A plumber steps out of his truck, walks $66 \mathrm{~m}$ east and $35 \mathrm{~m}$ south, and then takes an elevator $12 \mathrm{~m}$ into the subbasement of a building where a bad leak is occurring. What is the displacement of the plumber relative to his truck? Give your answer in components; also give the magnitude and angles, with respect to the $x$ axis, in the vertical and horizontal plane. Assume $x$ is east, $y$ is north, and $z$ is up.

In the great hurricane of 1938, winds of 85 mi/h blew over a boxcar in Providence, Rhode Island. The boxcar was 10 ft high, 40 ft long, and 6 ft wide, with a 3-ft clearance above tracks 4.8 ft apart. What wind speed would topple a boxcar weighing 40,000 lbf?

A preheater involves the use of condensing steam at $100^{\circ} \mathrm{C}$ on the inside of a bank of tubes to heat air that enters at 1 atm and $25^{\circ} \mathrm{C}$. The air moves at 5 m/s in cross flow over the tubes. Each tube is 1 m long and has an outside diameter of 10 mm. The bank consists of 196 tubes in a square, aligned array for which $S_{T}=S_{L}=15 \mathrm{mm}$. What is the total rate of heat transfer to the air? What is the pressure drop associated with the airflow?

A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete $\left(k=0.79 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}, \alpha=5.94 \times 10^{-7} \mathrm{m}^{2} / \mathrm{s}\right.,$ $\alpha=5.94 \times 10^{-7} \mathrm{m}^{2} / \mathrm{s},$ $\rho=1600 \mathrm{kg} / \mathrm{m}^{3},$ and $c_{p}=0.84 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K} )$ cooled to $14^\circ C$ during a cold night is heated again during the day by being exposed to ambient air at an average temperature of $28^\circ C$ with an average heat transfer coefficient of $14 W/m^2 \cdot K.$ Using analytical one-term approximation method (not the Heisler charts), determine (a) how long it will take for the column surface temperature to rise to $27^\circ C,$ (b) the amount of heat transfer until the center temperature reaches to $28^\circ C,$ and (c) the amount of heat transfer until the surface temperature reaches to $27^\circ C.$

From time t = 0 to t = 5 hr radioactive steam is released from a nuclear power plant accident located at x = -1 mile and y = 3 miles. The following wind conditions are expected: $\mathbf{V}=10 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$ mph for 0 < t < 3 hr, $\mathbf{V}=15 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}$ mph for 3 < t < 10 hr, and $\mathbf{V}=5 \hat{\mathbf{i}}$ mph for t > 10 hr. Draw to scale the expected streakline of the steam for t = 3, 10, and 15 hr.

A motor boat pulls a long, smooth, water-soaked log (0.5 m in diameter and 50 m long) at a speed of 1.7 m/s. Assuming total submergence, estimate the force required to overcome the shear force of the log. Assume a water temperature of 10$^{\circ}C$ and that the boundary layer is tripped at the front of the log.

A centrifuge consists of four cylindrical containers, each of mass m, at a radial distance r from the rotation axis. Determine the time t required to bring the centrifuge to an angular velocity $\omega$ from rest under a constant torque M applied to the shaft. The diameter of each container is small compared with r, and the mass of the shaft and supporting arms is small compared with m.

A liquid food product is processed in a continuous-flow sterilizer. The liquid enters the sterilizer at a temperature and flow rate of Tm,i,h=20C, mdot = 1kg/s, respectively. A time-at-temperature constraint requires that the product be held at a mean temperature of Tm=90C for 10s to kill bacteria, while a second constraint is that the local product temperature cannot exceed Tmax = 230C in order to preserve a pleasing taste. The sterilizer consists of an upstream, Lh=5m heating section characterized by uniform heat flux, an intermediate insulated sterilizing section, and a downstream cooling section of length Lc=10m. The cooling section is composed of an uninsulated tube exposed to a quiescent environment at Tinfinity=20C. The thin-walled tubing is of diameter D = 40mm. Food properties are similar to those of liquid water at T=330K.

Find (a) the Heat flux required in the heating section to ensure a maximum mean product temperature of Tm=90C (b) the Location and value of the maximum local product temperature (c) the Minimum length of the sterilizing section needed to satisfy the time-at-temperature constraint.

Air temperature rises from a morning low of $\hspace{1mm} 42^\circ \text{F} \hspace{1mm}$ to an afternoon high of $\hspace{1mm} 70^\circ \text{F}.$

$$\begin{array}{l l } \text{(a) Express these temperatures in $^{\circ} \mathrm{R}, \mathrm{K},$ and $^{\circ} \mathrm{C}$.}\\ \text{(b) Determine the temperature change in $^{\circ} \mathrm{F},^{\circ} \mathrm{R}, \mathrm{K},$ and $^{\circ} \mathrm{C}$ from morning low to afternoon high. }\\ \text{(c) What conclusion do you draw about temperature change for $^{\circ} \mathrm{F}$ and $^{\circ} \mathrm{R}$ scales? }\\ \text{(d) What conclusion do you draw about temperature change for $^{\circ} C$ and K scales?}\\ \end{array}$$

A rectangular bar of length L has a slot in the middle half of its length. The bar has width b, thickness t, and modulus of elasticity E. The slot has width b/4. (a) Obtain a formula for the elongation $\delta$ of the bar due to the axial loads P. (b) Calculate the elongation of the bar if the material is high-strength steel, the axial stress in the middle region is 160 MPa, the length is 750 mm, and the modulus of elasticity is 210 GPa.

The van travels over the hill described by $y=\left(-1.5\left(10^{-3}\right) x^2+15\right) \mathrm{ft}$. If it has a constant speed of $75 \mathrm{ft} / \mathrm{s}$, determine the $x$ and $y$ components of the van's velocity and acceleration when $x-50 \mathrm{ft}$.

The 10 kg sphere C is released from rest when $\theta=0^{\circ}$ and the tension in the spring is 100 N . Determine the speed of the sphere at the instant $\theta=90^{\circ} .$ Neglect the mass of rod AB and the size of the sphere.

Determine the clamping force on the board A if the screw is tightened with a torque of $M=8 \mathrm{N} \cdot \mathrm{m}.$ The square-threaded screw has a mean radius of 10 mm and a lead of 3 mm, and the coefficient of static friction is $\mu_{s}=0.35$.

Two identical slender rods $A B$ and $B C$ are welded together to form an L-shaped assembly. The assembly is pressed against a spring at $D$ and released from the position shown. Knowing that the maximum angle of rotation of the assembly in its subsequent motion is $90^{\circ}$ counterclockwise, find the magnitude of the angular velocity of the assembly as it passes through the position where rod $A B$ forms an angle of $30^{\circ}$ with the horizontal.