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

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.

Underline the main clause in given sentence. Then circle the subordinate clause.
If the door is open, you can go right into the house.

Explain why you cannot cool your kitchen by leaving your refrigerator door open on a hot day. (Why does turning on a room air conditioner cool down the room, but opening a refrigerator door does not?)

Colorful fireworks often involve the decomposition of barium nitrate and potassium chlorate and the reaction of the metals magnesium, aluminum, and iron with oxygen. (a) Write the formulas of barium nitrate and potassium chlorate. (b) The decomposition of solid potassium chlorate leads to the formation of solid potassium chloride and diatomic oxygen gas. Write an equation for the reaction. (c) The decomposition of solid barium nitrate leads to the formation of solid barium oxide, diatomic nitrogen gas, and diatomic oxygen gas. Write an equation for the reaction. (d) Write separate equations for the reactions of the solid metals magnesium, aluminum, and iron with diatomic oxygen gas to yield the corresponding metal oxides. (Assume the iron oxide contains $\mathrm{Fe}^{3+}$ ions.)

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?

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.

Manganese is available from its ore pyrolusite, which is manganese(IV) oxide, $\mathrm{MnO}_2$. Some manganese metal is prepared from $\mathrm{MnO}_2$ by reduction with aluminum metal. Write the balanced equation for this reduction.

Solve previous problem for the case where the assembly starts from rest with an initial angular acceleration $\alpha=900 \mathrm{rad} / \mathrm{s}^{2}$ as a result of a starting torque (couple) M applied to the shaft in the same sense as N. Neglect the moment of inertia of the shaft about its z-axis and calculate M.

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.

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?

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 a playground, there is a small merry-go-round of radius 1.20 m and mass 180 kg. Its radius of gyration is 91.0 cm. A child of mass 44.0 kg runs at a speed of 3.00 m/s along a path that is tangent to the rim of the initially stationary merry-go-round and then jumps on. Neglect friction between the bearings and the shaft of the merry-go-round. Calculate

the angular speed of the merry-go-round and child after the child has jumped onto the merry-go-round.

Two tomato strains, A and B, both produce fruit that weighs, on average, $1 \mathrm{lb}$ each. All of the variance is due to $V_{\mathrm{G}}$. When these two strains are crossed to each other, the $F_1$ offspring display heterosis with regard to fruit weight, with an average weight of 2 $\mathrm{lb}$. You take these $\mathrm{F}_1$ offspring and backcross them to strain A. You then grow several plants from this cross and measure the weights of their fruit. What would be the expected results for each of the following scenarios?
A. Heterosis is due to a single overdominant gene.
B. Heterosis is due to two dominant genes, one in each strain.
C. Heterosis is due to two overdominant genes.
D. Heterosis is due to dominance of several genes each from strains $\mathrm{A}$ and $\mathrm{B}$.