Answer
$P=579N$
$a=8.35m/s^2$
Work Step by Step
We can determine the required force and acceleration as follows:
We apply the equation of motion in x-direction
$\Sigma F_x=ma_x$
$\implies -Pcos30=60a$
This simplifies to:
$a=-0.01443P$ [eq(1)]
The moment of inertia about $A$ is given as
$\Sigma M_A=ma(0.3)$
$\implies -W(0.3)+N_B(0.5)+Pcos 30(0.4)-Psin30(0.08)=-60\times a (0.3)$
$\implies -0.3(60\times 9.81)+0.5N_B+0.3464P-0.04P=-18a$
$\implies -176.58+0.5N_B+0.3064P=-18a$
We plug in the value of $a$ from equation (1)
$-176.58+0.5N_B+0.3064P=-18(-0.01443P)$
This simplifies to:
$N_B=353.16-0.09332P$ [eq(2)]
Now, we apply the equation of motion in y-direction
$\Sigma F_y=ma_y$
$\implies N_A+N_B-W+Psin30=ma_y$
$\implies 0+N_B-(60\times 9.81)+Psin30=60(0)$
This simplifies to:
$N_B=588.6-0.5P$ [eq(3)]
Comparing eq(2) and eq(3), we obtain:
$353.16-0.09332P=588.6-0.5P$
This simplifies to:
$P=579N$
We plug in this value in eq(1) to obtian:
$a=-0.01443\times 579$
$\implies a=8.35m/s^2$
