The A-36 steel bolt is tightened within a hole so that the reactive torque on the shank AB can be expressed by the equation

$$t = (kx^{2/3}) N · m/m,$$

where x is in meters. If a torque of T = 50 N · m is applied to the bolt head, determine the constant k and the amount of twist in the 50-mm length of the shank. Assume the shank has a constant radius of 4 mm.

In the earlier example given, was treated the merry-go-round plus child as a system (shown in the given figure) whose angular momentum is conserved. The merry-go-round is initially at rest, so its initial angular momentum is zero, but at the end it is rotating, so its final angular momentum is nonzero. The angular momentum of the merry-go-round alone thus changes, which can only happen if there is a torque on the merry-go-round. What force provides this torque?

(a) The force of gravity on the merry-go-round

(b) The force of air drag on the merry-go-round

(c) The force produced by the child when she jumps off

(d) The force of friction at the axle of the merry-go-round

The steel and aluminum plate assembly is bolted together and fastened to the wall. Each plate has a constant width in the z direction of 200 mm and thickness of 20 mm If the density of A and B is $\rho_s=7.85 \mathrm{Mg} / \mathrm{m}^3$, and for $C$, $\rho_{a l}=2.71 \mathrm{Mg} / \mathrm{m}^3$, determine the location $\bar{x}$ of the center of mass. Neglect the size of the bolts.

Using conversion factors, solve the following clinical problem: A nurse practitioner prepares 500. mL of an IV of normal saline solution to be delivered at a rate of 80. mL/h. What is the infusion time, in hours, to deliver 500. mL?

A soccer player $20.0 \mathrm{~m}$ from the goal stands ready to score. In the way stands a goalkeeper, $1.70 \mathrm{~m}$ tall and $5.00 \mathrm{~m}$ out from the goal, whose crossbar is at $2.44 \mathrm{~m}$ high. The striker kicks the ball toward the goal at $18 \mathrm{~m} / \mathrm{s}$. Determine whether the ball makes it over the goalkeeper and/or over the goal for each of the following launch angles (above the horizontal): (c) $30^{\circ}$.

If you leave me refrigerator door open and the refrigerator runs continuously, does the kitchen get colder or warmer? Explain.

Two small children, Daniel and Christine, were playing a game to see who would be the first to reach the door. The children started the game by standing 20 meters away from the door, and then they each alternated doing the following:

i. Daniel moved one-half the distance between himself and the door on each move.

ii. Christine moved 1 meter toward the door on each move.

(a) How far was each child from the door after the first move?

(b) After four moves, was Daniel or Christine closer to the door? Show your work.

(c) Daniel thought that the game was unfair because he would never reach the door. Explain why his statement is correct or incorrect.

The table lists the measurements of a lot bounded by a stream and two straight roads that meet at right angles, where x and y are measured in feet.

Use the model in part (a) to estimate the area of the lot.

The viscosity of a fluid is to be measured by a viscometer constructed of two 5-ft-long concentric cylinders. The inner diameter of the outer cylinder is 6 in, and the gap between the two cylinders is 0.035 in. The outer cylinder is rotated at 250 rpm, and the torque is measured to be $1.2 lbf \cdot ft.$ Determine the viscosity of the fluid.

What is the net torque about the axle on the pulley in the figure below? If your net torque is negative; do not forget to add a negative sign in your answer. Remember in our convention, counter-clockwise means positive.

When the growth of a spherical cell depends on the flow of nutrients through the surface, it is reasonable to assume that the growth rate, $d V / d t$, is proportional to the surface area, S. Assume that for a particular cell $d V / d t=\dfrac{1}{3} \cdot S$. At what rate is its radius $r$ increasing?

A point source with volume flow Q = 30 m³/s is immersed in a uniform stream of speed 4 m/s. A Rankine half-body of revolution results. Compute (a) the distance from source to the stagnation point and (b) the two points (r, θ) on the body surface where the local velocity equals 4.5 m/s.

The 80-kg ventilation door OD with mass center at G is held in the open position shown by means of a moment M applied at A to the opening linkage. Member AB is parallel to the door for the $30^{\circ}$ position shown. Determine M.

A heat flux meter attached to the inner surface of a 3 -cm-thick refrigerator door indicates a heat flux of $32 \mathrm{~W} / \mathrm{m}^2$ via the door. Also, the temperatures of the inner and the outer surfaces of the door are measured to be $7^{\circ} \mathrm{C}$ and $15^{\circ} \mathrm{C}$, respectively. Find the average thermal conductivity of the refrigerator door.