The simply supported beam shown in Figure P8.48a/49a carries a uniformly distributed load $w$ on overhang $B C$. The beam is constructed of a Southern pine [ $E=12 \mathrm{GPa}]$ timber that is reinforced on its upper surface by a steel $[E=200 \mathrm{GPa}$ ] plate (Figure P8.48bl $49 b$ ). The beam spans are $L=4 \mathrm{~m}$ and $a=1.25 \mathrm{~m}$. The wood beam has dimensions of $b_w=150 \mathrm{~mm}$ and $d_w=280 \mathrm{~mm}$. The steel plate dimensions are $b_s=230 \mathrm{~mm}$ and $t_s=6 \mathrm{~mm}$. Assume that the allowable bending stresses of the wood and the steel are $9 \mathrm{MPa}$ and $165 \mathrm{MPa}$, respectively. Determine the largest acceptable magnitude for distributed load $w$. (You may neglect the weight of the beam in your calculations.)

Find the power input for a compressor that compresses helium from $150 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ to $400 \mathrm{kPa}$ and $200^{\circ} \mathrm{C}$. Helium enters this compressor via a $0.1-\mathrm{m}^2$ pipe at a velocity of $15 \mathrm{~m} / \mathrm{s}$. What is the increase in the flow power during this process?

Let $f(x)=2 x^{2}-x$ and g(x) = 3x - 1. Write an equation for each of the following function operations. a. f(g(-2)) b. g(f(x)) c. $\frac{g(x+2)}{f(x+2)}$

A 12-m-long and 5-m-high wall is constructed of two layers of 1-cm-thick sheetrock $(k=0.17 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$ spaced 16 cm by wood studs $(k=0.11 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$ whose cross section is $16 \mathrm{cm} \times 5 \mathrm{cm}.$ The studs are placed vertically 60 cm apart, and the space between them is filled with fiberglass insulation $(k=0.034 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}).$ The house is maintained at $20^{\circ} \mathrm{C}$ and the ambient temperature outside is $-9^{\circ} \mathrm{C}.$ Taking the heat transfer coefficients at the inner and outer surfaces of the house to be 8.3 and $34 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ respectively, determine (a) the thermal resistance of the wall considering a representative section of it and (b) the rate of heat transfer through the wall.

When is a neutron unstable?

The velocity of the water in the pipe is given by $V_{1}=0.50 \mathrm{t} \mathrm{m} / \mathrm{s}$ and $V_{2}=1.0 \mathrm{t} \mathrm{m} / \mathrm{s}$, where t is in seconds. Determine the local acceleration at points (1) and (2). Is the average convective acceleration between these two points negative, zero, or positive? Explain.

Solve the equation for the specified variable.

$V=l w h ;$ for $l$

Gasoline having a specific gravity of $0.8$ is flowing in the pipe at a rate of $5 \mathrm{cfs}$. What is the pressure at section 2 when the pressure at section 1 is $18 \mathrm{psig}$ and the head loss is $6 \mathrm{ft}$ between the two sections? Suppose $\alpha=1.0$ at all locations.

A 1.12-m-long organ pipe has one end open. Among its possible standing-wave frequencies is $225 \mathrm{~Hz}$. The next higher frequency is $375 \mathrm{~Hz}$. Do not assume that the speed of sound is $343 \mathrm{~m} / \mathrm{s}$. Find (b) the sound speed.

Let $f ( x ) = x ^ { 2 } - 3 x + 1$ $g ( x ) = \frac { 2 } { \sqrt { x } }$ and $h ( x ) = \sqrt { 2 - x }$ Find f ( 1 ) , g ( 1 ) , h ( 1 ) , g ( a ), and $g ( x^2 ).$

Which of the following is NOT part of the evidence presented to support the view that humans are strongly motivated by a need to belong? a. Students who rated themselves as “very happy” also tended to have satisfying close relationships. b. Social exclusion—such as exile or solitary confinement—is considered a severe form of punishment. c. As adults, adopted children tend to resemble their biological parents and to yearn for an affiliation with them. d. Children who are extremely neglected become withdrawn, frightened, and speechless.

What must be the pressure difference between the two ends of a $1.9$-$\mathrm{km}$ section of pipe, $29 \mathrm{~cm}$ in diameter, if it is to transport oil $\left(\rho=950 \mathrm{~kg} / \mathrm{m}^3, \eta=0.20 \mathrm{~Pa} \cdot \mathrm{s}\right)$ at a rate of $650 \mathrm{~cm}^3 / \mathrm{s} ?$

For laminar boundary layers it is reasonable to expect that $\delta / \delta_{t} \approx \mathrm{Pr}^{n},$ where n is a positive exponent. Consider laminar boundary layer flow over a flat plate with air at $100^\circ C$ and 1 atm, the thermal boundary layer thickness is approximately 15% larger than the velocity boundary layer thickness. Determine the ratio of $\delta / \delta_{t}$ if the fluid is engine oil (unused) under the same flow conditions.

Consider the Izod impact strength problem described. (a) Construct a 90% PI for the impact strength of a single specimen of PVC pipe. (b) Find a tolerance interval for the impact strength that includes 95% of the specimens in the population with 95% confidence. An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1.0 ft-lb/in. The sample average and standard deviation obtained were $\overline{x}=1.121$ and s = 0.328, respectively. Test $H_0: \mu=1.0$ versus $H_1:\mu=1.0 > 1.0$ using $\alpha = 0.01$ and draw conclusions. State any necessary assumptions about the underlying distribution of the data.