A trough has a parabolic cross section $y=ax^2$, where $a$ is a constant. The height is $H$ meters and the length is $L$ meters. The trough is filled with water. For this problem, approximate the weight density of water to be $\rho g = 10^4$ Newtons per cubic meter.

What is the work required to pump the water over the top of the trough?
Work = Newton-meters. (Your answer will involve $L$, $H$, and $a$.)
What is the force due to hydrostatic pressure on one flat parabolic side?
Force = Newtons.