Will two limp pieces of paper held a few inches apart come closer together or move farther apart if you blow between them? Explain.\s* Q31. A gust of wind blows sideways across an open outward-swinging door. Will the door slam shut or swing open as a result of this? 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 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.

Building Quadrilaterals Now use strands of spaghetti to conduct this quadrilateral-building experiment at least three times. Keep a record of your findings, including sketches of the shapes you make.

• Mark any three points along the length of a strand of spaghetti and break the spaghetti at those three points.
• Try to build a quadrilateral with the pieces end-to-end.
• If a quadrilateral can be built, try to build another, differently shaped quadrilateral with the same side lengths.

a. Was it possible to build a quadrilateral in each case? If a quadrilateral could be built, could you build a differently shaped quadrilateral using the same four segments? Compare your findings with those of others.

b. If a quadrilateral can be built from four side lengths, how are the side lengths related? Use a ruler and compass to test your conjecture for segments of length $3 \mathrm{~cm}, 5 \mathrm{~cm}, 8 \mathrm{~cm}$, and $10 \mathrm{~cm}$. For segments of length $4 \mathrm{~cm}, 4 \mathrm{~cm}, 7 \mathrm{~cm}$, and $15 \mathrm{~cm}$. For segments of length $2 \mathrm{~cm}, 4 \mathrm{~cm}, 8 \mathrm{~cm}$, and $16 \mathrm{~cm}$.

c. Suppose $a, b, c$, and $d$ are consecutive side lengths of any quadrilateral. Write an equation or inequality relating $a, b, c$, and $d$. How many different equations or inequalities can you write relating $a, b, c$, and $d$ ?

d. Write in words the relationship that must be satisfied by the four side lengths of any quadrilateral (do not use letters to name side lengths).

Special Quadrilaterals Quadrilaterals are more complicated than triangles. They bremore sides and more angles you discovered that using the ume four side lengths of a quadrilateral, you could build quite different shapes. Qudriaterals are classified as convex - as in the case of the quadrilateral below on thlefi-or nonconvex-as in the case of the quadrilateral on the right.

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.

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.)

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.

In the half-reaction $\mathrm{NO}_{3}^{-} \rightarrow \mathrm{NH}_{4}^{+}$, on which side of the equation should electrons be added? Add the correct number of electrons to the side on which they are needed, and rewrite the equation.

Write a balanced equation describing each of the following chemical reactions. (a) Solid potassium chlorate, $\mathrm{KClO}_3$, decomposes to form solid potassium chloride and diatomic oxygen gas. (b) Solid aluminum metal reacts with solid diatomic iodine to form solid $\mathrm{Al}_2 \mathrm{I}_6$. (c) When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced. (d) Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water.

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

Getting into a car involves these steps. Open the car door. Sit down. Close the door. Buckle the seat belt. Describe the steps you take in getting out of a car. How are they related to the steps involved in getting into a car?

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

Garage door openers originally had a series of four on/off switches so that homeowners could personalize the frequencies that opened their garage doors. If all garage door openers were set at the same frequency, anyone with a garage door opener could open anyone else's garage door.

3. How many different positions are possible with 8 consecutive on/off switches?

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) $30^{\circ}$.