Three blocks of masses `m_(1)=2kg m_(2)=3kg and m_(3)=4 kg` are in contact with each other on a frictionless horizontal surface as shown in
(a) Find
(a) horizontal force F needed to push the block as one unit with an acceleration of `2m//s^(2)`
(b) the resultant force on each block and
(c) the magnitude of contact forces between blocks.

Answer

(a) `18 N;`
(b) `4N, 6N, 8N;`
(c) `14 N` between `m_(1)` and `m_(2)` and 8 N between `m_(2)` and `m_(3)`

Explanation

(a) `F_(net)=Mxxa`
`F=(m_(1)+m_(2)+m_(3))9`
`F=9xx2=18N`

Resultant force on `m_(1)`
`F_(R)=m_(1)xxa=2xx2=4N`
Resultant force on `m_(2)`
`F_(R)=m_(2)xxa=3xx2=6N`
Resultant force on `m_(3)`
`F_(R)=m_(3)xxa=4xx2=8N`
(c) `F-N_(1)=m_(1)xxa`
`18-N_(1)=4`
`N_(1)=14N " between " m_(1) and m_(2)`
`N_(1)-N_(2)=m_(2)xxa`
`14-N_(2)=6`
`N_(2)=8N " between "m_(2) and m_(3)`