Workshop Calculation: Mass, Density, Force, Work, Power and Energy
Mass, density, force, work, power and energy
This domain tests the SI relationships between mass, volume, density, weight, force, work, power and energy. Workshop questions commonly involve the mass of a bar, the force to lift a load and the power needed over a given time.
Core rules
- Density ρ = mass/volume; mass = ρV; volume = m/ρ.
- 1 g/cm³ = 1000 kg/m³; steel is about 7.85 g/cm³ or 7850 kg/m³.
- Weight is a force: W = mg, with g ≈ 9.81 m/s². Mass is in kg; weight is in N.
- Work done by a constant force along the displacement: W = Fs (joules).
- Power = work/time = energy/time (watts); 1 kW = 1000 W.
- Energy is the capacity to do work; 1 kWh = 3.6 MJ.
Worked example
A steel block measures 0.20 m × 0.10 m × 0.10 m, so V = 0.002 m³. With ρ = 7850 kg/m³, mass = 7850 × 0.002 = 15.7 kg. Weight = mg = 15.7 × 9.81 = 154 N approximately. Lifting it 2 m does work = 154 × 2 = 308 J. If the lift takes 4 s, average power = 308/4 = 77 W. The reasoning is to find mass from density and volume, convert mass to weight, then apply work and power definitions.
Traps
- Treating mass in kg as weight in N.
- Mixing g/cm³ with kg/m³ without the factor of 1000.
- Counting a force perpendicular to motion as doing work.
- Confusing power (W) with energy (J or kWh).
- Using g = 10 when the question expects 9.81.