Question

Two balls of identical mass of 1.179 kg and with identical charges placed on them hang from the ceiling on identical strings of lengths 1.110 m as shown. If the angle with respect to thee vertical that the strings form is 28.5 degrees, what is the charge on each ball? Please give your answer in micro-coulomb (i.e. do not enter a unit, but calculate your answer in micro- coulomb) Submit Answer Incorrect. Tries 4/20 Previous Tries

First Person got it wrong and they said .03 or .009

Answer 1

First find distance d

$sin\theta =(d/2)/l$

$sin28.5 =(d/2)/1.11m$

$1.11sin28.5 =d/2$

${\color{Red} d=1.06m}$

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Find Tension

Consider all vertical forces

$\sum F_{y}=0$

$Tcos28.5 =mg$

$T =1.179kg*9.81/cos28.5$

${\color{Red} T =13.16N}$

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Consider all Horizontal Forces

$\sum F_{x}=0$

$F=Tsin28.5$

$kq^{2}/d^{2}=Tsin28.5$

charges are identical

$9*10^{9}*q^{2}/(1.06m)^{2}=13.16N*sin28.5$

$q^{2}=13.16*sin28.5*1.06^{2}/(9*10^{9})$

$q=2.8*10^{-5}C$

ANSWER: ${\color{Red} q=28\mu C}$

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