We wish to produce a 1-mm-diameter copper wire having a minimum yield strength of $60,000 \mathrm{psi}$ and a minimum % elongation of $5 \%$. We start with a $20-\mathrm{mm}-$ diameter rod. Design the process by which the wire can be drawn. Include important details and explain.

A $3105$ aluminum bar is reduced from a $1\ \text{in.}$ diameter, to a $0.8 \ \mathrm{in}$. diameter, to a $0.6-\text{in.}$ diameter, to a final $0.4 \ \mathrm{in}$. diameter. Determine the $\%$ $\mathrm{CW}$ and the properties after each step of the process. Calculate the total percent cold work. Note $3105$ designates a particular aluminum alloy.

The following data were obtained when a cold-worked metal was annealed. (a) Estimate the recovery, recrystallization, and grain growth temperatures; (b) recommend a suitable temperature for a stress-relief heat treatment; (c) recommend a suitable temperature for a hot-working process; and (d) estimate the melting temperature of the alloy.

A $3105$ aluminum plate is reduced from $1.75\ \text{in.}$ to $1.15\ \text{in.}$ Determine the final properties of the plate. Note 3105 designates a particular aluminum alloy. (See Figure 8-24.)

A true stress-true strain curve is shown in Figure 8-22. Determine the strainhardening exponent for the metal.

A $0.505$-in.-diameter metal bar with a $2-\text{in.}$ gage length $l_0$ is subjected to a tensile test. The following measurements are made in the plastic region:

Determine the strain-hardening exponent for the metal. Is the metal most likely to be $\mathrm{FCC}, \mathrm{BCC}$, or $\mathrm{HCP}$ ? Explain.

Human skin, especially when damp, is a reasonable conductor of electricity. If we assume a resistance of less than $10\;\text{M}\mathrm{\Omega}$ for a fingertip pressed across two terminals, design a circuit which provides a $+1\;\text{V}$ output if this nonmechanical switch is "closed" and $-1\;\text{V}$ if it is "open."

Calculate the maximum force that a $0.2-\text{in.}$ diameter rod of $\mathrm{Al}_2 \mathrm{O}_3$, having a yield strength of $35,000\ \text{psi,}$ can withstand with no plastic deformation. Express your answer in both lbs and $\mathrm{N}$.

Two parts of a machine are held together by bolts, each of which carries a static tensile load of 3100 N.

(a) What size of class 5.8 coarse-thread metric bolt is required using a safety factor of 4 (based on proof strength)?

(b) What is the least number of threads that must be engaged for the thread shear strength to be equal to the bolt tensile strength if the nuts are made of steel whose yield and proof strengths are 70 percent those of the bolt steel?

How is the friction factor for flow in a pipe related to the pressure loss? How is the pressure loss related to the pumping power requirement for a given mass flow rate?

How does the wall shear stress $au w$ vary along the flow direction in the fully developed region in (a) laminar flow and (b) turbulent flow?

Use the method of partial fractions to verify the integration formula. ∫ 1/ (a²-x²) dx = 1/2a ln|a+x / a-x| + C

Find grad . Graph some level curves f=const. Indicate ∇f by arrows at some points of these curves. (y+6)²+(x-4)²

During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40 km × 0.40 km and that mud has a density of 1900 kg/m³. What is the mass of the mud sitting above a 4.0 m² area of the valley floor?