Block A has a mass of `30 kg` and block B has a mass of `15 kg` . The coefficient of friction between all surface of contact are `mu_(s) = 0.15` and `mu_(k) = 0.10` Knowing that `theta = 30^(@)` and that the magnitude of the force `F` applied to block A is `250 N` Determine (a) acceleration of block A and (b) the tension in the rope

Answer

`a_(A) = 5.2 ms^(-2), T = 215 N`

Explanation

`m_(A)g sin theta + F - T - f = m_(A) alpha`…(i)

` f = mu_(k) m_(A) g cos theta`….(ii)
`T - m_(B) sin theta - F - f' = m_(B) alpha`..(iii)
`f' = mu_(k) .N'`…(iv)
`= mu_(k) (m_(A) g cos theta + m_(B)g cos theta)`
Solving above equation `a_(A) = 5.2 ms^(-2), T = 215 N`