Define Poisson's ratio.

Sketch the given region R and then find its area. R is the region bounded by the curve $y = x^2 - 2x$ and the x axis. [Hint: Note that the region is below the x axis.

Imagine instead that you choose to take payments spread over 20 years, starting with $1,500,000 in year 1 and growing by 5 percent each year. a. How much money would you receive in year 2? In year 5? b. Write an equation to show how much money you receive in any given year. c. How much money will you have received after 20 years? Be ready to explain your thinking to the class.

Carbon monoxide (CO) has a dipole moment of approximately $8.0 \cdot 10^{-30} \mathrm{C} \mathrm{m}$. If the two atoms are separated by $1.2 \cdot 10^{-10} \mathrm{~m}$, find the net charge on each atom and the maximum amount of torque the molecule would experience in an electric field of $500.0 \mathrm{~N} / \mathrm{C}$.

Explaining the clues you use, make inferences about the speaker's character in (a) lines $31$-$43$ of "My Last Duchess" and (b) lines $18$- $20$ of "Life in a Love."

A peacock mantis shrimp smashes its prey with a hammer-like appendage by storing energy in a springlike section of exoskeleton on its appendage. The spring has a force constant of $5.9 \times 10^4 \mathrm{~N} / \mathrm{m}$. What power does the shrimp generate if it unleashes the energy in $0.0018$ s? (The power per mass of the shrimp appendage is more than 20 times greater than that generated by muscle alone, showcasing the shrimp's ability to harness the potential energy of its spring.)

Find the volume of the given solid. The solid tetrahedron with vertices (0, 0, 0), (0, 0, 1), (0, 2, 0), and (2, 2, 0)

_____ open water area of a lake or pond that is well lit and dominated by plankton.

Compute the torsional shear stress in a circular shaft $0.40\ \text{in}$ in diameter that is due to a steady torque of $88.0\ \mathrm{lb} \cdot$ in. Specify a suitable aluminum alloy for the rod.

The small block of mass m slides along the radial slot of the disk while the disk rotates in the horizontal plane about its center O. The block is released from rest $\dot{r}$relative to the disk and moves outward with an increasing velocity for the torque M that must be applied to the disk to maintain a constant angular velocity $\omega$ of the disk.

Design a wormgear set for the below specifications to produce the desired velocity ratio when transmitting the given torque at the output shaft for the given output rotational speed:

$$\begin{array}{ccc} \boldsymbol{V} \boldsymbol{R} & \begin{array}{c} \text { Torque } \\ (\mathbf{lb} \cdot \mathrm{in}) \end{array} & \begin{array}{c} \text { Output speed } \\ (\mathbf{r p m}) \end{array} \\ \hline 40 & 4200 & 45 \end{array}$$

A$3-\mathrm{ft}$-long steel pipe is subjected to a torque of $1200\ \mathrm{lb} \cdot \mathrm{ft}$ at each end. The pipe is made of $0.2 \% \mathrm{C}$ hardened steel, failure is by yielding, and the factor of safety is $1.5$. Find the nominal diameter of the lightest standard-weight steel pipe that can be used for the shaft.

You have a fixed length $L$ of wire and wish to make a single loop that will experience the maximum torque in a magnetic field. Is it better to make the coil circular or square, or doesn't it matter?

A $4.00 \times 10^{2} \mathrm{N} \cdot \mathrm{m}$ torque is produced applying a force 1.60 m from the fulcrum and at an angle of $80.0^{\circ}$ to the lever. How large is the force?