Problems

01

CoM of a house

A “house” is the region bounded by the (non-regular) pentagon with vertex points at $(\mathrm{0,5})$, $(\mathrm{2,3})$, $(\mathrm{2,0})$, $(-\mathrm{2,0})$, $(-\mathrm{2,3})$. Find the CoM of the house using additivity of moments.

02

CoM of region between curves

Find the CoM of the region between the graph of $y=e^x$ and the graph of $y=1$ over $x\in [\mathrm{0,1}]$.

03

FlatCoMMan

Find the center of mass of FlatCoMMan. Assume a constant mass density $\rho$. Use additivity of moments.

04

CoM from Simpson’s

Use Simpson’s rule (with 6 subintervals) to estimate the CoM of this region:

You will need to estimate $M_x$ and $M_y$ and $m$ with three separate integrals. You can use a calculator for your arithmetic.