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Sample Senegal Baccalauréat Série T1 Practice Questions
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1In mechanical engineering kinematics, how many degrees of freedom (DoF) are eliminated (restrained) by an ideal pivot joint (liaison pivot) in three-dimensional space?
A.5 degrees of freedom (restraining 3 translations and 2 rotations)
B.4 degrees of freedom (restraining 2 translations and 2 rotations)
C.3 degrees of freedom (restraining 3 translations only)
D.1 degree of freedom (restraining 1 rotation only)
Explanation: In 3D space, a rigid body possesses 6 degrees of freedom (3 translations Tx, Ty, Tz and 3 rotations Rx, Ry, Rz). A standard revolute or pivot joint allows only a single rotation around its axis (e.g., Rz = 1) while blocking all 3 translations (Tx=0, Ty=0, Tz=0) and the remaining 2 rotations (Rx=0, Ry=0), thereby restraining 6 - 1 = 5 degrees of freedom.
2A cylindrical steel tie-rod of original length L0 = 2.0 m and cross-sectional area S = 100 mm² is subjected to an axial tensile force N = 21 kN. If Young's modulus for steel is E = 210 GPa (210,000 MPa), what is the total elastic elongation (ΔL) of the rod?
A.1.0 mm
B.2.0 mm
C.0.2 mm
D.4.0 mm
Explanation: Applying Hooke's Law for uniaxial tension: ΔL = (N * L0) / (E * S). Substituting the values: N = 21,000 N, L0 = 2000 mm, E = 210,000 N/mm², S = 100 mm². Thus: ΔL = (21,000 * 2000) / (210,000 * 100) = 42,000,000 / 21,000,000 = 2.0 mm.
3A spur gear has a module m = 2.5 mm and z = 36 teeth. What is the pitch diameter (d) and the circular pitch (p) of this gear?
A.d = 72 mm and p = 5.0 mm
B.d = 144 mm and p = 15.7 mm
C.d = 90 mm and p ≈ 7.85 mm
D.d = 90 mm and p = 2.5 mm
Explanation: In standard spur gearing: pitch diameter d = m * z = 2.5 mm * 36 = 90 mm. The circular pitch (pas primitif) is p = π * m = π * 2.5 mm ≈ 7.854 mm.
4An electric motor delivers a mechanical power P = 7.5 kW at a rotational speed N = 1432 rpm. What is the output torque (C) produced at the motor shaft?
A.25.0 N·m
B.105.0 N·m
C.75.0 N·m
D.50.0 N·m
Explanation: Mechanical power is related to torque by P = C * ω, where angular velocity ω = (2 * π * N) / 60. Here ω = (2 * π * 1432) / 60 ≈ 149.96 rad/s ≈ 150 rad/s. Torque C = P / ω = 7500 W / 149.96 rad/s ≈ 50.01 N·m.
5In the strength of materials (RDM), what is the condition of elastic resistance for a machine member subjected to pure tensile normal stress σ under an allowable stress Rpe?
A.σ = N / S ≤ Rpe, where Rpe = Re / s (with s being the safety factor)
B.σ = N * S ≤ Re * s
C.σ = N / (2S) ≥ Rpe
D.σ = (N * s) / S ≤ Rm
Explanation: The basic resistance criterion in pure tension states that the acting normal stress σ = N / S must not exceed the elastic practical resistance (résistance pratique à l'extension, Rpe). Rpe is defined as the yield strength Re divided by a safety factor s (Rpe = Re / s), ensuring the material remains safely within its elastic regime.
6Which type of rolling-element bearing is specifically designed to accommodate combined loads consisting of both heavy radial forces and significant unidirectional axial thrust forces?
A.Needle roller bearing (roulement à aiguilles)
B.Tapered roller bearing (roulement à rouleaux coniques)
C.Self-aligning ball bearing (roulement à rotule sur billes)
D.Deep groove radial ball bearing with non-locating snap ring
Explanation: Tapered roller bearings (roulements à rouleaux coniques) feature raceways arranged at an angle to the bearing axis. This geometry enables them to withstand large simultaneous radial and unidirectional axial loads. They are typically mounted in opposing pairs (O or X configurations) on machine tool spindles and automotive hubs.
7A solid circular drive shaft of diameter d = 40 mm is subjected to a pure twisting torque Mt = 500 N·m. What is the maximum torsional shear stress (τmax) induced in the outer fibers of the shaft? (Take π ≈ 3.1416)
A.19.9 MPa
B.79.6 MPa
C.39.8 MPa
D.159.2 MPa
Explanation: For a circular shaft in torsion, maximum shear stress occurs at the outer surface: τmax = Mt / (I0 / R) = (16 * Mt) / (π * d³). Here d = 40 mm = 0.04 m, Mt = 500 N·m. Substituting: τmax = (16 * 500) / (π * 0.04³) = 8000 / (π * 0.000064) = 8000 / 0.00020106 ≈ 39,788,735 Pa ≈ 39.8 MPa (or 39.8 N/mm²).
8A two-stage reduction gearbox has driving pinion 1 with z1 = 18 teeth meshing with gear 2 with z2 = 72 teeth. Gear 2 is mounted on an intermediate shaft that also carries pinion 3 with z3 = 20 teeth, which meshes with output gear 4 with z4 = 80 teeth. If input shaft speed is N_in = 1440 rpm, what is the output speed (N_out)?
A.360 rpm
B.180 rpm
C.240 rpm
D.90 rpm
Explanation: The overall reduction ratio of a compound gear train is the product of the individual stage ratios: r = (z1 / z2) * (z3 / z4) = (18 / 72) * (20 / 80) = (1 / 4) * (1 / 4) = 1 / 16. Therefore, output speed N_out = N_in * r = 1440 rpm / 16 = 90 rpm.
9Which ISO tolerance fit is classified as a transition fit (ajustement incertain) where parts may exhibit either a small clearance or a slight interference depending on actual manufactured dimensions?
A.H7/js6
B.H7/g6
C.H7/p6
D.H7/f7
Explanation: In the ISO system of limits and fits, hole H has a lower deviation of zero (EI = 0). Shaft letter 'js' provides a symmetrical tolerance zone centered around the nominal size (es = +IT/2, ei = -IT/2). Consequently, H7/js6 represents a classic transition fit where mating parts can assemble with either light clearance or light interference.
10A rectangular steel beam of width b = 40 mm and height h = 90 mm is subjected to pure bending. What is the elastic section modulus (I_Gz / v) of this cross-section with respect to its neutral bending axis?
A.27,000 mm³
B.54,000 mm³
C.108,000 mm³
D.81,000 mm³
Explanation: For a rectangular cross-section of width b and depth h, the second moment of area is I_Gz = (b * h³) / 12, and the distance to the extreme fiber is v = h / 2. The elastic section modulus is (I_Gz / v) = (b * h²) / 6. Substituting b = 40 mm and h = 90 mm: (40 * 90²) / 6 = (40 * 8100) / 6 = 324,000 / 6 = 54,000 mm³.
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