Two bodies A and B of mass 5 kg and 10 kg contact with each other rest on a table against a rigid The coefficient of friction between the bodies and the table is 0.15 A force of 200 N is applied horizontal on A What are (a) the reaction of thee wall (b) the the action , reaction forces between A & B ? What happens when the wall is removed ? Does the answer to (b) Change , when the bodies are in motion ? Ignore differnce between `mu_(s)` and `mu_(k)`
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Explanation

Here , mass of body `A , m_(1) = 5 kg`
Mass of body `B, M_(2) = 10 kg`
Coefficient of friction between the bodies an the table `mu = 0.15`
Horizontal force applied on `A F = 200 N`
(a) Force of limiting friction acting to the left
`f = mu (m_(1) + m_(2)) g = 0.15 (5 + 10) xx 10 = 22 .5 N`
`:.` Net force to the right exerted on the partition
`F' = 200 - 22.5 = 177.5N`
Reaction of partition `= 177.5 N` to the left
(b) Force of limiting friction acting on body A
`f_(1) = mu m_(1) g = 0 .15 xx 5 xx 10 = 7.5 N`
`:.` Net force exerted by body A on body B
`F'' = F - f_(1) = 200 - 7.5 = 192.5 N`
This is to right
Reaction of body B on body `A = 192.5 N` to the left
When the partition is removed the system of two bodies will move under the action of net force
`F'' = 177.5 N`
Accelertion produced in the system `a = (F)/( m_(1) m_(2) ) = (177.5)/((5 + 10 ))= 11.83 ms^(-2)`
Force producing motion in body A `F_(1) = m_(1) a = 5 xx 11.83 = 59.1 N`
`:.` Net force exerted by body A on B when partion is removed ` = F'' - F_(1) = 192 . 5 - 59.1 = 133.4 N`
Hence the reaction of body B on body A when partition is removed = 133.4 N to the left Thus answers to (b) do change .