Two balls have the same mass of 1.478 kg and identical charges of 22.0 ?C. They

Question

Two balls have the same mass of 1.478 kg and identical charges of 22.0 ?C. They hang from the ceiling on strings of identical length as shown in the figure. If the angle with respect to the vertical of the strings is 28.0

Two balls have the same mass of 1.478 kg and identical charges of 22.0 ?C Two balls have the same mass of 1.478 kg and identical charges of 22.0 ?C. They hang from the ceiling on strings of identical length as shown in the figure. If the angle with respect to the vertical of the strings is 28.0 degree , what is the length of the strings?

Explanation / Answer

applying force balance for the balls ,

T cos? - mg = 0

or T = mg /cos ? = (1.4780 * 9.8 ) / cos 28 ;

=16.405 N ;

and

Tsin ? = electrostatic force =( 1/ 4? ?0 ) * ( 22 *22 e-12) / d^2 ;

or d^2 = ( 1/ 4? ?0 ) * ( 22*22 e-12) / [ Tsin ? ] ;

or d^2 = ( 9 e 9 ) * ( 22 *22 e-12) / [ 16.405 sin 28 ] ;

or d = .752 m ;

now [ d/2 ] / l = sin ? = sin 28;

or l = d / ( 2 sin 28 ) = 0 .752 / ( 2 sin 28 ) = 0.8 m , hence the answer

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