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In the adjacent figure, masses of A,B an...

In the adjacent figure, masses of A,B and C are 1kg, 3kg
and 2kg respectively. Find: (a) the acceleration of the system and (b) tensions in the string Neglect friction. `(g=10ms^(-2))`

Text Solution

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(a) IN this case net pulling force
= `m_(A)g sin 60^(@)+m_(B)g sin60^(@)-m_(C)g sin 30^(@)`
`=(M_(A)+m_(B))g sin 60^(@)-m_(C)g sin30^(@)`
`=(1+3)xx10xx(sqrt3)/(2)-2xx10xx1/2`
`=20sqrt3-10=20xx1.732-10=24.64N`
Total mass being pulled = 1+ 3+2= 6 kg

`therefore` Acceleration of the system a `=(24.64)/(6)=4.1m//s^(2)`
(b) For the tension `T_(1)` in the string between A and B, `m_(A)g sin 60^(@)-T_(1)=(m_(A))(a) therefore T_(1)=m_(A)g sin60^(@)-m_(A)a=m_(A)(g sin60^(@)-a)`
`impliesT_(1)=(1)(10xx(sqrt3)/(2)-4.1)=4.56N`
For the tension `T_(2)` in the string between B and C.
`T_(2)-m_(C)g sin30^(@)=m_(C)a`
`impliesT_(2)=m_(C)(a+g sin30^(@))=2[4.1+10((1)/(2))]=18.2N`
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