Answer
$P=785N$
Work Step by Step
We can determine the required force as follows:
We know that
$\Sigma M_A=\Sigma M_{kA}$
$\implies W(0.25)=ma(0.5)$
$\implies 150\times 9.81\times 0.25=150\times 0.5\times a$
This simplifies to:
$a=4.905m/s^2$
Now, we apply the equation of motion in x-direction as follows:
$\Sigma F_x=ma_x$
$\implies -P=-(m_{crate}+m_{cart})a$
We plug in the known values to obtain:
$P=(150+10)(4.905)$
$P=785N$
