A uniform rope of cross-sectional area 0.50 cm² breaks when the tensile stress in it reaches

$$6.00 × 10^6 N/m^2.$$

(a) What is the maximum load that can be lifted slowly at a constant speed by the rope? (b) What is the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s²?

Normal forces of magnitude

$$1.0 × 10^6 N$$

are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from 50.000 cm to 49.995 cm. What is the bulk modulus of the liquid?

(a) Based on Tiresias' prediction, which heroic qualities will Odysseus need to rely upon as he continues his journey? Explain.

Two workers carry a uniform $15.0$-ft plank that weighs $22.0 \mathrm{lb}$. A load of blocks weighing $165\ \mathrm{lb}$ is located $7.00\ \mathrm{ft}$ from the first worker. How much force does each employee need to use to lift the board and load?

Use a graphing utility to graph the power series. The series represents a well-known function. Identify the function from the graph of its power series.

$$f(x)=\sum_{n=0}^{\infty}(-1)^n x^n, \quad-1<x<1$$

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $g(x)=\frac{x^{3}}{x^{2}-4}$

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $g(x)=2 x^{3}+x^{2}+1$

A steel control rod is 5.5 ft long and must not stretch more than 0.04 in. when a 2-kip tensile load is applied to it. Knowing that $E=29 \times 106$ psi, determine (a) the smallest diameter rod that should be used, (b) the corresponding normal stress caused by the load.

Calculate $\frac{d y}{d x}$. You need not expand your answers. $y=\frac{3 x-1}{(x-5)(x-4)(x-1)}$

There are 1,012 souvenir paperweights that need to be packed in boxes. Each box will hold 12 paperweights. How many boxes will be needed?

What factor would you need to multiply by $(3d + 1)$ to get $9 d^{2}+6 d+1 ?$

The tee shape shown in Figure P8.64b/65b is used as a short post to support a load of $P=4,600 \mathrm{lb}$. The load $P$ is applied at a distance of 5 in. from the surface of the flange, as shown in Figure P8.64a/65a. Determine the normal stresses at points $H$ and $K$, which are located on section $a-a$.

Explain why the following statement does not need to be justified. “The midpoint of a segment is a point on the segment that divides it into two congruent segments.”

If you want to tile the kitchen with $12" \times 12"$ tiles, how many tiles will you need to buy?