Stepwise problems - Thu. 11:59pm
Hydrostatic pressure
01
Fluid force on a triangular plate
Find the total force on the submerged vertical plate that is an isosceles triangle with base
and height , and assume it is submerged with the upper vertex below the surface. Liquid is oil with density .
Moments and CoM
02
Center of mass of a house
A “house” is the region bounded by the (non-regular) pentagon with vertex points at
, , , , . Find the CoM of the house using additivity of moments.
03
CoM of region between curves
Find the CoM of the region between the graph of
and the graph of over .
Regular problems - Sat. 11:59pm
Hydrostatic pressure
04
Fluid force on a parabolic plate
A parabolic plate is submerged vertically in water as in the figure:
The shape of the plate is bounded below by
and above by the line . (Note that increases going up in this coordinate system.) Compute the total fluid force on this plate.
(Hint: your integrand should contain
as a factor.)
05
Fluid force on various plates
For diagrams (a)-(i) below, set up an integral to compute the hydrostatic force on the plate.
Moments and CoM
06
FlatCoMMan
Find the center of mass of FlatCoMMan. Assume a constant mass density
. Use additivity of moments.
07
CoM from Simpson’s
Use Simpson’s rule (with 6 subintervals) to estimate the centroid of this region:
You will need to estimate
and and with three separate integrals. You can use a calculator for your arithmetic.
