Mechanics and Materials

WPH11Unit 16 topics · 22 questions

Key equations

The relationships this unit leans on most. Check your formulae or data booklet for which ones the exam gives you.

$v = u + at$: final velocity from initial velocity $u$ , acceleration $a$ and time

1.4Work, energy and power3 questions

a

t

$s = \tfrac{1}{2}(u + v)t$

displacement from the average of the start and end velocities

$s = ut + \tfrac{1}{2}at^2$

displacement under constant acceleration

$v^2 = u^2 + 2as$

links velocities and displacement without time

$\Sigma F = ma$: resultant force equals mass × acceleration (Newton's second law)
$W = mg$: weight from mass and gravitational field strength $g$
$\text{moment} = Fx$: force × perpendicular distance from the pivot

$\Delta W = F\Delta s$: work done by a force along its line of action
$E_k = \tfrac{1}{2}mv^2$: kinetic energy
$\Delta E_{\text{grav}} = mg\Delta h$: change in gravitational potential energy near the Earth
$P = \dfrac{E}{t} = \dfrac{W}{t}$
$\text{efficiency} = \dfrac{\text{useful output}}{\text{total input}}$: for energy or power; never more than 1 (100%)

$\rho = \dfrac{m}{V}$: density from mass and volume
$\text{upthrust} = \text{weight of fluid displaced}$: Archimedes' principle
$F = 6\pi\eta r v$: Stokes' law: drag on a small sphere in laminar flow ( $\eta$ = viscosity)

$\Delta F = k\Delta x$: Hooke's law, up to the limit of proportionality
$\sigma = \dfrac{F}{A}$: stress: force per cross-sectional area
$\varepsilon = \dfrac{\Delta x}{x}$: strain: extension over original length (no units)
$E = \dfrac{\sigma}{\varepsilon}$: Young modulus
$\Delta E_{\text{el}} = \tfrac{1}{2}F\Delta x$

power is the rate of transferring energy or doing work

x

elastic strain energy: area under a force–extension line