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In the arrangement shown , assume negligible friction b/w blocks and table. Show that the tension in the string is 2 m1F / (4m1+m2)
hi,
see if the block m2 moves x distance due to force F , then by the constranit of constant length of string m1 has to move 2x distance
from here we can conclude that ,
accl. of m1 = 2 accl. of m2
a1 = 2 a2 ....................(1)
for block 1 ,
T = m1 a1.........
or, T = m1 *2 * a2........(2)
for block 2,
F - 2T = m2 a2 ..................(3)
from Eq. 2 &3 ,elliminating T, we get
F = ( m2 + 4 m1 ) a2 , putting in (2)
T = 2m1 F / (4m1 + m2 )
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