Considering the lift equation
$$L = C_L \frac{1}{2}\rho v^2 s$$
Given $P$ is 1,000 ft, $\rho$ is 0.002308, and $V$ is the cruise speed of a Piper Archer or 126 knots, we get
$$L = (0.4) (0.002308) (\frac{1}{2}) (126)^2 (160)$$
or 1,172.5 Newtons.
What are the pencil-and-paper formulae for calculating the best-climb and best-glide rates?