Question

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0×4.1cm 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.

Answer 1

Answer:

$5.22\cdot 10^5 Pa$

Step-by-step explanation:

The pressure exerted by an object is given by:

$p=\frac{F}{A}$

where

F is the magnitude of the force

A is the area of the surface perpendicular to the force

In this problem, the force is the weight of the books + the shelf, which is given by

$F=mg$

where

m = 262 kg is the total mass

$g=9.8 m/s^2$ is the acceleration of gravity

Substituting,

$F=(262)(9.8)=2568 N$

The area of the four legs is:

$A=4(3.0 cm\cdot 4.1 cm)=4(12.3 cm^2)=49.2 cm^2 = 49.2\cdot 10^{-4} m^2$

Therefore, the pressure exerted on them is:

$p=\frac{F}{A}=\frac{2568}{49.2\cdot 10^{-4}}=5.22\cdot 10^5 Pa$