FSG Preperation Quiz

In the illustrated thermodynamic cycle of an ideal gas, the values for pressure p₁=7 bar and volume V₁=0.6 m³ at point 1, volume V₂=3.3 m³ and temperature T₂=800 °C at point 2 and pressure p3=0,6 bar at point 3 are given. The volume at point 1 is the same as at point 4. The volume at point 2 is the same as at point 3. The pressure in point 4 is to be calculated in bar! Round the solution to one decimal place.

Calculate the voltage U_AB between A and B in multiples of Voltage U_q. Enter the exact solution as a completely simplified and reduced fraction in the format numerator/denominator. Numerator and denominator must be integers, e.g. 1/2

A thin-walled (t ≪ a) cross-section is shown in the figure in gray. All relevant dimensions are given in the drawing. The drawing itself is not to scale. Calculate the second moment of area of the cross-section about the x-axis through point O using the thin-walled assumption and resulting simplification. Enter the exact solution: I_xx=?

Your team decides to use aluminum cables instead of copper to save weight. As there is no proper sizing table for these cables you try to calculate the proper fusing value yourself. The cross-section of one cable is A. You measured the thickness of the insulation which is t. From previous experiments you know, that the cables will face a maximum ambient temperature of T_amb inside your vehicle and that the heat transfer coefficient between the wire and ambient through the insulator is λ. The coefficient is estimated in relation to the average diameter of the conductor and the conductor with insulator. Which fuse value must be chosen to have the maximum possible current without exceeding a temperature of T_max inside the cable. The fuses are available in 1 A size steps. The fuse is considered to be ideal, I.e. It trips immeadiately if the rated current is exceeded. The resistivity of aluminum is assumed to be ρ_{AL .} The linear approximation for temperature dependence with the temperature coefficient α is used. The following conditions are assumed:

>> Cross section of cable A = 1.5 mm²

>> Thickness of insulation t = 0.35 mm

>> Maximum ambient temperature Tamb = 50 °C

>> Maximum wire temperature Tmax = 70 °C

>> Heat transfer coefficient between wire and insulator λ = 6 mW / (K * m) 

>> Resistivity of aluminum ρ_AL=26.4 nΩm

>> Temperature coefficient α=0.0041 1/K

Enter the calculated fuse size.

The shown finite state machine is used to check if an input data stream matches with some regular expression. The data matches the regular expression if the final state q_d is reached at the end of the input stream. What regualar expression(s) will be checked by the state machine? You may select one or more answers.

An idealized FSE vehicle is driven by 4 identical, ideal wheel hub drives (no losses, no inertia) and has a weight distribution of 50/50. The aerodynamic balance is 50/50 as well and independent from vehicle speed. The following diagram shows the wheel torque (of one single wheel) T over the vehicle speed v for a perfect full accelaration without wheel slip. Calculate v₁ and v₂ as shown in the picture in km/h. Dynamic load transfer is neglected. The motor is assumed to be limited only by its maximum torque and maximum power. Given parameters:

>> Vehicle mass m = 200 kg

>> Dynamic rolling radius of each tire r_dyn = 200 mm

>> Aerodynamic lift coefficient of the vehicle c_l = -1.35

>> Aerodynamic cross sectional area of the vehicle A = 1.3 m²

>> Tire friction coefficient μ = 1.2

>> Gravity g = 9.81 m/s2

>> Air density ρ_Air = 1.2 kg/m³

>> Maximum wheel torque (each) T_max = 145 Nm

>> Maximum wheel hub drive power (each) P_max = 20 kW

Round both solutions to one decimal place. Give the solution in the following format: v₁, v₂, e.g. 1.2, 3.4

During Autocross, a Formula Student vehicle accelerates from 30 km/h to 100 km/h. Assume that there is no friction and no aerodynamic drag. The mass of the vehicle is m = 180 kg. The amount of energy needed for this accelaration is denoted by E. What would be the theoretical velocity v_c if the vehicle is accelerated from standstill using the same amount of energy E? Enter the solution in km/h and round to one decimal place. What would be the theoretical velocity v_F of Fred, the FSG race Alpaka as shown in the picture, accelerating from standstill and using 1/10th of the energy E? Fred's initial mass in standstill is 50 kg. When reaching 20km/h, Fred will loose 750g of mass in no time. Assume, that the lost mass does not provide any thrust and has no initial relative velocity with respect to Fred. Fred is free of friction and aerodynamic drag. Round both solutions to one decimal place. Give the solution in the following format: v_c , v_F , e.g. 1.2, 3.4