Workshop Calculation and Science
Workshop Calculation and Science tests the numerical and physical reasoning used at the machine or bench: areas, volumes, mass, taper, force, stress, work, power, and simple electricity.
Core formulas
- Circle area A = πd²/4; circumference = πd.
- Cylinder volume V = πd²L/4; mass = volume × density.
- Taper = (D − d)/L; half-angle tan θ = (D − d)/(2L).
- Stress σ = F/A; strain ε = ΔL/L; Young's modulus E = σ/ε.
- Work = force × distance; power = work/time; efficiency = output/input.
Worked example
A 20 mm diameter mild steel bar carries a tensile load of 30 kN. Calculate the stress. A = πd²/4 = π × 20²/4 = 314.16 mm². σ = F/A = 30000/314.16 = 95.5 N/mm² (MPa). If the yield strength is 250 MPa, the factor of safety is 250/95.5 ≈ 2.6. The reasoning: convert kN to N, use the diameter directly in the area formula, and keep the result in N/mm², which is the same as MPa.
Traps
Using radius in πd²/4; forgetting to convert kN to N; mixing mass (kg) with weight (N); using the included taper angle instead of the half-angle; rounding intermediate values too early.