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Question Number 208789 by Tawa11 last updated on 23/Jun/24
Why is surface tension formula divided by  2L  that is,    surface tension  =  (F/(2L))  why divided by  2L.  Where did the 2 come from?    Example.  Calculate the force required to lift a needle  4cm long off the surface of water, if surface  tension of water is  7.3 × 10^(−4) Nm^(− 1)     Why is the formula   surface tension  =  (F/(2L))  why not      surface tension  =  (F/L)
$$\mathrm{Why}\:\mathrm{is}\:\mathrm{surface}\:\mathrm{tension}\:\mathrm{formula}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L} \\ $$$$\mathrm{that}\:\mathrm{is},\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L}. \\ $$$$\mathrm{Where}\:\mathrm{did}\:\mathrm{the}\:\mathrm{2}\:\mathrm{come}\:\mathrm{from}? \\ $$$$ \\ $$$$\mathrm{Example}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{force}\:\mathrm{required}\:\mathrm{to}\:\mathrm{lift}\:\mathrm{a}\:\mathrm{needle} \\ $$$$\mathrm{4cm}\:\mathrm{long}\:\mathrm{off}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{water},\:\mathrm{if}\:\mathrm{surface} \\ $$$$\mathrm{tension}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{−\mathrm{4}} \mathrm{Nm}^{−\:\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{the}\:\mathrm{formula}\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{not}\:\:\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{L}} \\ $$
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 2 comes from.  to be exact, it is (F/(2L+2D)), but since  the thickness D is very small   compared with its length L, so we  can say (F/(2L+2B))≈(F/(2L))
$${surface}\:=\:{perimeter} \\ $$$${if}\:{the}\:{width}\:{of}\:{your}\:{hand}\:{is}\:{L},\:{and} \\ $$$${you}\:{put}\:{your}\:{hand}\:{into}\:{water},\: \\ $$$${your}\:{hand}\:{has}\:{two}\:{sides},\:{both}\: \\ $$$${sides}\:{cantact}\:{water}.\:\:{this}\:{is} \\ $$$${where}\:{the}\:\mathrm{2}\:{comes}\:{from}. \\ $$$${to}\:{be}\:{exact},\:{it}\:{is}\:\frac{{F}}{\mathrm{2}{L}+\mathrm{2}{D}},\:{but}\:{since} \\ $$$${the}\:{thickness}\:{D}\:{is}\:{very}\:{small}\: \\ $$$${compared}\:{with}\:{its}\:{length}\:{L},\:{so}\:{we} \\ $$$${can}\:{say}\:\frac{{F}}{\mathrm{2}{L}+\mathrm{2}{B}}\approx\frac{{F}}{\mathrm{2}{L}} \\ $$
Commented by mr W last updated on 23/Jun/24
Commented by Tawa11 last updated on 23/Jun/24
Thanks sir.  I appreciate.
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$

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