FSG#003

3. The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and is made of a flat layer of concrete whose thermal conductivity is k 0.8 W/m · °C . The temperatures of the inner and the outer surfaces of the roof one night are measured to be 15°C and 4°C, respectively, for a period of 10 hours. Determine the rate of heat loss through the roof that night. Answer in kW (xxx.xx)

4. Calculate the output voltage (Vost) when loaded with a 1kΩ resistor (Answer in V, keep 2 decimals, xxx.xx)

5. A series resistance-capacitance bridge as shown below has a standard capacitor for C1, and R3= 10kΩ. Balance is achieved with 100Hz supply frequency when R1=125Ω and R4=14.7kΩ. Calculate the resistive and capacitive components of measured capacitor (answer in the form xuF, yOhm and round to 2 decimals)

7. Homogenous cylinder with mass mk and radius R=0,5m is adjusted in weightless vertical metal pipe which main axis is coincident with cylinder axis. One side of the pipe is placed at the floor so that there are no turning frictions, and the other side is adjusted at the center m of a thin and homogenous stick with m=3kg and lenght l=2m. The stick has at its edges 2 small spheres with equal mass m1=m2=0.5kg. A thin weightless rope is wrapped around the cylinder is passing through the pulley of mass m=4kg and radius r=0.1m, and at its free edge there is body Σ of mass m=3kg. Initially the system stays still and after t=0 we let it move and until t1=2sec the pulley has done N=20/π rotations. Assume the pulley has no turning frictions and the rope is always stretched and does NOT slide at cylinder's perimeter or at the pulley. (Moment of inertia of the pulley I(pulley)=1/2m*(r^2) and moment of inertia of the stick for the axis that tangently passes through its center I(stick)=1/12m*(l^2) and g=10m/s^2) Calculate: a) The acceleration of body Σ b) Force from the rope to body Σ during t=0 -> t=2 sec c) Torque of the system as of the axis of the cylinder at t1=2sec (Answer type: " (x, y, z) " where x is (a) at m/s^2, y is (b) at Joules and z is (c) at kg*(m^2)/s

Answer in x,x,x

Δυσκολία 11/10 αλλά το CRT μπορεί.

10. The following water tank is simply touching the floor with no support, has a bottom surface area of A=20 cm^2 and it contains water of density ρ=1000 kg/m^3 up until h=1m. The tank is then sealed by a plug which has placed on it a spring with k=1000 N/m and a body of m=10 kg attached on the other end. The system is balancing. We then push the body on top a distance of d=0.2m towards the ground. Determine if the tank will bounce upwards when the body oscillates. The tank & plug weigh together 3 kg. g=9.81m^2/s

12. Air at 100°F is flowing (laminar flow) over a flat plate 1 ft wide. Estimate the drag. The air speed is 7.2 ft/sec. (Reynolds number is given 4*10^4)