For $P=8.5 \mathrm{~kips}$, determine the minimum plate thickness $t$ required if the allowable stress is $18 \mathrm{~ksi}$.

Find the number of possible license plate numbers (with no letters or digits excluded) for each of the following conditions:

6 digits

Two slots have been cut in plate $F G$ and the plate has been placed so that the slots fit two fixed pins $A$ and $B$. Knowing that at the instant shown the angular velocity of crank $D E$ is $6 \mathrm{~rad} / \mathrm{s}$ clockwise, determine $(a)$ the velocity of point $F,(b)$ the velocity of point $G$.

Assume a baseball hit at home plate follows a parabolic path having equation

$$y = -\dfrac{3}{4000} x^2+\dfrac{3}{10} x+3,$$

where $x$ and $y$ are both measured in feet.

(a) Find the maximum height of the baseball. (b) Does the baseball clear an $8$-foot fence that is $385$ feet from home plate?

It takes 100,000 years for a plate to move about 2 kilometers. What is the rate of motion in centimeters per year?

A parallel-plate capacitor has circular plates of 8.20 cm radius and 1.30 mm separation. (a) Calculate the capacitance.

Determine the required minimum thickness $t$ of member $A B$ and edge distance $b$ of the frame if $P=9$ kip and the factor of safety against failure is $2 .$ The wood has a normal failure stress of $\sigma_{\text { fail }}=6$ ksi, and a shear failure stress of $\tau_{\text { fail }}=1.5$ ksi.

A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of $5 \mathrm{~m} / \mathrm{s}$. The two stationary surfaces are spaced $4 \mathrm{~cm}$ apart, and the medium between them is filled with oil whose viscosity is $0.9 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. The part of the plate immersed in oil at any given time is $2$-$\mathrm{m}$ long and $0.5$-$\mathrm{m}$ wide. If the plate moves through the mid-plane between the surfaces, find the force required to maintain this motion. What would your response be if the plate was $1 \mathrm{~cm}$ from the bottom surface $\left(h_2\right)$ and $3 \mathrm{~cm}$ from the top surface $\left(h_1\right)$ ?

A baseball diamond's home plate has three right angles. The other two angles are congruent. Find their measure.

The assembly shown in Figure P5.45 consists of a steel $\left[E_1=30,000 \mathrm{ksi} ; A_1=1.25 \mathrm{in}^2\right]$ rod (1), a rigid bearing plate $B$ that is securely fastened to rod (1), and a bronze $\left[E_2=15,000 \mathrm{ksi}\right.$; $A_2=3.75 \mathrm{in}^2{ }^2$ ] post (2). The yield strengths of the steel and bronze are $62 \mathrm{ksi}$ and $75 \mathrm{ksi}$, respectively. A clearance of $0.125 \mathrm{in}$. exists between the bearing plate $B$ and bronze post (2) before the assembly is loaded. After a load of $P=65$ kips is applied to the bearing plate, determine (a) the normal stresses in bars (1) and (2). (b) the factors of safety with respect to yield for each of the members. (c) the vertical displacement of bearing plate $B$.

What was Wegener's hypothesis called?

A. seafloor spreading

B. plate tectonics

C. continental drift

D. slab pull

Under what conditions can the outer surface of a vertical cylinder be treated as a vertical plate in natural convection calculations?

A vertical flat plate is maintained at a constant temperature of $120^{\circ} \mathrm{F}$ and exposed to atmospheric air at $70^{\circ} \mathrm{F}$. At a distance of $14\ \mathrm{in}$. from the leading edge of the plate the boundary layer thickness is $1.0\ \mathrm{in}$. Find the thickness of the boundary layer at a distance of $24\ \mathrm{in}$. from the leading edge.

A parallel-plate capacitor has capacitance $C_{0}=5.00 \mathrm{pF}$ when there is air between the plates. The separation between the plates is $1.50 \mathrm{~mm}$. (a) What is the maximum magnitude of charge $Q$ that can be placed on each plate if the electric field in the region between the plates is not to exceed $3.00 \times 10^{4} \mathrm{~V} / \mathrm{m}$ ? (b) A dielectric with $K=2.70$ is inserted between the plates of the capacitor, completely filling the volume between the plates. Now what is the maximum magnitude of charge on each plate if the electric fieldbetween the plates is not to exceed $3.00 \times 10^{4} \mathrm{~V} / \mathrm{n}$ ? maximum magnitude of charge on each plate if the electric field between the plates is not to exceed $3.00 \times 10^{4} \mathrm{~V} / \mathrm{n}$ ?