Answer
(a) $F_N = 62~N$
(b) $F_N = 30~N$
Work Step by Step
(a) $\sum F = \frac{mv^2}{r}$
$F_N-mg = \frac{mv^2}{r}$
$F_N = \frac{mv^2}{r}+mg$
$F_N = \frac{(1.60~kg)(12.0~m/s)^2}{5.00~m}+(1.60~kg)(9.80~m/s^2)$
$F_N = 62~N$
(b) $\sum F = \frac{mv^2}{r}$
$F_N+mg = \frac{mv^2}{r}$
$F_N = \frac{mv^2}{r}-mg$
$F_N = \frac{(1.60~kg)(12.0~m/s)^2}{5.00~m}-(1.60~kg)(9.80~m/s^2)$
$F_N = 30~N$