A force of \(120\,\mathrm{N}\) acts on an area of \(0.040\,\mathrm{m}^{2}\). Calculate the pressure.
\(P = F/A = 120/0.040 = 3000\,\mathrm{Pa}\).
Pressure & Moments
8 exam-style questions on pressure in solids, liquids and gases, and moments. Tap Show answer for full working.
3 Easy3 Medium2 Hard
A force of \(8.0\,\mathrm{N}\) acts at a perpendicular distance of \(0.25\,\mathrm{m}\) from a pivot. Calculate the moment.
Moment \(= F\times d = 8.0\times0.25 = 2.0\,\mathrm{N\,m}\).
State the principle of moments.
For an object in equilibrium, the total clockwise moment about a pivot equals the total anticlockwise moment about the same pivot.
Calculate the pressure at a depth of \(12\,\mathrm{m}\) in a lake. (Density of water \(= 1000\,\mathrm{kg\,m}^{-3}\), \(g = 9.8\,\mathrm{N\,kg}^{-1}\).)
\(P = \rho gh = 1000\times9.8\times12 = 118\,000\,\mathrm{Pa}\) (\(1.18\times10^{5}\,\mathrm{Pa}\)).
A see-saw is balanced. A child of weight \(300\,\mathrm{N}\) sits \(2.0\,\mathrm{m}\) from the pivot. Where must a child of weight \(400\,\mathrm{N}\) sit to balance the see-saw?
\(300\times2.0 = 400\times d \Rightarrow d = 600/400 = 1.5\,\mathrm{m}\) from the pivot (on the other side).
Explain why a sharp knife cuts more easily than a blunt knife when the same force is applied.
A sharp knife has a smaller contact area. Pressure \(P = F/A\), so for the same force a smaller area gives a larger pressure, which is more likely to cut the material.
A hydraulic system has a small piston of area \(0.0020\,\mathrm{m}^{2}\) and a large piston of area \(0.080\,\mathrm{m}^{2}\). A force of \(50\,\mathrm{N}\) is applied to the small piston. Calculate the pressure in the fluid and the force on the large piston.
\(P = F/A = 50/0.0020 = 25\,000\,\mathrm{Pa}\).
Force on large piston \(= P\times A = 25000\times0.080 = 2000\,\mathrm{N}\).
A gas is trapped in a syringe. The volume is reduced from \(50\,\mathrm{cm}^{3}\) to \(20\,\mathrm{cm}^{3}\) at constant temperature. The initial pressure is \(100\,\mathrm{kPa}\). Calculate the final pressure. State the law used.
Boyle’s law: \(pV = \mathrm{constant}\) (at constant temperature).
\(p_{2} = p_{1}V_{1}/V_{2} = 100\times50/20 = 250\,\mathrm{kPa}\).