Static Fields 2024
Determine the total mass of each of the slabs below.
- (2pts)
A square slab of side length \(L\) with thickness \(h\), resting on a
table top at \(z=0\), whose mass density is given by
\begin{equation*}
\rho=A\pi\sin\left[\tfrac{\pi z}h\right].
\end{equation*}
- (2pts)
A square slab of side length \(L\) with thickness \(h\), resting on a
table top at \(z=0\), whose mass density is given by
\begin{equation*}
\rho = 2A \Big[\Theta(z)-\Theta(z-h) \Big]
\end{equation*}
- (2pts)
An infinitesimally thin square sheet of side length \(L\), resting on
a table top at \(z=0\), whose surface density is given by
\(\sigma=2Ah\).
- (2pts)
An infinitesimally thin square sheet of side length \(L\), resting on
a table top at \(z=0\), whose mass density is given by
\(\rho=2Ah\,\delta(z)\).
- (2pts)
What are the dimensions of \(A\)?
- (2pts)
Write several sentences comparing your answers to the different cases above.