Question Number 208789 by Tawa11 last updated on 23/Jun/24
$$\mathrm{Why}\:\mathrm{is}\:\mathrm{surface}\:\mathrm{tension}\:\mathrm{formula}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L} \\ $$$$\mathrm{that}\:\mathrm{is},\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L}. \\ $$$$\mathrm{Where}\:\mathrm{did}\:\mathrm{the}\:\mathrm{2}\:\mathrm{come}\:\mathrm{from}? \\ $$$$ \\ $$$$\mathrm{Example}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{force}\:\mathrm{required}\:\mathrm{to}\:\mathrm{lift}\:\mathrm{a}\:\mathrm{needle} \\ $$$$\mathrm{4cm}\:\mathrm{long}\:\mathrm{off}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{water},\:\mathrm{if}\:\mathrm{surface} \\ $$$$\mathrm{tension}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{−\mathrm{4}} \mathrm{Nm}^{−\:\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{the}\:\mathrm{formula}\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{not}\:\:\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{L}} \\ $$
Commented by mr W last updated on 23/Jun/24
$${surface}\:=\:{perimeter} \\ $$$${if}\:{the}\:{width}\:{of}\:{your}\:{hand}\:{is}\:{L},\:{and} \\ $$$${you}\:{put}\:{your}\:{hand}\:{into}\:{water},\: \\ $$$${your}\:{hand}\:{has}\:{two}\:{sides},\:{both}\: \\ $$$${sides}\:{cantact}\:{water}.\:\:{this}\:{is} \\ $$$${where}\:{the}\:\mathrm{2}\:{comes}\:{from}. \\ $$$${to}\:{be}\:{exact},\:{it}\:{is}\:\frac{{F}}{\mathrm{2}{L}+\mathrm{2}{D}},\:{but}\:{since} \\ $$$${the}\:{thickness}\:{D}\:{is}\:{very}\:{small}\: \\ $$$${compared}\:{with}\:{its}\:{length}\:{L},\:{so}\:{we} \\ $$$${can}\:{say}\:\frac{{F}}{\mathrm{2}{L}+\mathrm{2}{B}}\approx\frac{{F}}{\mathrm{2}{L}} \\ $$
Commented by mr W last updated on 23/Jun/24
Commented by Tawa11 last updated on 23/Jun/24
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$