Answer
$250N$
Work Step by Step
We can find the required force as follows:
The vertical component of force is given as
$\Sigma F_y=N-mg-Fsin\theta=ma_y=0$
This can be rearranged as:
$N=mg+Fsin\theta$
Now the horizontal component of force is given as
$\Sigma F_x=Fcos\theta-\mu_sN=ma_x=0$
$\implies Fcos\theta=\mu_sN$
$\implies Fcos\theta=\mu_s(mg+Fsin\theta)$
This simplifies to:
$F=\frac{\mu_smg}{cos\theta-\mu_s sin\theta}$
We plug in the known values to obtain:
$F=\frac{(0.57)(32)(9.81)}{cos21^{\circ}-(0.57)sin21^{\circ}}$
$F=250N$
