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Chapter 10: Problem 16

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of \(4.0 \times 5.0 \mathrm{~cm}\) in contact with the floor. The total mass of the shelves plus the books stacked on them is $200 \mathrm{~kg}$. Calculate the pressure in atmospheres exerted by the shelf footings on the surface.

Short Answer

Expert verified
The pressure exerted by the shelf footings on the surface can be calculated using the following steps: the total weight of the shelves and books is 200 kg × 9.81 m/s², the total area of the four legs is 4 × \( \frac{20.0}{10000} \) m², the pressure in Pascals is (200 kg × 9.81 m/s²) / (4 × \( \frac{20.0}{10000} \) m²), and finally, the pressure in atmospheres is [(200 kg × 9.81 m/s²) / (4 × \( \frac{20.0}{10000} \) m²)] / 101325.

Step by step solution

01

Find the total weight of the shelves and books

To find the total weight, we will use the formula Weight = Mass × Acceleration due to gravity, where the mass is given in kg, and the acceleration due to gravity is approximately 9.81 m/s². Mass of shelves and books = 200 kg Acceleration due to gravity = 9.81 m/s² Weight = Mass × Acceleration due to gravity Weight = 200 kg × 9.81 m/s²
02

Calculate the total area of the four legs

Next, we need to calculate the total area in contact with the floor by multiplying the cross-sectional dimensions of each leg and then multiplying the result by the number of legs. Dimensions of each leg: 4.0 cm × 5.0 cm = 20.0 cm² Area of one leg = 20.0 cm² Now let's convert this area from cm² to m² to keep our units consistent (1 m² = 10,000 cm²): Area of one leg = \( \frac{20.0}{10000} \) m² There are 4 legs, so the total area of the four legs is: Total area = 4 × Area of one leg Total area = 4 × \( \frac{20.0}{10000} \) m²
03

Calculate the pressure exerted by the footings in Pascals

Now that we have the weight and the total area, we can calculate the pressure using the formula Pressure = Force / Area. Pressure in Pascals = Weight / Total area Pressure in Pascals = (200 kg × 9.81 m/s²) / (4 × \( \frac{20.0}{10000} \) m²)
04

Convert the pressure to atmospheres

To convert the pressure in Pascals to atmospheres, we will use the conversion factor 1 atmosphere = 101325 Pa. Pressure in atmospheres = Pressure in Pascals / 101325 Pressure in atmospheres = [(200 kg × 9.81 m/s²) / (4 × \( \frac{20.0}{10000} \) m²)] / 101325 Now, we can calculate the pressure in atmospheres exerted by the shelf footings on the surface.

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Most popular questions from this chapter

Natural gas is very abundant in many Middle Eastern oil fields. However, the costs of shipping the gas to markets in other parts of the world are high because it is necessary to liquefy the gas, which is mainly methane and has a boiling point at atmospheric pressure of \(-164^{\circ} \mathrm{C}\). One possible strategy is to oxidize the methane to methanol, $\mathrm{CH}_{3} \mathrm{OH},\( which has a boiling point of \)65^{\circ} \mathrm{C}$ and can therefore be shipped more readily. Suppose that $3.03 \times 10^{8} \mathrm{~m}^{3}\( of methane at atmospheric pressure and \)25^{\circ} \mathrm{C}$ is oxidized to methanol. (a) What volume of methanol is formed if the density of \(\mathrm{CH}_{3} \mathrm{OH}\) is $0.791 \mathrm{~g} / \mathrm{mL} ?(\mathbf{b})$ Write balanced chemical equations for the oxidations of methane and methanol to \(\mathrm{CO}_{2}(g)\) and $\mathrm{H}_{2} \mathrm{O}(l) .$ Calculate the total enthalpy change for complete combustion of the \(3.03 \times 10^{8} \mathrm{~m}^{3}\) of methane just described and for complete combustion of the equivalent amount of methanol, as calculated in part (a). (c) Methane, when liquefied, has a density of $0.466 \mathrm{~g} / \mathrm{mL} ;\( the density of methanol at \)25^{\circ} \mathrm{C}\( is \)0.791 \mathrm{~g} / \mathrm{mL}$. Compare the enthalpy change upon combustion of a unit volume of liquid methane and liquid methanol. From the standpoint of energy production, which substance has the higher enthalpy of combustion per unit volume?

The Goodyear blimps, which frequently fly over sporting events, hold approximately \(4955 \mathrm{~m}^{3}\) of helium. If the gas is at $23{ }^{\circ} \mathrm{C}\( and \)101.33 \mathrm{kPa},$ what mass of helium is in a blimp?

A neon sign is made of glass tubing whose inside diameter is $3.0 \mathrm{~cm}\( and length is \)10.0 \mathrm{~m}$. If the sign contains neon at a pressure of \(265 \mathrm{~Pa}\) at \(30^{\circ} \mathrm{C}\), how many grams of neon are in the sign? (The volume of a cylinder is \(\pi r^{2} h\).)

You have a gas at \(25^{\circ} \mathrm{C}\) confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? (a) Lifting up on the piston to double the volume while keeping the temperature constant; (b) Heating the gas so that its temperature rises from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), while keeping the volume constant; (c) Pushing down on the piston to halve the volume while keeping the temperature constant.

(a) List two experimental conditions under which gases deviate from ideal behavior. (b) List two reasons why the gases deviate from ideal behavior.
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