The Young modulus of a material has the unit Pa.
(a) Show that the pascal can be expressed in SI base units as kg m$^{-1}$ s$^{-2}$. [2]
(b) The Young modulus of a polymer is 3.2 GPa. Write this value in Pa, using standard form. [1]
- (a) Pa = N m$^{-2}$ (from pressure = force / area)(1)
- (a) N = kg m s$^{-2}$ (from $F = ma$) so Pa = kg m s$^{-2}$ $\times$ m$^{-2}$ = kg m$^{-1}$ s$^{-2}$ (must see both steps; answer given)(1)
- (b) $3.2 \times 10^{9}$ Pa(1)
- Answer: (a) Pa = N m$^{-2}$ = kg m s$^{-2}$ m$^{-2}$ = kg m$^{-1}$ s$^{-2}$ (b) $3.2\times10^{9}$ Pa
- Examiner tip: In 'show that' unit questions every substitution must be written out — just stating the final unit scores nothing.