answer string | choices dict | id string | kind string | lang string | question string | steps list | subject string | text string | topic string |
|---|---|---|---|---|---|---|---|---|---|
The net moment is 1100 N·m clockwise. | null | eng_0151 | worked_example | en | 500 N at 4 m clockwise, 300 N at 3 m counter-clockwise. What is the net moment? | [
"M1 = 500×4 = 2000 N·m.",
"M2 = 300×3 = 900 N·m.",
"Net 1100 N·m."
] | engineering | Answer: 1100 N·m.
Steps:
1. M1 = 500×4 = 2000 N·m.
2. M2 = 300×3 = 900 N·m.
3. Net 1100 N·m. | statics |
Entropy measures energy dispersal and disorder, rising in irreversible processes. | null | eng_0152 | concept | en | What is entropy? | [
"Joules per K.",
"Always grows.",
"Limits engines."
] | engineering | Answer: Dispersal measure.
Steps:
1. Joules per K.
2. Always grows.
3. Limits engines. | thermodynamics |
The stored charge is 6000 μC. | null | eng_0153 | worked_example | en | Capacitor 600 μF charged to 10 V. What charge is stored? | [
"C = 600 μF, V = 10 V.",
"Q = CV = 6000 μC.",
"Result 6000 μC."
] | engineering | Answer: 6000 μC.
Steps:
1. C = 600 μF, V = 10 V.
2. Q = CV = 6000 μC.
3. Result 6000 μC. | circuits |
A time constant is the time to reach 63 percent of a step response. | null | eng_0154 | concept | en | What is a time constant? | [
"Tau in s.",
"One tau mark.",
"Speed gauge."
] | engineering | Answer: 63 percent time.
Steps:
1. Tau in s.
2. One tau mark.
3. Speed gauge. | control |
Hydrostatický tlak roste s hloubkou jako ró gé há. | null | eng_0155 | concept | cs | Co je hydrostatický tlak? | [
"Hloubka v m.",
"Krát ró gé.",
"kPa rozdíl."
] | engineering | Answer: Ró gé há.
Steps:
1. Hloubka v m.
2. Krát ró gé.
3. kPa rozdíl. | fluids |
The strain is 700 microstrain. | {
"A": "600 microstrain",
"B": "800 microstrain",
"C": "700 microstrain",
"D": "900 microstrain"
} | eng_0156 | multiple_choice | en | Bar 1000 mm stretches 0.7 mm. What is the strain? | [
"ΔL = 0.7 mm, L = 1000 mm.",
"ε = 700 microstrain.",
"Select option C (700 microstrain)."
] | engineering | Answer: 700 microstrain.
Steps:
1. ΔL = 0.7 mm, L = 1000 mm.
2. ε = 700 microstrain.
3. Select option C (700 microstrain).
Answer: (C) | materials |
Equilibrium needs zero net force and zero net moment on a body. | null | eng_0157 | concept | en | What are equilibrium conditions? | [
"Sum Fx zero.",
"Sum Fy zero.",
"Sum M zero."
] | engineering | Answer: Zero force and moment.
Steps:
1. Sum Fx zero.
2. Sum Fy zero.
3. Sum M zero. | statics |
The ideal gas law links pressure, volume, and temperature as pV equals nRT. | null | eng_0158 | concept | en | What is the ideal gas law? | [
"p in Pa.",
"V in m³.",
"T in K."
] | engineering | Answer: pV equals nRT.
Steps:
1. p in Pa.
2. V in m³.
3. T in K. | thermodynamics |
The power lost is 240 W. | null | eng_0159 | worked_example | en | Current 2 A through 60 Ω. What power is lost? | [
"I = 2 A, R = 60 Ω.",
"P = I²R = 240 W.",
"Result 240 W."
] | engineering | Answer: 240 W.
Steps:
1. I = 2 A, R = 60 Ω.
2. P = I²R = 240 W.
3. Result 240 W. | circuits |
The D output is 20 V. | null | eng_0160 | worked_example | en | Error jumps 0 to 100 units in 2 s with Kd = 0.4 s. What is the D output? | [
"Slope = 100/2 units/s.",
"u = 0.4×slope = 20 V.",
"Result 20 V."
] | engineering | Answer: 20 V.
Steps:
1. Slope = 100/2 units/s.
2. u = 0.4×slope = 20 V.
3. Result 20 V. | control |
The exit velocity is 10 m/s. | null | eng_0161 | worked_example | en | Tank head 5 m (take g = 10 m/s²). What is the Torricelli velocity? | [
"h = 5 m, g = 10 m/s².",
"v = √(2gh) = 10 m/s.",
"Result 10 m/s."
] | engineering | Answer: 10 m/s.
Steps:
1. h = 5 m, g = 10 m/s².
2. v = √(2gh) = 10 m/s.
3. Result 10 m/s. | fluids |
Transverse strain is -1140 microstrain. | null | eng_0162 | worked_example | en | Bar stretches 3800 microstrain, Poisson ratio 0.3. What is transverse strain? | [
"εa = 3800 microstrain, ν = 0.3.",
"εt = −νεa = -1140 microstrain.",
"Result -1140 microstrain."
] | engineering | Answer: -1140 microstrain.
Steps:
1. εa = 3800 microstrain, ν = 0.3.
2. εt = −νεa = -1140 microstrain.
3. Result -1140 microstrain. | materials |
A moment is force times perpendicular distance, tending to rotate, in newton metres. | null | eng_0163 | concept | en | What is a moment? | [
"Force in N.",
"Arm in m.",
"M in N·m."
] | engineering | Answer: Force times distance.
Steps:
1. Force in N.
2. Arm in m.
3. M in N·m. | statics |
The temperature is 147 °C. | null | eng_0164 | worked_example | en | Temperature is 420 K. What is it in Celsius? | [
"T = 420 K.",
"C = 420 − 273 = 147 °C.",
"Result 147 °C."
] | engineering | Answer: 147 °C.
Steps:
1. T = 420 K.
2. C = 420 − 273 = 147 °C.
3. Result 147 °C. | thermodynamics |
Proud je 14 A. | null | eng_0165 | worked_example | cs | Napětí 84 V na 6 Ω. Jaký je proud? | [
"V = 84 V, R = 6 Ω.",
"I = V/R = 14 A.",
"Result 14 A."
] | engineering | Answer: 14 A.
Steps:
1. V = 84 V, R = 6 Ω.
2. I = V/R = 14 A.
3. Result 14 A. | circuits |
The total gain is 24. | {
"A": "22 (dimensionless)",
"B": "24 (dimensionless)",
"C": "26 (dimensionless)",
"D": "28 (dimensionless)"
} | eng_0166 | multiple_choice | en | Two series blocks have gains 2 and 12. What is the total gain? | [
"K1 = 2, K2 = 12 (dimensionless).",
"K = 24 (dimensionless).",
"Select option B (24 (dimensionless))."
] | engineering | Answer: 24 (dimensionless).
Steps:
1. K1 = 2, K2 = 12 (dimensionless).
2. K = 24 (dimensionless).
3. Select option B (24 (dimensionless)).
Answer: (B) | control |
The Reynolds number is the dimensionless ratio of inertial to viscous forces. | null | eng_0167 | concept | en | What is the Reynolds number? | [
"Rho v D.",
"Over mu.",
"Below 2300 calm."
] | engineering | Answer: Inertia over viscous.
Steps:
1. Rho v D.
2. Over mu.
3. Below 2300 calm. | fluids |
Estimated strength is 1400 MPa. | null | eng_0168 | worked_example | en | Steel hardness 400 HB. Estimate tensile strength (UTS ≈ 3.5·HB). | [
"Hardness = 400 HB.",
"UTS ≈ 3.5×400 = 1400 MPa.",
"Result 1400 MPa."
] | engineering | Answer: 1400 MPa.
Steps:
1. Hardness = 400 HB.
2. UTS ≈ 3.5×400 = 1400 MPa.
3. Result 1400 MPa. | materials |
The moment arm is 26 m. | null | eng_0169 | worked_example | en | Moment 3900 N·m comes from 150 N force. What is the moment arm? | [
"M = 3900 N·m, F = 150 N.",
"d = M/F = 26 m.",
"Result 26 m."
] | engineering | Answer: 26 m.
Steps:
1. M = 3900 N·m, F = 150 N.
2. d = M/F = 26 m.
3. Result 26 m. | statics |
The temperature is 343 K. | {
"A": "338 K",
"B": "348 K",
"C": "343 K",
"D": "353 K"
} | eng_0170 | multiple_choice | en | Temperature is 70 °C. What is it in kelvin? | [
"T = 70 °C.",
"K = 70 + 273 = 343 K.",
"Select option C (343 K)."
] | engineering | Answer: 343 K.
Steps:
1. T = 70 °C.
2. K = 70 + 273 = 343 K.
3. Select option C (343 K).
Answer: (C) | thermodynamics |
Total resistance is 1500 Ω. | {
"A": "1500 Ω",
"B": "1400 Ω",
"C": "1600 Ω",
"D": "1550 Ω"
} | eng_0171 | multiple_choice | en | Resistors 100 Ω and 1400 Ω in series. What is total resistance? | [
"R1 = 100 Ω, R2 = 1400 Ω.",
"R = 1500 Ω.",
"Select option A (1500 Ω)."
] | engineering | Answer: 1500 Ω.
Steps:
1. R1 = 100 Ω, R2 = 1400 Ω.
2. R = 1500 Ω.
3. Select option A (1500 Ω).
Answer: (A) | circuits |
The closed-loop gain is 0.9. | null | eng_0172 | worked_example | en | Unity feedback loop, forward gain 9. What is the closed-loop gain? | [
"K = 9 (dimensionless).",
"T = K/(1+K) = 0.9 (dimensionless).",
"Result 0.9 (dimensionless)."
] | engineering | Answer: 0.9 (dimensionless).
Steps:
1. K = 9 (dimensionless).
2. T = K/(1+K) = 0.9 (dimensionless).
3. Result 0.9 (dimensionless). | control |
The mass flow is 10 kg/s. | null | eng_0173 | worked_example | en | Water flows 10 L/s. What is the mass flow in kg/s? | [
"Q = 10 L/s, ρ = 1000 kg/m³.",
"ṁ = 10 kg/s.",
"Result 10 kg/s."
] | engineering | Answer: 10 kg/s.
Steps:
1. Q = 10 L/s, ρ = 1000 kg/m³.
2. ṁ = 10 kg/s.
3. Result 10 kg/s. | fluids |
The stress is 90 MPa. | {
"A": "80 MPa",
"B": "100 MPa",
"C": "110 MPa",
"D": "90 MPa"
} | eng_0174 | multiple_choice | en | Steel (E = 200 GPa) at strain 450 microstrain. What is the stress? | [
"E = 200 GPa, ε = 450 microstrain.",
"σ = Eε = 90 MPa.",
"Select option D (90 MPa)."
] | engineering | Answer: 90 MPa.
Steps:
1. E = 200 GPa, ε = 450 microstrain.
2. σ = Eε = 90 MPa.
3. Select option D (90 MPa).
Answer: (D) | materials |
The horizontal component is 420 N. | null | eng_0175 | worked_example | en | Force 700 N pulls at a 3-4-5 angle. What is the horizontal component? | [
"F = 700 N, cos = 3/5.",
"Fx = 0.6×700 = 420 N.",
"Result 420 N."
] | engineering | Answer: 420 N.
Steps:
1. F = 700 N, cos = 3/5.
2. Fx = 0.6×700 = 420 N.
3. Result 420 N. | statics |
Specific heat is heat per unit mass and degree, in joules per kilogram kelvin. | null | eng_0176 | concept | en | What is specific heat? | [
"Mass in kg.",
"Delta T in K.",
"Q in J."
] | engineering | Answer: Heat per kg K.
Steps:
1. Mass in kg.
2. Delta T in K.
3. Q in J. | thermodynamics |
Parallel resistors combine by reciprocal sum, lowering total resistance. | null | eng_0177 | concept | en | How do parallel resistors combine? | [
"Same voltage.",
"Currents split.",
"R drops."
] | engineering | Answer: Reciprocal sum.
Steps:
1. Same voltage.
2. Currents split.
3. R drops. | circuits |
Settling time is how long output takes to stay within an error band. | null | eng_0178 | concept | en | What is settling time? | [
"2 percent band.",
"About 4 tau.",
"Wait done."
] | engineering | Answer: Stay in band.
Steps:
1. 2 percent band.
2. About 4 tau.
3. Wait done. | control |
Gauge pressure is 117.72 kPa. | {
"A": "112.72 kPa",
"B": "122.72 kPa",
"C": "117.72 kPa",
"D": "127.72 kPa"
} | eng_0179 | multiple_choice | en | Water depth is 12 m. What is gauge pressure? | [
"ρ = 1000 kg/m³, h = 12 m.",
"p = ρgh = 117.72 kPa.",
"Select option C (117.72 kPa)."
] | engineering | Answer: 117.72 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 12 m.
2. p = ρgh = 117.72 kPa.
3. Select option C (117.72 kPa).
Answer: (C) | fluids |
Hookeův zákon říká, že napětí je úměrné deformaci v pružné oblasti. | null | eng_0180 | concept | cs | Co je Hookeův zákon? | [
"Sigma rovná E.",
"Epsilon malé.",
"Odtížení vrátí."
] | engineering | Answer: Napětí drží deformaci.
Steps:
1. Sigma rovná E.
2. Epsilon malé.
3. Odtížení vrátí. | materials |
Rovnováha žádá nulovou sílu i nulový moment na těleso. | null | eng_0181 | concept | cs | Co jsou podmínky rovnováhy? | [
"Součet Fx nula.",
"Součet Fy nula.",
"Součet M nula."
] | engineering | Answer: Nulová síla i moment.
Steps:
1. Součet Fx nula.
2. Součet Fy nula.
3. Součet M nula. | statics |
The work done is 320 kJ. | {
"A": "300 kJ",
"B": "340 kJ",
"C": "360 kJ",
"D": "320 kJ"
} | eng_0182 | multiple_choice | en | Gas expands at 200 kPa by 1.6 m³. What work is done? | [
"p = 200 kPa, ΔV = 1.6 m³.",
"W = pΔV = 320 kJ.",
"Select option D (320 kJ)."
] | engineering | Answer: 320 kJ.
Steps:
1. p = 200 kPa, ΔV = 1.6 m³.
2. W = pΔV = 320 kJ.
3. Select option D (320 kJ).
Answer: (D) | thermodynamics |
Odpor je 17 Ω. | null | eng_0183 | worked_example | cs | Napětí 51 V žene 3 A. Jaký je odpor? | [
"V = 51 V, I = 3 A.",
"R = V/I = 17 Ω.",
"Result 17 Ω."
] | engineering | Answer: 17 Ω.
Steps:
1. V = 51 V, I = 3 A.
2. R = V/I = 17 Ω.
3. Result 17 Ω. | circuits |
The steady value is 55 units. | {
"A": "50 units",
"B": "60 units",
"C": "55 units",
"D": "65 units"
} | eng_0184 | multiple_choice | en | System K/(10s+1) with K = 55 gets a unit step. What is the steady value? | [
"DC gain K = 55 (dimensionless).",
"Step final = 55 units.",
"Select option C (55 units)."
] | engineering | Answer: 55 units.
Steps:
1. DC gain K = 55 (dimensionless).
2. Step final = 55 units.
3. Select option C (55 units).
Answer: (C) | control |
Dynamic pressure is 1815 Pa. | null | eng_0185 | worked_example | en | Air (ρ = 1.2 kg/m³) moves 55 m/s. What is the dynamic pressure? | [
"ρ = 1.2 kg/m³, v = 55 m/s.",
"q = ½ρv² = 1815 Pa.",
"Result 1815 Pa."
] | engineering | Answer: 1815 Pa.
Steps:
1. ρ = 1.2 kg/m³, v = 55 m/s.
2. q = ½ρv² = 1815 Pa.
3. Result 1815 Pa. | fluids |
Ultimate tensile strength is the maximum engineering stress before necking. | null | eng_0186 | concept | en | What is ultimate tensile strength? | [
"Climb curve.",
"Top breaks soon.",
"MPa scale."
] | engineering | Answer: Peak stress.
Steps:
1. Climb curve.
2. Top breaks soon.
3. MPa scale. | materials |
The vertical component is 600 N. | null | eng_0187 | worked_example | en | Force 750 N pulls at a 3-4-5 angle. What is the vertical component? | [
"F = 750 N, sin = 4/5.",
"Fy = 0.8×750 = 600 N.",
"Result 600 N."
] | engineering | Answer: 600 N.
Steps:
1. F = 750 N, sin = 4/5.
2. Fy = 0.8×750 = 600 N.
3. Result 600 N. | statics |
Carnot efficiency is 70%. | {
"A": "70%",
"B": "75%",
"C": "65%",
"D": "80%"
} | eng_0188 | multiple_choice | en | Carnot engine between 300 K and 1000 K. What is its efficiency? | [
"Tc = 300 K, Th = 1000 K.",
"η = 1 − 300/1000 = 70%.",
"Select option A (70%)."
] | engineering | Answer: 70%.
Steps:
1. Tc = 300 K, Th = 1000 K.
2. η = 1 − 300/1000 = 70%.
3. Select option A (70%).
Answer: (A) | thermodynamics |
The tap voltage is 19 V. | null | eng_0189 | worked_example | en | Divider with two 1000 Ω resistors fed 38 V. What is the tap voltage? | [
"Vin = 38 V, halves.",
"Vout = 19 V.",
"Result 19 V."
] | engineering | Answer: 19 V.
Steps:
1. Vin = 38 V, halves.
2. Vout = 19 V.
3. Result 19 V. | circuits |
Settling time is about 52 s. | {
"A": "48 s",
"B": "56 s",
"C": "60 s",
"D": "52 s"
} | eng_0190 | multiple_choice | en | First-order system has time constant 13 s. What is 2% settling time? | [
"τ = 13 s.",
"ts ≈ 4τ = 52 s.",
"Select option D (52 s)."
] | engineering | Answer: 52 s.
Steps:
1. τ = 13 s.
2. ts ≈ 4τ = 52 s.
3. Select option D (52 s).
Answer: (D) | control |
Outlet velocity is 26 m/s. | {
"A": "24 m/s",
"B": "28 m/s",
"C": "30 m/s",
"D": "26 m/s"
} | eng_0191 | multiple_choice | en | Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 13 m/s. What is outlet velocity? | [
"A1v1 = 0.02×13 m³/s.",
"v2 = 26 m/s.",
"Select option D (26 m/s)."
] | engineering | Answer: 26 m/s.
Steps:
1. A1v1 = 0.02×13 m³/s.
2. v2 = 26 m/s.
3. Select option D (26 m/s).
Answer: (D) | fluids |
Elongation is 5 mm. | {
"A": "5 mm",
"B": "6 mm",
"C": "4 mm",
"D": "7 mm"
} | eng_0192 | multiple_choice | en | Force 50 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation? | [
"F = 50 kN, L = 2 m.",
"ΔL = FL/AE = 5 mm.",
"Select option A (5 mm)."
] | engineering | Answer: 5 mm.
Steps:
1. F = 50 kN, L = 2 m.
2. ΔL = FL/AE = 5 mm.
3. Select option A (5 mm).
Answer: (A) | materials |
A couple is two equal opposite parallel forces giving pure moment without net force. | null | eng_0193 | concept | en | What is a couple? | [
"Equal forces.",
"Opposite sense.",
"No net force."
] | engineering | Answer: Pure moment.
Steps:
1. Equal forces.
2. Opposite sense.
3. No net force. | statics |
Enthalpy is internal energy plus pressure-volume work, handy for flow processes. | null | eng_0194 | concept | en | What is enthalpy? | [
"Internal plus.",
"Flow work.",
"kJ per kg."
] | engineering | Answer: U plus pV.
Steps:
1. Internal plus.
2. Flow work.
3. kJ per kg. | thermodynamics |
The equivalent is 75 Ω. | {
"A": "80 Ω",
"B": "75 Ω",
"C": "70 Ω",
"D": "85 Ω"
} | eng_0195 | multiple_choice | en | Two 150 Ω resistors in parallel. What is the equivalent? | [
"R = 150 Ω each.",
"Req = R/2 = 75 Ω.",
"Select option B (75 Ω)."
] | engineering | Answer: 75 Ω.
Steps:
1. R = 150 Ω each.
2. Req = R/2 = 75 Ω.
3. Select option B (75 Ω).
Answer: (B) | circuits |
Overshoot is the peak excursion past the final value in percent. | null | eng_0196 | concept | en | What is overshoot? | [
"Percent peak.",
"Damping sets.",
"Less is calm."
] | engineering | Answer: Peak past final.
Steps:
1. Percent peak.
2. Damping sets.
3. Less is calm. | control |
The volume is 26 m³. | null | eng_0197 | worked_example | en | Tank base area 2 m², depth 13 m. What is the water volume? | [
"A = 2 m², h = 13 m.",
"V = Ah = 26 m³.",
"Result 26 m³."
] | engineering | Answer: 26 m³.
Steps:
1. A = 2 m², h = 13 m.
2. V = Ah = 26 m³.
3. Result 26 m³. | fluids |
The factor of safety is 3. | {
"A": "3.5 (dimensionless)",
"B": "3 (dimensionless)",
"C": "2.5 (dimensionless)",
"D": "4 (dimensionless)"
} | eng_0198 | multiple_choice | en | Yield 300 MPa, working stress 100 MPa. What is the factor of safety? | [
"σy = 300 MPa, σw = 100 MPa.",
"n = 3 (dimensionless).",
"Select option B (3 (dimensionless))."
] | engineering | Answer: 3 (dimensionless).
Steps:
1. σy = 300 MPa, σw = 100 MPa.
2. n = 3 (dimensionless).
3. Select option B (3 (dimensionless)).
Answer: (B) | materials |
A resultant is the single force replacing a system with the same effect. | null | eng_0199 | concept | en | What is a resultant force? | [
"Add vectors.",
"Same effect.",
"One force."
] | engineering | Answer: Single replacement.
Steps:
1. Add vectors.
2. Same effect.
3. One force. | statics |
The specific volume is 7 m³/kg. | null | eng_0200 | worked_example | en | Gas fills 28 m³ with mass 4 kg. What is the specific volume? | [
"V = 28 m³, m = 4 kg.",
"v = V/m = 7 m³/kg.",
"Result 7 m³/kg."
] | engineering | Answer: 7 m³/kg.
Steps:
1. V = 28 m³, m = 4 kg.
2. v = V/m = 7 m³/kg.
3. Result 7 m³/kg. | thermodynamics |
Spotřeba je 1600 Wh. | {
"A": "1500 Wh",
"B": "1700 Wh",
"C": "1600 Wh",
"D": "1650 Wh"
} | eng_0201 | multiple_choice | cs | Žárovka 800 W svítí 2 h. Kolik energie spotřebuje? | [
"P = 800 W, t = 2 h.",
"E = Pt = 1600 Wh.",
"Vyber možnost C (1600 Wh)."
] | engineering | Answer: 1600 Wh.
Steps:
1. P = 800 W, t = 2 h.
2. E = Pt = 1600 Wh.
3. Vyber možnost C (1600 Wh).
Answer: (C) | circuits |
A transfer function is output over input in Laplace form for linear systems. | null | eng_0202 | concept | en | What is a transfer function? | [
"Laplace s.",
"Gain plus dynamics.",
"Blocks multiply."
] | engineering | Answer: Output over input.
Steps:
1. Laplace s.
2. Gain plus dynamics.
3. Blocks multiply. | control |
The flow rate is 28 L/s. | {
"A": "28 L/s",
"B": "26 L/s",
"C": "30 L/s",
"D": "32 L/s"
} | eng_0203 | multiple_choice | en | Pipe area 20 cm², velocity 14 m/s. What is flow in litres per second? | [
"A = 20 cm², v = 14 m/s.",
"Q = Av = 28 L/s.",
"Select option A (28 L/s)."
] | engineering | Answer: 28 L/s.
Steps:
1. A = 20 cm², v = 14 m/s.
2. Q = Av = 28 L/s.
3. Select option A (28 L/s).
Answer: (A) | fluids |
The stress is 120 MPa. | {
"A": "110 MPa",
"B": "130 MPa",
"C": "120 MPa",
"D": "140 MPa"
} | eng_0204 | multiple_choice | en | Tensile force 12 kN on 100 mm² bar. What is the stress? | [
"F = 12 kN, A = 100 mm².",
"σ = F/A = 120 MPa.",
"Select option C (120 MPa)."
] | engineering | Answer: 120 MPa.
Steps:
1. F = 12 kN, A = 100 mm².
2. σ = F/A = 120 MPa.
3. Select option C (120 MPa).
Answer: (C) | materials |
The reaction at B is 1600 N. | null | eng_0205 | worked_example | en | Beam 6 m, load 2400 N at 4 m from A. What is reaction at B? | [
"F = 2400 N, span 6 m.",
"RB = 2400×4/6 = 1600 N.",
"Result 1600 N."
] | engineering | Answer: 1600 N.
Steps:
1. F = 2400 N, span 6 m.
2. RB = 2400×4/6 = 1600 N.
3. Result 1600 N. | statics |
Potřebné teplo je 150.48 kJ. | {
"A": "160.48 kJ",
"B": "150.48 kJ",
"C": "140.48 kJ",
"D": "170.48 kJ"
} | eng_0206 | multiple_choice | cs | 2 kg vody se ohřejí o 18 K (c = 4,18 kJ/(kg·K)). Kolik tepla? | [
"m = 2 kg, ΔT = 18 K.",
"Q = mcΔT = 150.48 kJ.",
"Vyber možnost B (150.48 kJ)."
] | engineering | Answer: 150.48 kJ.
Steps:
1. m = 2 kg, ΔT = 18 K.
2. Q = mcΔT = 150.48 kJ.
3. Vyber možnost B (150.48 kJ).
Answer: (B) | thermodynamics |
Electric power is voltage times current, measured in watts. | null | eng_0207 | concept | en | What is electric power? | [
"Volts times amps.",
"Watts out.",
"Heat or work."
] | engineering | Answer: V times I.
Steps:
1. Volts times amps.
2. Watts out.
3. Heat or work. | circuits |
Steady-state error is 5%. | {
"A": "5%",
"B": "7%",
"C": "3%",
"D": "10%"
} | eng_0208 | multiple_choice | en | Type-0 loop has position constant Kp = 19. What is step steady-state error? | [
"Kp = 19 (dimensionless).",
"ess = 100/20 = 5%.",
"Select option A (5%)."
] | engineering | Answer: 5%.
Steps:
1. Kp = 19 (dimensionless).
2. ess = 100/20 = 5%.
3. Select option A (5%).
Answer: (A) | control |
Hydraulický výkon je 3139.2 W. | null | eng_0209 | worked_example | cs | Čerpadlo zvedá 0,02 m³/s vody o 16 m. Jaký hydraulický výkon je třeba? | [
"Q = 0.02 m³/s, H = 16 m.",
"P = ρgQH = 3139.2 W.",
"Result 3139.2 W."
] | engineering | Answer: 3139.2 W.
Steps:
1. Q = 0.02 m³/s, H = 16 m.
2. P = ρgQH = 3139.2 W.
3. Result 3139.2 W. | fluids |
The mass is 133.45 kg. | null | eng_0210 | worked_example | en | Steel part volume 0.017 m³ (ρ = 7850 kg/m³). What is its mass? | [
"V = 0.017 m³, ρ = 7850 kg/m³.",
"m = ρV = 133.45 kg.",
"Result 133.45 kg."
] | engineering | Answer: 133.45 kg.
Steps:
1. V = 0.017 m³, ρ = 7850 kg/m³.
2. m = ρV = 133.45 kg.
3. Result 133.45 kg. | materials |
Moment je síla krát kolmá vzdálenost, jednotka newtonmetr. | null | eng_0211 | concept | cs | Co je moment síly? | [
"Síla v N.",
"Rameno v m.",
"Moment v N·m."
] | engineering | Answer: Síla krát rameno.
Steps:
1. Síla v N.
2. Rameno v m.
3. Moment v N·m. | statics |
The Carnot cycle is the ideal reversible engine setting maximum efficiency between temperatures. | null | eng_0212 | concept | en | What is the Carnot cycle? | [
"Two isotherms.",
"Two adiabats.",
"Sets limit."
] | engineering | Answer: Ideal max engine.
Steps:
1. Two isotherms.
2. Two adiabats.
3. Sets limit. | thermodynamics |
The leaving current is 20 A. | null | eng_0213 | worked_example | en | Currents 2 A and 18 A enter a node. What current leaves? | [
"I1 = 2 A, I2 = 18 A.",
"I3 = 20 A.",
"Result 20 A."
] | engineering | Answer: 20 A.
Steps:
1. I1 = 2 A, I2 = 18 A.
2. I3 = 20 A.
3. Result 20 A. | circuits |
The error is 65 units. | null | eng_0214 | worked_example | en | Setpoint 650 units, measurement 585 units. What is the error? | [
"r = 650 units, y = 585 units.",
"e = r−y = 65 units.",
"Result 65 units."
] | engineering | Answer: 65 units.
Steps:
1. r = 650 units, y = 585 units.
2. e = r−y = 65 units.
3. Result 65 units. | control |
Archimédův zákon říká, že vztlak je tíha vytlačené kapaliny. | null | eng_0215 | concept | cs | Co je Archimédův zákon? | [
"Objem ponořen.",
"Krát ró gé.",
"Lehké plave."
] | engineering | Answer: Tíha vytlačeného.
Steps:
1. Objem ponořen.
2. Krát ró gé.
3. Lehké plave. | fluids |
The strain is 1200 microstrain. | {
"A": "1100 microstrain",
"B": "1300 microstrain",
"C": "1400 microstrain",
"D": "1200 microstrain"
} | eng_0216 | multiple_choice | en | Bar 1000 mm stretches 1.2 mm. What is the strain? | [
"ΔL = 1.2 mm, L = 1000 mm.",
"ε = 1200 microstrain.",
"Select option D (1200 microstrain)."
] | engineering | Answer: 1200 microstrain.
Steps:
1. ΔL = 1.2 mm, L = 1000 mm.
2. ε = 1200 microstrain.
3. Select option D (1200 microstrain).
Answer: (D) | materials |
Tření je odpor proti skluzu, nejvýše mí krát normálová síla. | null | eng_0217 | concept | cs | Co je tření? | [
"Normála v N.",
"Mí faktor.",
"Brání skluzu."
] | engineering | Answer: Mí krát normála.
Steps:
1. Normála v N.
2. Mí faktor.
3. Brání skluzu. | statics |
The power is 800 W. | null | eng_0218 | worked_example | en | Work 8000 J is done in 10 s. What is the power? | [
"W = 8000 J, t = 10 s.",
"P = W/t = 800 W.",
"Result 800 W."
] | engineering | Answer: 800 W.
Steps:
1. W = 8000 J, t = 10 s.
2. P = W/t = 800 W.
3. Result 800 W. | thermodynamics |
Proudy vstupující do uzlu se rovnají proudům vystupujícím. | null | eng_0219 | concept | cs | Co je Kirchhoffův zákon proudů? | [
"Součet v A.",
"Vstup rovná výstup.",
"Náboj se drží."
] | engineering | Answer: Proudy se rovnají.
Steps:
1. Součet v A.
2. Vstup rovná výstup.
3. Náboj se drží. | circuits |
The final value is 42 units. | null | eng_0220 | worked_example | en | Gain 14 system gets a step of amplitude 3. What is the final value? | [
"K = 14 (dimensionless), step 3 units.",
"Final = 3×14 = 42 units.",
"Result 42 units."
] | engineering | Answer: 42 units.
Steps:
1. K = 14 (dimensionless), step 3 units.
2. Final = 3×14 = 42 units.
3. Result 42 units. | control |
The Reynolds number is 350000. | {
"A": "325000 (dimensionless)",
"B": "350000 (dimensionless)",
"C": "375000 (dimensionless)",
"D": "400000 (dimensionless)"
} | eng_0221 | multiple_choice | en | Water at 7 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number? | [
"ρ = 1000 kg/m³, v = 7 m/s, D = 0.05 m.",
"Re = ρvD/μ = 350000 (dimensionless).",
"Select option B (350000 (dimensionless))."
] | engineering | Answer: 350000 (dimensionless).
Steps:
1. ρ = 1000 kg/m³, v = 7 m/s, D = 0.05 m.
2. Re = ρvD/μ = 350000 (dimensionless).
3. Select option B (350000 (dimensionless)).
Answer: (B) | fluids |
Mez kluzu je napětí, kde začíná trvalá deformace. | null | eng_0222 | concept | cs | Co je mez kluzu? | [
"Pod ní pružné.",
"Nad ní ohne.",
"Limit návrhu."
] | engineering | Answer: Začátek plastiky.
Steps:
1. Pod ní pružné.
2. Nad ní ohne.
3. Limit návrhu. | materials |
Each end reaction is 1000 N. | null | eng_0223 | worked_example | en | Uniform beam weighs 2000 N over 8 m. What is each end reaction? | [
"W = 2000 N, midspan 4 m.",
"R = W/2 = 1000 N.",
"Result 1000 N."
] | engineering | Answer: 1000 N.
Steps:
1. W = 2000 N, midspan 4 m.
2. R = W/2 = 1000 N.
3. Result 1000 N. | statics |
A heat engine turns heat into work between hot and cold reservoirs. | null | eng_0224 | concept | en | What is a heat engine? | [
"Hot source.",
"Cold sink.",
"Work out."
] | engineering | Answer: Heat to work.
Steps:
1. Hot source.
2. Cold sink.
3. Work out. | thermodynamics |
The stored charge is 9000 μC. | null | eng_0225 | worked_example | en | Capacitor 900 μF charged to 10 V. What charge is stored? | [
"C = 900 μF, V = 10 V.",
"Q = CV = 9000 μC.",
"Result 9000 μC."
] | engineering | Answer: 9000 μC.
Steps:
1. C = 900 μF, V = 10 V.
2. Q = CV = 9000 μC.
3. Result 9000 μC. | circuits |
Ustálená odchylka je trvalý rozdíl cíle a výstupu. | null | eng_0226 | concept | cs | Co je ustálená odchylka? | [
"Počkej dlouho.",
"Odečti offset.",
"Typ určuje."
] | engineering | Answer: Trvalý rozdíl.
Steps:
1. Počkej dlouho.
2. Odečti offset.
3. Typ určuje. | control |
Base pressure is 166.77 kPa. | null | eng_0227 | worked_example | en | Still water column 17 m high. What is pressure at the base? | [
"ρ = 1000 kg/m³, h = 17 m.",
"p = ρgh = 166.77 kPa.",
"Result 166.77 kPa."
] | engineering | Answer: 166.77 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 17 m.
2. p = ρgh = 166.77 kPa.
3. Result 166.77 kPa. | fluids |
The stress is 140 MPa. | {
"A": "140 MPa",
"B": "130 MPa",
"C": "150 MPa",
"D": "160 MPa"
} | eng_0228 | multiple_choice | en | Steel (E = 200 GPa) at strain 700 microstrain. What is the stress? | [
"E = 200 GPa, ε = 700 microstrain.",
"σ = Eε = 140 MPa.",
"Select option A (140 MPa)."
] | engineering | Answer: 140 MPa.
Steps:
1. E = 200 GPa, ε = 700 microstrain.
2. σ = Eε = 140 MPa.
3. Select option A (140 MPa).
Answer: (A) | materials |
The balancing reaction is 900 N upward. | {
"A": "950 N",
"B": "900 N",
"C": "850 N",
"D": "1000 N"
} | eng_0229 | multiple_choice | en | Downward forces 360 N and 540 N act on a beam. What upward reaction balances them? | [
"F1 = 360 N, F2 = 540 N.",
"R = 360+540 = 900 N.",
"Select option B (900 N)."
] | engineering | Answer: 900 N.
Steps:
1. F1 = 360 N, F2 = 540 N.
2. R = 360+540 = 900 N.
3. Select option B (900 N).
Answer: (B) | statics |
Internal energy rises 100 kJ. | {
"A": "105 kJ",
"B": "95 kJ",
"C": "100 kJ",
"D": "110 kJ"
} | eng_0230 | multiple_choice | en | System gains 190 kJ of heat and does 90 kJ of work. What is internal energy change? | [
"Q = 190 kJ, W = 90 kJ.",
"ΔU = Q−W = 100 kJ.",
"Select option C (100 kJ)."
] | engineering | Answer: 100 kJ.
Steps:
1. Q = 190 kJ, W = 90 kJ.
2. ΔU = Q−W = 100 kJ.
3. Select option C (100 kJ).
Answer: (C) | thermodynamics |
The power lost is 360 W. | null | eng_0231 | worked_example | en | Current 2 A through 90 Ω. What power is lost? | [
"I = 2 A, R = 90 Ω.",
"P = I²R = 360 W.",
"Result 360 W."
] | engineering | Answer: 360 W.
Steps:
1. I = 2 A, R = 90 Ω.
2. P = I²R = 360 W.
3. Result 360 W. | circuits |
Settling time is about 45 s. | null | eng_0232 | worked_example | en | Time constant 15 s. What is 5% settling time? | [
"τ = 15 s.",
"ts ≈ 3τ = 45 s.",
"Result 45 s."
] | engineering | Answer: 45 s.
Steps:
1. τ = 15 s.
2. ts ≈ 3τ = 45 s.
3. Result 45 s. | control |
The exit velocity is 15 m/s. | null | eng_0233 | worked_example | en | Tank head 11.25 m (take g = 10 m/s²). What is the Torricelli velocity? | [
"h = 11.25 m, g = 10 m/s².",
"v = √(2gh) = 15 m/s.",
"Result 15 m/s."
] | engineering | Answer: 15 m/s.
Steps:
1. h = 11.25 m, g = 10 m/s².
2. v = √(2gh) = 15 m/s.
3. Result 15 m/s. | fluids |
Ductile materials stretch plastically before breaking, while brittle ones snap with little strain. | null | eng_0234 | concept | en | How do ductile and brittle differ? | [
"Steel stretches.",
"Glass snaps.",
"Elongation tells."
] | engineering | Answer: Stretch versus snap.
Steps:
1. Steel stretches.
2. Glass snaps.
3. Elongation tells. | materials |
A free-body diagram shows an isolated body with all acting forces and reactions. | null | eng_0235 | concept | en | What is a free-body diagram? | [
"Cut free.",
"Draw forces.",
"Solve equilibrium."
] | engineering | Answer: Isolated body sketch.
Steps:
1. Cut free.
2. Draw forces.
3. Solve equilibrium. | statics |
The temperature is 368 K. | {
"A": "363 K",
"B": "373 K",
"C": "378 K",
"D": "368 K"
} | eng_0236 | multiple_choice | en | Temperature is 95 °C. What is it in kelvin? | [
"T = 95 °C.",
"K = 95 + 273 = 368 K.",
"Select option D (368 K)."
] | engineering | Answer: 368 K.
Steps:
1. T = 95 °C.
2. K = 95 + 273 = 368 K.
3. Select option D (368 K).
Answer: (D) | thermodynamics |
A capacitor stores charge and blocks steady direct current. | null | eng_0237 | concept | en | What does a capacitor do? | [
"Plates hold Q.",
"DC blocked.",
"AC passes."
] | engineering | Answer: Stores charge.
Steps:
1. Plates hold Q.
2. DC blocked.
3. AC passes. | circuits |
Poles are transfer function roots setting speed and stability of modes. | null | eng_0238 | concept | en | What are poles? | [
"Denominator zero.",
"Left is stable.",
"Right blows."
] | engineering | Answer: Stability roots.
Steps:
1. Denominator zero.
2. Left is stable.
3. Right blows. | control |
Vztlak je 156960 N. | {
"A": "147150 N",
"B": "166770 N",
"C": "156960 N",
"D": "176580 N"
} | eng_0239 | multiple_choice | cs | Trup vytlačí 16 m³ vody. Jaký je vztlak? | [
"V = 16 m³, ρ = 1000 kg/m³.",
"F = ρgV = 156960 N.",
"Vyber možnost C (156960 N)."
] | engineering | Answer: 156960 N.
Steps:
1. V = 16 m³, ρ = 1000 kg/m³.
2. F = ρgV = 156960 N.
3. Vyber možnost C (156960 N).
Answer: (C) | fluids |
Elongation is 7.5 mm. | {
"A": "8.5 mm",
"B": "7.5 mm",
"C": "6.5 mm",
"D": "9.5 mm"
} | eng_0240 | multiple_choice | en | Force 75 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation? | [
"F = 75 kN, L = 2 m.",
"ΔL = FL/AE = 7.5 mm.",
"Select option B (7.5 mm)."
] | engineering | Answer: 7.5 mm.
Steps:
1. F = 75 kN, L = 2 m.
2. ΔL = FL/AE = 7.5 mm.
3. Select option B (7.5 mm).
Answer: (B) | materials |
Coulomb friction caps at mu times normal force and opposes slipping. | null | eng_0241 | concept | en | What is Coulomb friction? | [
"Normal in N.",
"Mu factor.",
"Opposes motion."
] | engineering | Answer: Mu times normal.
Steps:
1. Normal in N.
2. Mu factor.
3. Opposes motion. | statics |
The efficiency is 25%. | null | eng_0242 | worked_example | en | Engine turns 250 J of 1000 J heat into work. What is the efficiency? | [
"W = 250 J, Q = 1000 J.",
"η = W/Q = 25%.",
"Result 25%."
] | engineering | Answer: 25%.
Steps:
1. W = 250 J, Q = 1000 J.
2. η = W/Q = 25%.
3. Result 25%. | thermodynamics |
The voltage is 204 V. | {
"A": "192 V",
"B": "216 V",
"C": "228 V",
"D": "204 V"
} | eng_0243 | multiple_choice | en | Current 17 A flows through 12 Ω. What is the voltage? | [
"I = 17 A, R = 12 Ω.",
"V = IR = 204 V.",
"Select option D (204 V)."
] | engineering | Answer: 204 V.
Steps:
1. I = 17 A, R = 12 Ω.
2. V = IR = 204 V.
3. Select option D (204 V).
Answer: (D) | circuits |
The Routh criterion tests stability from characteristic coefficients without solving. | null | eng_0244 | concept | en | What is the Routh criterion? | [
"Build array.",
"First column.",
"Sign flips bad."
] | engineering | Answer: Table test.
Steps:
1. Build array.
2. First column.
3. Sign flips bad. | control |
Torricelli's law gives exit velocity as root of two g h under gravity. | null | eng_0245 | concept | en | What is Torricelli's law? | [
"Head in m.",
"g pulls.",
"v in m/s."
] | engineering | Answer: Root two g h.
Steps:
1. Head in m.
2. g pulls.
3. v in m/s. | fluids |
Hardness is resistance to surface indentation, ranked by Brinell or Rockwell scales. | null | eng_0246 | concept | en | What is hardness? | [
"Press indenter.",
"Small dent hard.",
"Wear link."
] | engineering | Answer: Dent resistance.
Steps:
1. Press indenter.
2. Small dent hard.
3. Wear link. | materials |
Výsledný moment je 740 N·m po směru. | null | eng_0247 | worked_example | cs | 500 N ve 4 m po směru, 420 N ve 3 m proti směru. Jaký je výsledný moment? | [
"M1 = 500×4 = 2000 N·m.",
"M2 = 420×3 = 1260 N·m.",
"Net 740 N·m."
] | engineering | Answer: 740 N·m.
Steps:
1. M1 = 500×4 = 2000 N·m.
2. M2 = 420×3 = 1260 N·m.
3. Net 740 N·m. | statics |
Refrigerator COP is cooling delivered per unit of work input. | null | eng_0248 | concept | en | What is a refrigerator COP? | [
"Q cold.",
"W in.",
"Ratio counts."
] | engineering | Answer: Cooling per work.
Steps:
1. Q cold.
2. W in.
3. Ratio counts. | thermodynamics |
The current is 20 A. | null | eng_0249 | worked_example | en | Voltage 120 V across 6 Ω. What is the current? | [
"V = 120 V, R = 6 Ω.",
"I = V/R = 20 A.",
"Result 20 A."
] | engineering | Answer: 20 A.
Steps:
1. V = 120 V, R = 6 Ω.
2. I = V/R = 20 A.
3. Result 20 A. | circuits |
A Bode plot shows gain and phase versus frequency on log scales. | null | eng_0250 | concept | en | What is a Bode plot? | [
"dB magnitude.",
"Degrees phase.",
"Margins read."
] | engineering | Answer: Gain phase curves.
Steps:
1. dB magnitude.
2. Degrees phase.
3. Margins read. | control |
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