A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0×4.1 cm in contact with the floor. The total mass of the shelves plus the books stacked on them is 262 kg. Calculate the pressure in pascals exerted by the shelf footings on the surface.

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Convert the cross-sectional dimensions of each leg from centimeters to meters by dividing each dimension by 100.

Calculate the area of contact for one leg by multiplying the converted dimensions (in meters).

Multiply the area of one leg by 4 to find the total contact area for all four legs.

Calculate the force exerted by the shelves using the formula: Force (N) = mass (kg) × acceleration due to gravity (9.8 m/s²).

Determine the pressure exerted by dividing the total force by the total contact area, using the formula: Pressure (Pa) = Force (N) / Area (m²).

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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. In the context of this question, it is calculated using the formula P = F/A, where P is pressure, F is the force (in this case, the weight of the bookshelves), and A is the area of contact with the floor. Understanding this concept is crucial for determining how the weight of the shelves translates into pressure on the floor.

Force and Weight

Force is a vector quantity that causes an object to accelerate, and weight is the force exerted by gravity on an object. The weight of the bookshelves can be calculated using the formula W = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²). This concept is essential for finding the total force acting on the floor, which is necessary for calculating pressure.

Area of Contact

The area of contact refers to the surface area over which a force is distributed. In this scenario, the area is determined by the cross-sectional dimensions of the legs of the bookshelf. The area can be calculated by multiplying the width and height of the leg's cross-section. This concept is important because it directly influences the pressure exerted on the floor; a larger area results in lower pressure for the same force.

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