Mass of a Slab

  • Static Fields 2024

    Determine the total mass of each of the slabs below.

    1. (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*}
    2. (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*}
    3. (2pts) An infinitesimally thin square sheet of side length \(L\), resting on a table top at \(z=0\), whose surface density is given by \(\sigma=2Ah\).
    4. (2pts) An infinitesimally thin square sheet of side length \(L\), resting on a table top at \(z=0\), whose mass density is given by \(\rho=2Ah\,\delta(z)\).
    5. (2pts) What are the dimensions of \(A\)?
    6. (2pts) Write several sentences comparing your answers to the different cases above.