Answer
$T=5.98kip$
Work Step by Step
We can determine the required force as follows:
First, we apply Newton's second law to car A
$\Sigma F_y=0$
$\implies N_A-20000cos\theta=0$
$\implies N_A=19923.894lb$
and $F_x=ma_x$
$\implies \mu_k N_A-20000sin\theta-T=m_A a$
We plug in the known values to obtain:
$(0.5)(19923.894)-20000sin 5^{\circ}-T=\frac{20000}{32.2}a$
$\implies T+621.118a=8218.832$..eq(1)
Now we apply Newton's second law to car A and B together
$\Sigma F_x=ma_x$
$\implies \mu_k N_A-(W_A+W_B)sin\theta=(W_A+W_B)a$
We plug in the known values to obtain:
$(0.5)(19923.894)-(20000+30000)sin 5^{\circ}=\frac{20000+30000}{32.2}a$
This simplifies to:
$a=3.609ft/s^2$
Now from eq(1), we obtain:
$T=8218.832-(621.118)(3.609)$
$\implies T=5977.168lb=5.98kip$
