- #1

Physics2013

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- 0

## Homework Statement

Seiche in a lake. The simplest motion of water in a lake can be approximated as simply the water surface tilting but remaining flat.

Imagine a lake of rectangular cross section of length L and with depth h where (h<<L). The problem resembles that of the simple pendulum, the kinetic energy is due to

*horizontal*

motion and potential energy due to small change in height.

So, imagine at some instant the water level at the increased end is

__+__Y

_{o}with respect to normal level. Show that the increased gravitational potential energy of whole mass system is given by

U=(1/6)bpgL(Yo

^{2})

## Homework Equations

U=mgh

Figure attatched!

## The Attempt at a Solution

I know the mass of the water will be defined as the volumeXdensity. the volume would be, if width of lake is defined as

*b*, Lbh. Density is denoted p. Thus, m=Lbhp.

The gravitational constant

*g*is applicable so g=g. Finally, as the height is rising as much as it is falling I can take the average height and thus, h = h+(1/2)Y

_{o}?

But, now plugging this into the equation U=mgh I have

U=(Lbhp)g(h+(1/2 Y

_{o}), and this is definitely not the 'answer' stated in the problem.

Could anyone help identify where is my logic going wrong?