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Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 16
Chapter 10, Problem 16

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0 x 4.1 in contact with the floor. The total mass of the shelves plus the books stacked on them is 266 kg.
Calculate the pressure in pascals exerted by the shelf footings on the surface.

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insert step 1> Convert the dimensions of the legs from inches to meters. Since 1 inch is equal to 0.0254 meters, multiply each dimension by 0.0254 to get the dimensions in meters.
insert step 2> Calculate the area of contact for one leg in square meters by multiplying the converted dimensions.
insert step 3> Since there are four legs, multiply the area of one leg by 4 to get the total contact area in square meters.
insert step 4> Calculate the force exerted by the shelves using the formula: Force (N) = mass (kg) * acceleration due to gravity (9.81 m/s^2).
insert step 5> Calculate the pressure exerted by the shelf footings using the formula: Pressure (Pa) = Force (N) / Total contact area (m^2).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Pressure

Pressure is defined as the force exerted per unit area. It is calculated using the formula P = F/A, where P is pressure, F is the force applied, and A is the area over which the force is distributed. In this context, the force is the weight of the bookshelves and books, which can be calculated using the mass and gravitational acceleration.
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Force due to Gravity

The force due to gravity acting on an object is calculated using the equation F = m*g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth). For the bookshelves, the total mass of 266 kg will be multiplied by g to find the total force exerted on the floor.
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Area of Contact

The area of contact is the surface area over which the force is applied. In this case, the area is determined by the cross-sectional dimensions of the legs of the bookshelf. To find the total area in contact with the floor, the area of one leg is calculated and then multiplied by the number of legs, which is essential for determining the pressure exerted.
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Related Practice
Textbook Question

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (a) bars

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Textbook Question

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (b) atmospheres

Textbook Question

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (c) pounds per square inch

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Textbook Question

(a) How high in meters must a column of ethanol be to exert a pressure equal to that of a 100-mm column of mercury? The density of ethanol is 0.79 g/mL, whereas that of mercury is 13.6 g/mL. Assume that the density of the water is 1.00 5 1.00 3 103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa 5 1 kg/ms2.

Textbook Question

(b) What pressure, in atmospheres, is exerted on the body of a diver if she is 10 m below the surface of the water when the atmospheric pressure is 100 kPa? Assume that the density of the water is 1.00 5 1.00 3 103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa 5 1 kg/ms2

Textbook Question

(a) The compound 1-iodododecane is a nonvolatile liquid with a density of 1.20 g>mL. The density of mercury is 13.6 g>mL. What do you predict for the height of a barometer column based on 1-iodododecane, when the atmospheric pressure is 749 torr?

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