A homemade capacitor is assembled by placing two $9 \mathrm{~in}$. pie pans $4 \mathrm{~cm}$ apart and connecting them to the opposite terminals of a $9 \mathrm{~V}$ battery. Which of the following values change if a dielectric is inserted: the capacitance, the charge on each plate, the electric field halfway between the plates and/or the work done by the battery to charge them.

The path of a baseball hit for a home run can be modeled by y = - x²/484 + x + 3 where x and y are in feet and home plate is the origin. The ball lands in the stands, which are modeled by 4y - x = - 352 for x ≥ 400. How far horizontally and vertically from home plate does the ball land?

Find the centroid of a thin, flat plate covering the region enclosed by the parabola $y^{2}=x,$ and the line x = 2y.

Temperatures are measured at various points on a heated plate. Estimate the temperature at (a). x = 4, y = 3.2, and (b). x = 4.3, y = 2.7.

The member is to be made from a steel plate that is $0.25$ in. thick. If a 1-in. hole is drilled through its center, determine the approximate width $w$ of the plate so that it can support an axial force of $3350 \mathrm{lb}$. The allowable stress is $\sigma_{\text {allow }}=22 \mathrm{ksi}$.

The uniform plate has a weight of $500 \mathrm{lb}$. Determine the tension in each of the supporting cables.

Fill in the blanks.

The force $F$ exerted by a fluid of constant weight density $\delta$ on one side of a submerged vertical plate from $y=c$ to $y=d$, where $c \leq d$, is given by $F=$ $\underline{\qquad\qquad}$, where $L(y)$ is the horizontal length of the plate at $y$ and $h(y)$ is the depth of the fluid at $y$.

Explain why images seen through flat, smooth, uniform, plate-glass windows are undistorted.

In this exercise, use the integration capabilities of a graphing utility to approximate the fluid force on the vertical plate bounded by the $x$-axis and the top half of the graph of the equation. Assume that the base of the plate is $12$ feet beneath the surface of the water.

$$\frac{x^2}{28}+\frac{y^2}{16}=1$$

Using tableware in your foods lab, correctly arrange a place setting. Use a dinner plate, salad plate, water glass, teaspoon, soup spoon, dinner fork, dinner knife, dessert fork, napkin, and place mat. Explain the placement of each item.

A parallel plate capacitor made of circular plates each of radius $R=6.0 \mathrm{~cm}$ has a capacitance $C=100 \mathrm{pF}$. The capacitor is connected to a $230 \mathrm{~V}$ ac supply with a (angular) frequency of $300 \mathrm{rad} \mathrm{s}^{-1}$. (a) What is the rms value of the conduction current? (b) Is the conduction current equal to the displacement current? (c) Determine the amplitude of $\mathbf{B}$ at a point $3.0 \mathrm{~cm}$ from the axis between the plates.

Two $\mathrm{L}102$ $\times 102 \times 12.7-\mathrm{mm}$ angles are welded to a $12-\mathrm{~mm}$ steel plate as shown. For $b=250 \mathrm{~mm}$, determine the moments of inertia of the combined section with respect to centroidal axes that are respectively parallel and perpendicular to the plate.

A potential difference of 10.0 V exists across the plates of a capacitor when the charge on each plate is 40.0 $\mu \mathrm{C}$. What is the capacitance of the capacitor? A. $2.00 \times 10^{-4} \mathrm{F}$, В. $4.00 \times 10^{-4} \mathrm{F}$, C. $2.00 \times 10^{-6} \mathrm{F}$, D. $4.00 \times 10^{-6} \mathrm{F}$.

Calculate the moment of inertia of the steel plate for rotation about a perpendicular axis passing through the origin.