Answer
$(a)\space7524\space N$
$(b)\space 15413\space N$
Work Step by Step
Please see the attached image first.
(a) Let's apply the equation $V=u+at$ to the car
$\rightarrow V=u+at$
Now plug the known values into this equation.
$312\space m/s= 0+\space a\times 9.48\space s$
$3.3\space m/s^{2}= a$
Let's apply the equation $F=ma$ to the car
$\rightarrow F=ma$
Now plug the known values into this equation.
$F=2280\space kg\times 3.3\space m/s^{2}=7524\space N$
(b) We know that centripetal acceleration of the car at the bend can be written as
$a_{1}=\frac{V^{2}}{r}=\frac{(31.2\space m/s^{2})^{2}}{166\space m}= 5.9\space m/s^{2}$
So, centripetal force $F_{1}=ma_{1}$
$F_{1}=2280\space kg\times5.9\space m/s^{2}$
$F_{1}=13452\space N$
Net force$= \sqrt {F^{2}+F_{1}^{2}}= \sqrt {(752N)^{2}+(13452N)^{2}}$
Net force $=15413\space N$
