answer string | choices dict | id string | kind string | lang string | question string | steps list | subject string | text string | topic string |
|---|---|---|---|---|---|---|---|---|---|
Bernoulliova rovnice směňuje tlak, rychlost a výšku podél proudnice. | null | eng_0251 | concept | cs | Co je Bernoulliova rovnice? | [
"Rychle znamená tlak dolů.",
"Vysoko pomalu.",
"Stálé ideální."
] | engineering | Answer: Směna energií.
Steps:
1. Rychle znamená tlak dolů.
2. Vysoko pomalu.
3. Stálé ideální. | fluids |
The modulus is 101.5 GPa. | null | eng_0252 | worked_example | en | Composite with fibre fraction 0.5 (Ef = 200 GPa, Em = 3 GPa). What is the modulus? | [
"Vf = 0.5, Ef = 200 GPa.",
"E = VfEf+VmEm = 101.5 GPa.",
"Result 101.5 GPa."
] | engineering | Answer: 101.5 GPa.
Steps:
1. Vf = 0.5, Ef = 200 GPa.
2. E = VfEf+VmEm = 101.5 GPa.
3. Result 101.5 GPa. | materials |
The moment arm is 38 m. | null | eng_0253 | worked_example | en | Moment 5700 N·m comes from 150 N force. What is the moment arm? | [
"M = 5700 N·m, F = 150 N.",
"d = M/F = 38 m.",
"Result 38 m."
] | engineering | Answer: 38 m.
Steps:
1. M = 5700 N·m, F = 150 N.
2. d = M/F = 38 m.
3. Result 38 m. | statics |
The new volume is 11 m³. | null | eng_0254 | worked_example | en | Gas 3 m³ at 300 K warms to 1100 K at constant pressure. What is the new volume? | [
"V1 = 3 m³, T1 = 300 K.",
"V2 = 3×1100/300 = 11 m³.",
"Result 11 m³."
] | engineering | Answer: 11 m³.
Steps:
1. V1 = 3 m³, T1 = 300 K.
2. V2 = 3×1100/300 = 11 m³.
3. Result 11 m³. | thermodynamics |
The power is 4140 W. | {
"A": "4140 W",
"B": "3910 W",
"C": "4370 W",
"D": "4255 W"
} | eng_0255 | multiple_choice | en | A 230 V appliance draws 18 A. What is its power? | [
"V = 230 V, I = 18 A.",
"P = VI = 4140 W.",
"Select option A (4140 W)."
] | engineering | Answer: 4140 W.
Steps:
1. V = 230 V, I = 18 A.
2. P = VI = 4140 W.
3. Select option A (4140 W).
Answer: (A) | circuits |
The integral output is 75 V. | null | eng_0256 | worked_example | en | Error 2 units lasts 75 s with Ki = 0.5 1/s. What is the integral output? | [
"e = 2 units, t = 75 s.",
"u = 0.5×2×75 = 75 V.",
"Result 75 V."
] | engineering | Answer: 75 V.
Steps:
1. e = 2 units, t = 75 s.
2. u = 0.5×2×75 = 75 V.
3. Result 75 V. | control |
The mass flow is 16 kg/s. | null | eng_0257 | worked_example | en | Water flows 16 L/s. What is the mass flow in kg/s? | [
"Q = 16 L/s, ρ = 1000 kg/m³.",
"ṁ = 16 kg/s.",
"Result 16 kg/s."
] | engineering | Answer: 16 kg/s.
Steps:
1. Q = 16 L/s, ρ = 1000 kg/m³.
2. ṁ = 16 kg/s.
3. Result 16 kg/s. | fluids |
Fatigue failure is cracking under repeated cyclic loads below static strength. | null | eng_0258 | concept | en | What is fatigue failure? | [
"Load cycles.",
"Crack grows.",
"Sudden break."
] | engineering | Answer: Cyclic cracking.
Steps:
1. Load cycles.
2. Crack grows.
3. Sudden break. | materials |
The horizontal component is 600 N. | null | eng_0259 | worked_example | en | Force 1000 N pulls at a 3-4-5 angle. What is the horizontal component? | [
"F = 1000 N, cos = 3/5.",
"Fx = 0.6×1000 = 600 N.",
"Result 600 N."
] | engineering | Answer: 600 N.
Steps:
1. F = 1000 N, cos = 3/5.
2. Fx = 0.6×1000 = 600 N.
3. Result 600 N. | statics |
An isothermal process holds temperature constant while heat and work exchange. | null | eng_0260 | concept | en | What is an isothermal process? | [
"T fixed.",
"Heat flows.",
"Work matches."
] | engineering | Answer: Constant temperature.
Steps:
1. T fixed.
2. Heat flows.
3. Work matches. | thermodynamics |
An inductor stores magnetic energy and resists current change. | null | eng_0261 | concept | en | What does an inductor do? | [
"Coil field.",
"Current lags.",
"DC passes."
] | engineering | Answer: Resists change.
Steps:
1. Coil field.
2. Current lags.
3. DC passes. | circuits |
The D output is 32 V. | null | eng_0262 | worked_example | en | Error jumps 0 to 160 units in 2 s with Kd = 0.4 s. What is the D output? | [
"Slope = 160/2 units/s.",
"u = 0.4×slope = 32 V.",
"Result 32 V."
] | engineering | Answer: 32 V.
Steps:
1. Slope = 160/2 units/s.
2. u = 0.4×slope = 32 V.
3. Result 32 V. | control |
Gauge pressure is 166.77 kPa. | {
"A": "161.77 kPa",
"B": "171.77 kPa",
"C": "176.77 kPa",
"D": "166.77 kPa"
} | eng_0263 | multiple_choice | en | Water depth is 17 m. What is gauge pressure? | [
"ρ = 1000 kg/m³, h = 17 m.",
"p = ρgh = 166.77 kPa.",
"Select option D (166.77 kPa)."
] | engineering | Answer: 166.77 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 17 m.
2. p = ρgh = 166.77 kPa.
3. Select option D (166.77 kPa).
Answer: (D) | fluids |
Bezpečnost je 2.5. | {
"A": "3.0 (dimensionless)",
"B": "2.0 (dimensionless)",
"C": "2.5 (dimensionless)",
"D": "3.5 (dimensionless)"
} | eng_0264 | multiple_choice | cs | Mez kluzu 300 MPa, provozní napětí 120 MPa. Jaká je bezpečnost? | [
"σy = 300 MPa, σw = 120 MPa.",
"n = 2.5 (dimensionless).",
"Vyber možnost C (2.5 (dimensionless))."
] | engineering | Answer: 2.5 (dimensionless).
Steps:
1. σy = 300 MPa, σw = 120 MPa.
2. n = 2.5 (dimensionless).
3. Vyber možnost C (2.5 (dimensionless)).
Answer: (C) | materials |
Těžiště je bod, kde je plocha či těleso v rovnováze. | null | eng_0265 | concept | cs | Co je těžiště? | [
"Symetrie střed.",
"Složené váží.",
"Váha zde."
] | engineering | Answer: Střed rovnováhy.
Steps:
1. Symetrie střed.
2. Složené váží.
3. Váha zde. | statics |
The pressure is 1900 kPa. | null | eng_0266 | worked_example | en | Gas 19 m³ at 100 kPa is squeezed to 1 m³ at constant temperature. What is the pressure? | [
"p1 = 100 kPa, V1 = 19 m³.",
"p2 = 100×19 = 1900 kPa.",
"Result 1900 kPa."
] | engineering | Answer: 1900 kPa.
Steps:
1. p1 = 100 kPa, V1 = 19 m³.
2. p2 = 100×19 = 1900 kPa.
3. Result 1900 kPa. | thermodynamics |
A short has near-zero resistance with large current, while an open has no path and zero current. | null | eng_0267 | concept | en | How do short and open circuits differ? | [
"Short: big amps.",
"Open: zero amps.",
"Opposite faults."
] | engineering | Answer: Zero versus none.
Steps:
1. Short: big amps.
2. Open: zero amps.
3. Opposite faults. | circuits |
Výstup regulátoru je 140 V. | {
"A": "130 V",
"B": "140 V",
"C": "150 V",
"D": "160 V"
} | eng_0268 | multiple_choice | cs | P-regulátor s Kp = 2 V/V vidí chybu 70 jednotek. Jaký je výstup? | [
"Kp = 2 V/V, e = 70 units.",
"u = Kp·e = 140 V.",
"Vyber možnost B (140 V)."
] | engineering | Answer: 140 V.
Steps:
1. Kp = 2 V/V, e = 70 units.
2. u = Kp·e = 140 V.
3. Vyber možnost B (140 V).
Answer: (B) | control |
Dynamic pressure is 4335 Pa. | null | eng_0269 | worked_example | en | Air (ρ = 1.2 kg/m³) moves 85 m/s. What is the dynamic pressure? | [
"ρ = 1.2 kg/m³, v = 85 m/s.",
"q = ½ρv² = 4335 Pa.",
"Result 4335 Pa."
] | engineering | Answer: 4335 Pa.
Steps:
1. ρ = 1.2 kg/m³, v = 85 m/s.
2. q = ½ρv² = 4335 Pa.
3. Result 4335 Pa. | fluids |
Creep is slow deformation under steady load at high temperature over time. | null | eng_0270 | concept | en | What is creep? | [
"Heat softens.",
"Load holds.",
"Strain creeps."
] | engineering | Answer: Slow hot sag.
Steps:
1. Heat softens.
2. Load holds.
3. Strain creeps. | materials |
Static friction holds up to a limit before motion, while kinetic acts during sliding, usually lower. | null | eng_0271 | concept | en | How do static and kinetic friction differ? | [
"Static holds.",
"Kinetic slides.",
"Static higher."
] | engineering | Answer: Before versus during.
Steps:
1. Static holds.
2. Kinetic slides.
3. Static higher. | statics |
Vykonaná práce je 420 kJ. | {
"A": "420 kJ",
"B": "400 kJ",
"C": "440 kJ",
"D": "460 kJ"
} | eng_0272 | multiple_choice | cs | Plyn expanduje při 200 kPa o 2.1 m³. Jaká je práce? | [
"p = 200 kPa, ΔV = 2.1 m³.",
"W = pΔV = 420 kJ.",
"Vyber možnost A (420 kJ)."
] | engineering | Answer: 420 kJ.
Steps:
1. p = 200 kPa, ΔV = 2.1 m³.
2. W = pΔV = 420 kJ.
3. Vyber možnost A (420 kJ).
Answer: (A) | thermodynamics |
The resistance is 23 Ω. | null | eng_0273 | worked_example | en | Voltage 69 V drives 3 A. What is the resistance? | [
"V = 69 V, I = 3 A.",
"R = V/I = 23 Ω.",
"Result 23 Ω."
] | engineering | Answer: 23 Ω.
Steps:
1. V = 69 V, I = 3 A.
2. R = V/I = 23 Ω.
3. Result 23 Ω. | circuits |
The closed-loop gain is 0.95. | null | eng_0274 | worked_example | en | Unity feedback loop, forward gain 19. What is the closed-loop gain? | [
"K = 19 (dimensionless).",
"T = K/(1+K) = 0.95 (dimensionless).",
"Result 0.95 (dimensionless)."
] | engineering | Answer: 0.95 (dimensionless).
Steps:
1. K = 19 (dimensionless).
2. T = K/(1+K) = 0.95 (dimensionless).
3. Result 0.95 (dimensionless). | control |
The volume is 38 m³. | null | eng_0275 | worked_example | en | Tank base area 2 m², depth 19 m. What is the water volume? | [
"A = 2 m², h = 19 m.",
"V = Ah = 38 m³.",
"Result 38 m³."
] | engineering | Answer: 38 m³.
Steps:
1. A = 2 m², h = 19 m.
2. V = Ah = 38 m³.
3. Result 38 m³. | fluids |
The shear stress is 80 MPa. | null | eng_0276 | worked_example | en | Shear force 40 kN on 500 mm² section. What is the shear stress? | [
"F = 40 kN, A = 500 mm².",
"τ = F/A = 80 MPa.",
"Result 80 MPa."
] | engineering | Answer: 80 MPa.
Steps:
1. F = 40 kN, A = 500 mm².
2. τ = F/A = 80 MPa.
3. Result 80 MPa. | materials |
Svislá složka je 840 N. | null | eng_0277 | worked_example | cs | Síla 1050 N táhne pod úhlem 3-4-5. Jaká je svislá složka? | [
"F = 1050 N, sin = 4/5.",
"Fy = 0.8×1050 = 840 N.",
"Result 840 N."
] | engineering | Answer: 840 N.
Steps:
1. F = 1050 N, sin = 4/5.
2. Fy = 0.8×1050 = 840 N.
3. Result 840 N. | statics |
Teplota je 207 °C. | null | eng_0278 | worked_example | cs | Teplota je 480 K. Kolik je to stupňů Celsia? | [
"T = 480 K.",
"C = 480 − 273 = 207 °C.",
"Result 207 °C."
] | engineering | Answer: 207 °C.
Steps:
1. T = 480 K.
2. C = 480 − 273 = 207 °C.
3. Result 207 °C. | thermodynamics |
A voltage divider splits input voltage across series resistors by ratio. | null | eng_0279 | concept | en | What is a voltage divider? | [
"Two resistors.",
"Tap middle.",
"Vout fraction."
] | engineering | Answer: Split by ratio.
Steps:
1. Two resistors.
2. Tap middle.
3. Vout fraction. | circuits |
The total gain is 34. | {
"A": "32 (dimensionless)",
"B": "36 (dimensionless)",
"C": "34 (dimensionless)",
"D": "38 (dimensionless)"
} | eng_0280 | multiple_choice | en | Two series blocks have gains 2 and 17. What is the total gain? | [
"K1 = 2, K2 = 17 (dimensionless).",
"K = 34 (dimensionless).",
"Select option C (34 (dimensionless))."
] | engineering | Answer: 34 (dimensionless).
Steps:
1. K1 = 2, K2 = 17 (dimensionless).
2. K = 34 (dimensionless).
3. Select option C (34 (dimensionless)).
Answer: (C) | control |
A manometer measures pressure from a liquid column height difference. | null | eng_0281 | concept | en | What does a manometer measure? | [
"Height in mm.",
"Times rho g.",
"Pa result."
] | engineering | Answer: Column pressure.
Steps:
1. Height in mm.
2. Times rho g.
3. Pa result. | fluids |
Teplotní napětí je 252 MPa. | null | eng_0282 | worked_example | cs | Ocelová tyč (E = 200 GPa, α = 12e-6/K) chladne o 105 K vetknutá. Jaké vznikne napětí? | [
"E = 200 GPa, ΔT = 105 K.",
"σ = EαΔT = 252 MPa.",
"Result 252 MPa."
] | engineering | Answer: 252 MPa.
Steps:
1. E = 200 GPa, ΔT = 105 K.
2. σ = EαΔT = 252 MPa.
3. Result 252 MPa. | materials |
The reaction at B is 2200 N. | null | eng_0283 | worked_example | en | Beam 6 m, load 3300 N at 4 m from A. What is reaction at B? | [
"F = 3300 N, span 6 m.",
"RB = 3300×4/6 = 2200 N.",
"Result 2200 N."
] | engineering | Answer: 2200 N.
Steps:
1. F = 3300 N, span 6 m.
2. RB = 3300×4/6 = 2200 N.
3. Result 2200 N. | statics |
The specific volume is 10 m³/kg. | null | eng_0284 | worked_example | en | Gas fills 40 m³ with mass 4 kg. What is the specific volume? | [
"V = 40 m³, m = 4 kg.",
"v = V/m = 10 m³/kg.",
"Result 10 m³/kg."
] | engineering | Answer: 10 m³/kg.
Steps:
1. V = 40 m³, m = 4 kg.
2. v = V/m = 10 m³/kg.
3. Result 10 m³/kg. | thermodynamics |
The tap voltage is 25 V. | null | eng_0285 | worked_example | en | Divider with two 1000 Ω resistors fed 50 V. What is the tap voltage? | [
"Vin = 50 V, halves.",
"Vout = 25 V.",
"Result 25 V."
] | engineering | Answer: 25 V.
Steps:
1. Vin = 50 V, halves.
2. Vout = 25 V.
3. Result 25 V. | circuits |
The error is 95 units. | null | eng_0286 | worked_example | en | Setpoint 950 units, measurement 855 units. What is the error? | [
"r = 950 units, y = 855 units.",
"e = r−y = 95 units.",
"Result 95 units."
] | engineering | Answer: 95 units.
Steps:
1. r = 950 units, y = 855 units.
2. e = r−y = 95 units.
3. Result 95 units. | control |
Cavitation is vapor bubble collapse from low pressure, eroding pumps and propellers. | null | eng_0287 | concept | en | What is cavitation? | [
"Pressure dips.",
"Bubbles burst.",
"Metal pits."
] | engineering | Answer: Bubble collapse.
Steps:
1. Pressure dips.
2. Bubbles burst.
3. Metal pits. | fluids |
Poisson's ratio is transverse shrink over axial stretch, about 0.3 for steel. | null | eng_0288 | concept | en | What is Poisson's ratio? | [
"Pull bar.",
"Sides pinch.",
"Ratio 0.3."
] | engineering | Answer: Side over length.
Steps:
1. Pull bar.
2. Sides pinch.
3. Ratio 0.3. | materials |
Each end reaction is 1300 N. | null | eng_0289 | worked_example | en | Uniform beam weighs 2600 N over 8 m. What is each end reaction? | [
"W = 2600 N, midspan 4 m.",
"R = W/2 = 1300 N.",
"Result 1300 N."
] | engineering | Answer: 1300 N.
Steps:
1. W = 2600 N, midspan 4 m.
2. R = W/2 = 1300 N.
3. Result 1300 N. | statics |
Carnot efficiency is 80%. | {
"A": "85%",
"B": "80%",
"C": "75%",
"D": "90%"
} | eng_0290 | multiple_choice | en | Carnot engine between 300 K and 1500 K. What is its efficiency? | [
"Tc = 300 K, Th = 1500 K.",
"η = 1 − 300/1500 = 80%.",
"Select option B (80%)."
] | engineering | Answer: 80%.
Steps:
1. Tc = 300 K, Th = 1500 K.
2. η = 1 − 300/1500 = 80%.
3. Select option B (80%).
Answer: (B) | thermodynamics |
Ground is the zero-volt reference node for all measurements. | null | eng_0291 | concept | en | What is ground in a circuit? | [
"0 V defined.",
"Currents return.",
"Safety sink."
] | engineering | Answer: Zero reference.
Steps:
1. 0 V defined.
2. Currents return.
3. Safety sink. | circuits |
The steady value is 80 units. | {
"A": "75 units",
"B": "85 units",
"C": "90 units",
"D": "80 units"
} | eng_0292 | multiple_choice | en | System K/(10s+1) with K = 80 gets a unit step. What is the steady value? | [
"DC gain K = 80 (dimensionless).",
"Step final = 80 units.",
"Select option D (80 units)."
] | engineering | Answer: 80 units.
Steps:
1. DC gain K = 80 (dimensionless).
2. Step final = 80 units.
3. Select option D (80 units).
Answer: (D) | control |
Outlet velocity is 36 m/s. | {
"A": "36 m/s",
"B": "34 m/s",
"C": "38 m/s",
"D": "40 m/s"
} | eng_0293 | multiple_choice | en | Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 18 m/s. What is outlet velocity? | [
"A1v1 = 0.02×18 m³/s.",
"v2 = 36 m/s.",
"Select option A (36 m/s)."
] | engineering | Answer: 36 m/s.
Steps:
1. A1v1 = 0.02×18 m³/s.
2. v2 = 36 m/s.
3. Select option A (36 m/s).
Answer: (A) | fluids |
The stress is 170 MPa. | {
"A": "160 MPa",
"B": "180 MPa",
"C": "190 MPa",
"D": "170 MPa"
} | eng_0294 | multiple_choice | en | Tensile force 17 kN on 100 mm² bar. What is the stress? | [
"F = 17 kN, A = 100 mm².",
"σ = F/A = 170 MPa.",
"Select option D (170 MPa)."
] | engineering | Answer: 170 MPa.
Steps:
1. F = 17 kN, A = 100 mm².
2. σ = F/A = 170 MPa.
3. Select option D (170 MPa).
Answer: (D) | materials |
The couple moment is 570 N·m. | {
"A": "600 N·m",
"B": "540 N·m",
"C": "570 N·m",
"D": "630 N·m"
} | eng_0295 | multiple_choice | en | A couple has forces 190 N spaced 3 m apart. What is its moment? | [
"F = 190 N, d = 3 m.",
"M = Fd = 570 N·m.",
"Select option C (570 N·m)."
] | engineering | Answer: 570 N·m.
Steps:
1. F = 190 N, d = 3 m.
2. M = Fd = 570 N·m.
3. Select option C (570 N·m).
Answer: (C) | statics |
The heat required is 192.28 kJ. | {
"A": "202.28 kJ",
"B": "182.28 kJ",
"C": "192.28 kJ",
"D": "212.28 kJ"
} | eng_0296 | multiple_choice | en | 2 kg of water warms by 23 K (c = 4.18 kJ/(kg·K)). How much heat? | [
"m = 2 kg, ΔT = 23 K.",
"Q = mcΔT = 192.28 kJ.",
"Select option C (192.28 kJ)."
] | engineering | Answer: 192.28 kJ.
Steps:
1. m = 2 kg, ΔT = 23 K.
2. Q = mcΔT = 192.28 kJ.
3. Select option C (192.28 kJ).
Answer: (C) | thermodynamics |
Sériové odpory se sčítají, celkový odpor je součet v ohmech. | null | eng_0297 | concept | cs | Co je sériové řazení odporů? | [
"Stejný proud.",
"Napětí dělí.",
"R součet."
] | engineering | Answer: Sčítání v sérii.
Steps:
1. Stejný proud.
2. Napětí dělí.
3. R součet. | circuits |
Doba ustálení je asi 72 s. | {
"A": "72 s",
"B": "68 s",
"C": "76 s",
"D": "80 s"
} | eng_0298 | multiple_choice | cs | Soustava má časovou konstantu 18 s. Jaká je doba ustálení 2 %? | [
"τ = 18 s.",
"ts ≈ 4τ = 72 s.",
"Vyber možnost A (72 s)."
] | engineering | Answer: 72 s.
Steps:
1. τ = 18 s.
2. ts ≈ 4τ = 72 s.
3. Vyber možnost A (72 s).
Answer: (A) | control |
Hydraulic power is 4316.4 W. | null | eng_0299 | worked_example | en | Pump lifts 0.02 m³/s of water 22 m. What hydraulic power is needed? | [
"Q = 0.02 m³/s, H = 22 m.",
"P = ρgQH = 4316.4 W.",
"Result 4316.4 W."
] | engineering | Answer: 4316.4 W.
Steps:
1. Q = 0.02 m³/s, H = 22 m.
2. P = ρgQH = 4316.4 W.
3. Result 4316.4 W. | fluids |
Shear stress is parallel force per area sliding layers past each other. | null | eng_0300 | concept | en | What is shear stress? | [
"Cut action.",
"Tau symbol.",
"Pa unit."
] | engineering | Answer: Sliding force.
Steps:
1. Cut action.
2. Tau symbol.
3. Pa unit. | materials |
The net moment is 380 N·m clockwise. | null | eng_0301 | worked_example | en | 500 N at 4 m clockwise, 540 N at 3 m counter-clockwise. What is the net moment? | [
"M1 = 500×4 = 2000 N·m.",
"M2 = 540×3 = 1620 N·m.",
"Net 380 N·m."
] | engineering | Answer: 380 N·m.
Steps:
1. M1 = 500×4 = 2000 N·m.
2. M2 = 540×3 = 1620 N·m.
3. Net 380 N·m. | statics |
Entropie měří rozptyl energie a vratně nikdy neklesá. | null | eng_0302 | concept | cs | Co je entropie? | [
"Jouly na K.",
"Stále roste.",
"Limituje stroje."
] | engineering | Answer: Míra rozptylu.
Steps:
1. Jouly na K.
2. Stále roste.
3. Limituje stroje. | thermodynamics |
DC holds steady polarity while AC alternates direction periodically. | null | eng_0303 | concept | en | How do AC and DC differ? | [
"Battery DC.",
"Mains AC.",
"Hz counts."
] | engineering | Answer: Steady versus alternating.
Steps:
1. Battery DC.
2. Mains AC.
3. Hz counts. | circuits |
Steady-state error is 4%. | {
"A": "6%",
"B": "4%",
"C": "2%",
"D": "9%"
} | eng_0304 | multiple_choice | en | Type-0 loop has position constant Kp = 24. What is step steady-state error? | [
"Kp = 24 (dimensionless).",
"ess = 100/25 = 4%.",
"Select option B (4%)."
] | engineering | Answer: 4%.
Steps:
1. Kp = 24 (dimensionless).
2. ess = 100/25 = 4%.
3. Select option B (4%).
Answer: (B) | control |
Base pressure is 225.63 kPa. | null | eng_0305 | worked_example | en | Still water column 23 m high. What is pressure at the base? | [
"ρ = 1000 kg/m³, h = 23 m.",
"p = ρgh = 225.63 kPa.",
"Result 225.63 kPa."
] | engineering | Answer: 225.63 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 23 m.
2. p = ρgh = 225.63 kPa.
3. Result 225.63 kPa. | fluids |
Transverse strain is -1500 microstrain. | null | eng_0306 | worked_example | en | Bar stretches 5000 microstrain, Poisson ratio 0.3. What is transverse strain? | [
"εa = 5000 microstrain, ν = 0.3.",
"εt = −νεa = -1500 microstrain.",
"Result -1500 microstrain."
] | engineering | Answer: -1500 microstrain.
Steps:
1. εa = 5000 microstrain, ν = 0.3.
2. εt = −νεa = -1500 microstrain.
3. Result -1500 microstrain. | materials |
A centroid is the geometric center where area or volume balances. | null | eng_0307 | concept | en | What is a centroid? | [
"Symmetric middle.",
"Composite weighs.",
"Used for weight."
] | engineering | Answer: Area balance point.
Steps:
1. Symmetric middle.
2. Composite weighs.
3. Used for weight. | statics |
Výkon je 1100 W. | null | eng_0308 | worked_example | cs | Práce 11000 J za 10 s. Jaký je výkon? | [
"W = 11000 J, t = 10 s.",
"P = W/t = 1100 W.",
"Result 1100 W."
] | engineering | Answer: 1100 W.
Steps:
1. W = 11000 J, t = 10 s.
2. P = W/t = 1100 W.
3. Result 1100 W. | thermodynamics |
The leaving current is 26 A. | null | eng_0309 | worked_example | en | Currents 2 A and 24 A enter a node. What current leaves? | [
"I1 = 2 A, I2 = 24 A.",
"I3 = 26 A.",
"Result 26 A."
] | engineering | Answer: 26 A.
Steps:
1. I1 = 2 A, I2 = 24 A.
2. I3 = 26 A.
3. Result 26 A. | circuits |
The final value is 60 units. | null | eng_0310 | worked_example | en | Gain 20 system gets a step of amplitude 3. What is the final value? | [
"K = 20 (dimensionless), step 3 units.",
"Final = 3×20 = 60 units.",
"Result 60 units."
] | engineering | Answer: 60 units.
Steps:
1. K = 20 (dimensionless), step 3 units.
2. Final = 3×20 = 60 units.
3. Result 60 units. | control |
Reynoldsovo číslo je bezrozměrný poměr setrvačných a vazkých sil. | null | eng_0311 | concept | cs | Co je Reynoldsovo číslo? | [
"Ró vé dé.",
"Lomeno mí.",
"Pod 2300 klid."
] | engineering | Answer: Setrvačnost lomeno vazkost.
Steps:
1. Ró vé dé.
2. Lomeno mí.
3. Pod 2300 klid. | fluids |
Deformace je 1700 mikrostrainu. | {
"A": "1700 microstrain",
"B": "1600 microstrain",
"C": "1800 microstrain",
"D": "1900 microstrain"
} | eng_0312 | multiple_choice | cs | Tyč 1000 mm se protáhne o 1.7 mm. Jaká je deformace? | [
"ΔL = 1.7 mm, L = 1000 mm.",
"ε = 1700 microstrain.",
"Vyber možnost A (1700 microstrain)."
] | engineering | Answer: 1700 microstrain.
Steps:
1. ΔL = 1.7 mm, L = 1000 mm.
2. ε = 1700 microstrain.
3. Vyber možnost A (1700 microstrain).
Answer: (A) | materials |
The resultant is 800 N. | {
"A": "750 N",
"B": "850 N",
"C": "900 N",
"D": "800 N"
} | eng_0313 | multiple_choice | en | Forces 480 N east and 640 N north act on a bolt. What is the resultant? | [
"Fx = 480 N, Fy = 640 N.",
"R = √(480²+640²) = 800 N.",
"Select option D (800 N)."
] | engineering | Answer: 800 N.
Steps:
1. Fx = 480 N, Fy = 640 N.
2. R = √(480²+640²) = 800 N.
3. Select option D (800 N).
Answer: (D) | statics |
An adiabatic process exchanges no heat, so work changes internal energy only. | null | eng_0314 | concept | en | What is an adiabatic process? | [
"Insulated walls.",
"Work only.",
"T shifts."
] | engineering | Answer: No heat exchange.
Steps:
1. Insulated walls.
2. Work only.
3. T shifts. | thermodynamics |
Kondenzátor ukládá náboj a stejnosměrný proud nepropustí. | null | eng_0315 | concept | cs | Co dělá kondenzátor? | [
"Desky drží Q.",
"DC stojí.",
"AC projde."
] | engineering | Answer: Ukládá náboj.
Steps:
1. Desky drží Q.
2. DC stojí.
3. AC projde. | circuits |
Doba ustálení je asi 63 s. | null | eng_0316 | worked_example | cs | Časová konstanta 21 s. Jaká je doba ustálení 5 %? | [
"τ = 21 s.",
"ts ≈ 3τ = 63 s.",
"Result 63 s."
] | engineering | Answer: 63 s.
Steps:
1. τ = 21 s.
2. ts ≈ 3τ = 63 s.
3. Result 63 s. | control |
A boundary layer is the thin slowed fluid film along a solid wall. | null | eng_0317 | concept | en | What is a boundary layer? | [
"Wall friction.",
"Thin grows.",
"Drag source."
] | engineering | Answer: Slowed wall film.
Steps:
1. Wall friction.
2. Thin grows.
3. Drag source. | fluids |
Toughness is energy absorbed before fracture, the area under the curve. | null | eng_0318 | concept | en | What is toughness? | [
"Strong plus ductile.",
"Area counts.",
"Impact resists."
] | engineering | Answer: Energy to break.
Steps:
1. Strong plus ductile.
2. Area counts.
3. Impact resists. | materials |
The moment is 1800 N·m. | {
"A": "1800 N·m",
"B": "1700 N·m",
"C": "1900 N·m",
"D": "1850 N·m"
} | eng_0319 | multiple_choice | en | Force 900 N acts at 2 m from a pivot. What is the moment? | [
"F = 900 N, d = 2 m.",
"M = Fd = 1800 N·m.",
"Select option A (1800 N·m)."
] | engineering | Answer: 1800 N·m.
Steps:
1. F = 900 N, d = 2 m.
2. M = Fd = 1800 N·m.
3. Select option A (1800 N·m).
Answer: (A) | statics |
The efficiency is 31%. | null | eng_0320 | worked_example | en | Engine turns 310 J of 1000 J heat into work. What is the efficiency? | [
"W = 310 J, Q = 1000 J.",
"η = W/Q = 31%.",
"Result 31%."
] | engineering | Answer: 31%.
Steps:
1. W = 310 J, Q = 1000 J.
2. η = W/Q = 31%.
3. Result 31%. | thermodynamics |
Total resistance is 2000 Ω. | {
"A": "1900 Ω",
"B": "2000 Ω",
"C": "2100 Ω",
"D": "2050 Ω"
} | eng_0321 | multiple_choice | en | Resistors 100 Ω and 1900 Ω in series. What is total resistance? | [
"R1 = 100 Ω, R2 = 1900 Ω.",
"R = 2000 Ω.",
"Select option B (2000 Ω)."
] | engineering | Answer: 2000 Ω.
Steps:
1. R1 = 100 Ω, R2 = 1900 Ω.
2. R = 2000 Ω.
3. Select option B (2000 Ω).
Answer: (B) | circuits |
The controller output is 190 V. | {
"A": "180 V",
"B": "200 V",
"C": "190 V",
"D": "210 V"
} | eng_0322 | multiple_choice | en | P-controller with Kp = 2 V/V sees error 95 units. What is the output? | [
"Kp = 2 V/V, e = 95 units.",
"u = Kp·e = 190 V.",
"Select option C (190 V)."
] | engineering | Answer: 190 V.
Steps:
1. Kp = 2 V/V, e = 95 units.
2. u = Kp·e = 190 V.
3. Select option C (190 V).
Answer: (C) | control |
Průtok je 38 L/s. | {
"A": "36 L/s",
"B": "38 L/s",
"C": "40 L/s",
"D": "42 L/s"
} | eng_0323 | multiple_choice | cs | Průřez 20 cm², rychlost 19 m/s. Jaký je průtok v litrech za sekundu? | [
"A = 20 cm², v = 19 m/s.",
"Q = Av = 38 L/s.",
"Vyber možnost B (38 L/s)."
] | engineering | Answer: 38 L/s.
Steps:
1. A = 20 cm², v = 19 m/s.
2. Q = Av = 38 L/s.
3. Vyber možnost B (38 L/s).
Answer: (B) | fluids |
Tvrdost je odpor povrchu proti vtlačení, stupnice Brinell či Rockwell. | null | eng_0324 | concept | cs | Co je tvrdost? | [
"Vtlač tělísko.",
"Malý důlek tvrdé.",
"Vazba na otěr."
] | engineering | Answer: Odpor důlku.
Steps:
1. Vtlač tělísko.
2. Malý důlek tvrdé.
3. Vazba na otěr. | materials |
The moment arm is 50 m. | null | eng_0325 | worked_example | en | Moment 7500 N·m comes from 150 N force. What is the moment arm? | [
"M = 7500 N·m, F = 150 N.",
"d = M/F = 50 m.",
"Result 50 m."
] | engineering | Answer: 50 m.
Steps:
1. M = 7500 N·m, F = 150 N.
2. d = M/F = 50 m.
3. Result 50 m. | statics |
Ideální plyn splňuje stavovou rovnici pV rovná nRT. | null | eng_0326 | concept | cs | Co je ideální plyn? | [
"p v Pa.",
"V v m³.",
"T v K."
] | engineering | Answer: pV rovná nRT.
Steps:
1. p v Pa.
2. V v m³.
3. T v K. | thermodynamics |
The stored charge is 12000 μC. | null | eng_0327 | worked_example | en | Capacitor 1200 μF charged to 10 V. What charge is stored? | [
"C = 1200 μF, V = 10 V.",
"Q = CV = 12000 μC.",
"Result 12000 μC."
] | engineering | Answer: 12000 μC.
Steps:
1. C = 1200 μF, V = 10 V.
2. Q = CV = 12000 μC.
3. Result 12000 μC. | circuits |
The integral output is 105 V. | null | eng_0328 | worked_example | en | Error 2 units lasts 105 s with Ki = 0.5 1/s. What is the integral output? | [
"e = 2 units, t = 105 s.",
"u = 0.5×2×105 = 105 V.",
"Result 105 V."
] | engineering | Answer: 105 V.
Steps:
1. e = 2 units, t = 105 s.
2. u = 0.5×2×105 = 105 V.
3. Result 105 V. | control |
The Reynolds number is 475000. | {
"A": "450000 (dimensionless)",
"B": "500000 (dimensionless)",
"C": "475000 (dimensionless)",
"D": "525000 (dimensionless)"
} | eng_0329 | multiple_choice | en | Water at 9.5 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number? | [
"ρ = 1000 kg/m³, v = 9.5 m/s, D = 0.05 m.",
"Re = ρvD/μ = 475000 (dimensionless).",
"Select option C (475000 (dimensionless))."
] | engineering | Answer: 475000 (dimensionless).
Steps:
1. ρ = 1000 kg/m³, v = 9.5 m/s, D = 0.05 m.
2. Re = ρvD/μ = 475000 (dimensionless).
3. Select option C (475000 (dimensionless)).
Answer: (C) | fluids |
Annealing heats and slowly cools metal to soften it and relieve stress. | null | eng_0330 | concept | en | What is annealing? | [
"Heat up.",
"Cool slow.",
"Ductile again."
] | engineering | Answer: Soften by heat.
Steps:
1. Heat up.
2. Cool slow.
3. Ductile again. | materials |
A pin gives two reaction components while a roller gives one normal to the surface. | null | eng_0331 | concept | en | How do pin and roller supports differ? | [
"Pin fixes x,y.",
"Roller normal.",
"Moments free."
] | engineering | Answer: Two versus one.
Steps:
1. Pin fixes x,y.
2. Roller normal.
3. Moments free. | statics |
The new volume is 14 m³. | null | eng_0332 | worked_example | en | Gas 3 m³ at 300 K warms to 1400 K at constant pressure. What is the new volume? | [
"V1 = 3 m³, T1 = 300 K.",
"V2 = 3×1400/300 = 14 m³.",
"Result 14 m³."
] | engineering | Answer: 14 m³.
Steps:
1. V1 = 3 m³, T1 = 300 K.
2. V2 = 3×1400/300 = 14 m³.
3. Result 14 m³. | thermodynamics |
The power lost is 480 W. | null | eng_0333 | worked_example | en | Current 2 A through 120 Ω. What power is lost? | [
"I = 2 A, R = 120 Ω.",
"P = I²R = 480 W.",
"Result 480 W."
] | engineering | Answer: 480 W.
Steps:
1. I = 2 A, R = 120 Ω.
2. P = I²R = 480 W.
3. Result 480 W. | circuits |
The D output is 44 V. | null | eng_0334 | worked_example | en | Error jumps 0 to 220 units in 2 s with Kd = 0.4 s. What is the D output? | [
"Slope = 220/2 units/s.",
"u = 0.4×slope = 44 V.",
"Result 44 V."
] | engineering | Answer: 44 V.
Steps:
1. Slope = 220/2 units/s.
2. u = 0.4×slope = 44 V.
3. Result 44 V. | control |
The exit velocity is 20 m/s. | null | eng_0335 | worked_example | en | Tank head 20 m (take g = 10 m/s²). What is the Torricelli velocity? | [
"h = 20 m, g = 10 m/s².",
"v = √(2gh) = 20 m/s.",
"Result 20 m/s."
] | engineering | Answer: 20 m/s.
Steps:
1. h = 20 m, g = 10 m/s².
2. v = √(2gh) = 20 m/s.
3. Result 20 m/s. | fluids |
Estimated strength is 1820 MPa. | null | eng_0336 | worked_example | en | Steel hardness 520 HB. Estimate tensile strength (UTS ≈ 3.5·HB). | [
"Hardness = 520 HB.",
"UTS ≈ 3.5×520 = 1820 MPa.",
"Result 1820 MPa."
] | engineering | Answer: 1820 MPa.
Steps:
1. Hardness = 520 HB.
2. UTS ≈ 3.5×520 = 1820 MPa.
3. Result 1820 MPa. | materials |
The horizontal component is 780 N. | null | eng_0337 | worked_example | en | Force 1300 N pulls at a 3-4-5 angle. What is the horizontal component? | [
"F = 1300 N, cos = 3/5.",
"Fx = 0.6×1300 = 780 N.",
"Result 780 N."
] | engineering | Answer: 780 N.
Steps:
1. F = 1300 N, cos = 3/5.
2. Fx = 0.6×1300 = 780 N.
3. Result 780 N. | statics |
Absolute zero is 0 K, the coldest limit where molecular motion is minimal. | null | eng_0338 | concept | en | What is absolute zero? | [
"Minus 273 C.",
"Unreachable limit.",
"Entropy base."
] | engineering | Answer: Zero kelvin.
Steps:
1. Minus 273 C.
2. Unreachable limit.
3. Entropy base. | thermodynamics |
Ekvivalent je 100 Ω. | {
"A": "105 Ω",
"B": "95 Ω",
"C": "100 Ω",
"D": "110 Ω"
} | eng_0339 | multiple_choice | cs | Dva odpory 200 Ω paralelně. Jaký je ekvivalent? | [
"R = 200 Ω each.",
"Req = R/2 = 100 Ω.",
"Vyber možnost C (100 Ω)."
] | engineering | Answer: 100 Ω.
Steps:
1. R = 200 Ω each.
2. Req = R/2 = 100 Ω.
3. Vyber možnost C (100 Ω).
Answer: (C) | circuits |
The closed-loop gain is 0.96. | null | eng_0340 | worked_example | en | Unity feedback loop, forward gain 24. What is the closed-loop gain? | [
"K = 24 (dimensionless).",
"T = K/(1+K) = 0.96 (dimensionless).",
"Result 0.96 (dimensionless)."
] | engineering | Answer: 0.96 (dimensionless).
Steps:
1. K = 24 (dimensionless).
2. T = K/(1+K) = 0.96 (dimensionless).
3. Result 0.96 (dimensionless). | control |
The mass flow is 22 kg/s. | null | eng_0341 | worked_example | en | Water flows 22 L/s. What is the mass flow in kg/s? | [
"Q = 22 L/s, ρ = 1000 kg/m³.",
"ṁ = 22 kg/s.",
"Result 22 kg/s."
] | engineering | Answer: 22 kg/s.
Steps:
1. Q = 22 L/s, ρ = 1000 kg/m³.
2. ṁ = 22 kg/s.
3. Result 22 kg/s. | fluids |
Napětí je 190 MPa. | {
"A": "180 MPa",
"B": "190 MPa",
"C": "200 MPa",
"D": "210 MPa"
} | eng_0342 | multiple_choice | cs | Ocel (E = 200 GPa) při deformaci 950 mikrostrainu. Jaké je napětí? | [
"E = 200 GPa, ε = 950 microstrain.",
"σ = Eε = 190 MPa.",
"Vyber možnost B (190 MPa)."
] | engineering | Answer: 190 MPa.
Steps:
1. E = 200 GPa, ε = 950 microstrain.
2. σ = Eε = 190 MPa.
3. Vyber možnost B (190 MPa).
Answer: (B) | materials |
Svislá složka je 1080 N. | null | eng_0343 | worked_example | cs | Síla 1350 N táhne pod úhlem 3-4-5. Jaká je svislá složka? | [
"F = 1350 N, sin = 4/5.",
"Fy = 0.8×1350 = 1080 N.",
"Result 1080 N."
] | engineering | Answer: 1080 N.
Steps:
1. F = 1350 N, sin = 4/5.
2. Fy = 0.8×1350 = 1080 N.
3. Result 1080 N. | statics |
Carnotův cyklus je ideální vratný oběh s největší účinností. | null | eng_0344 | concept | cs | Co je Carnotův cyklus? | [
"Dvě izotermy.",
"Dvě adiabaty.",
"Určuje limit."
] | engineering | Answer: Ideální maximum.
Steps:
1. Dvě izotermy.
2. Dvě adiabaty.
3. Určuje limit. | thermodynamics |
The current is 26 A. | null | eng_0345 | worked_example | en | Voltage 156 V across 6 Ω. What is the current? | [
"V = 156 V, R = 6 Ω.",
"I = V/R = 26 A.",
"Result 26 A."
] | engineering | Answer: 26 A.
Steps:
1. V = 156 V, R = 6 Ω.
2. I = V/R = 26 A.
3. Result 26 A. | circuits |
Časová konstanta je čas k 63 procentům skokové odezvy. | null | eng_0346 | concept | cs | Co je časová konstanta? | [
"Tau v s.",
"Značka tau.",
"Měřítko rychlosti."
] | engineering | Answer: Čas 63 procent.
Steps:
1. Tau v s.
2. Značka tau.
3. Měřítko rychlosti. | control |
Vztlak je 206010 N. | {
"A": "196200 N",
"B": "215820 N",
"C": "225630 N",
"D": "206010 N"
} | eng_0347 | multiple_choice | cs | Trup vytlačí 21 m³ vody. Jaký je vztlak? | [
"V = 21 m³, ρ = 1000 kg/m³.",
"F = ρgV = 206010 N.",
"Vyber možnost D (206010 N)."
] | engineering | Answer: 206010 N.
Steps:
1. V = 21 m³, ρ = 1000 kg/m³.
2. F = ρgV = 206010 N.
3. Vyber možnost D (206010 N).
Answer: (D) | fluids |
The mass is 180.55 kg. | null | eng_0348 | worked_example | en | Steel part volume 0.023 m³ (ρ = 7850 kg/m³). What is its mass? | [
"V = 0.023 m³, ρ = 7850 kg/m³.",
"m = ρV = 180.55 kg.",
"Result 180.55 kg."
] | engineering | Answer: 180.55 kg.
Steps:
1. V = 0.023 m³, ρ = 7850 kg/m³.
2. m = ρV = 180.55 kg.
3. Result 180.55 kg. | materials |
The method of joints solves truss member forces joint by joint with equilibrium. | null | eng_0349 | concept | en | What is the method of joints? | [
"Isolate joint.",
"Sum Fx,Fy zero.",
"Find members."
] | engineering | Answer: Joint by joint.
Steps:
1. Isolate joint.
2. Sum Fx,Fy zero.
3. Find members. | statics |
Tlak je 2500 kPa. | null | eng_0350 | worked_example | cs | Plyn 25 m³ při 100 kPa se stlačí na 1 m³ za stálé teploty. Jaký je tlak? | [
"p1 = 100 kPa, V1 = 25 m³.",
"p2 = 100×25 = 2500 kPa.",
"Result 2500 kPa."
] | engineering | Answer: 2500 kPa.
Steps:
1. p1 = 100 kPa, V1 = 25 m³.
2. p2 = 100×25 = 2500 kPa.
3. Result 2500 kPa. | thermodynamics |
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