connected in series. Each battery provides a voltage Ubat = 12 V and has a capacity cbat = 10 000 mA h. Between the batteries and the LEDs there is a resistor R. When n = 4 batteries are connected, a current ILED,4 = 25 mA passes through each LED. For this configuration, determine:

a) The value of the resistance R. [0,5 point]

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b) The energy consumed Etotal at time t = 8 h. [0,5 points]

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c) The time tbat,4 that the batteries can last. [0,5 points]

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For the configuration with only n = 3 batteries connected in series, determine:

d)The new ILED,3 intensity that flows through each LED. [0,5 points]

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e)The time tbat,3 that the batteries last.[0,5 points]

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