how much pressure (N/m2) must the table be able to withstand?

Question

A student has a glass coffee table in their dorm room that they want to stack some of their books on. However they are a little worried about how much pressure the table can withstand at any one point.

If the pile of books has a mass of 13.00 kg, a length of 30.48 cm, a width of 25.40 cm, and
a height of 28.33 cm, how much pressure (N/m2) must the table be able to withstand at any place
where the books are placed ?

Answer 1

Clarification is needed: Are the books placed face down(width & height touching the table) or standing up(width & height touching the table) or sideway standing up(length & height touching the table)?

Take face down as example:
Pressure = Force/Area

Area = 0.3048 * 0.2540 = 0.0774m^2
Force = 13.00kg * 9.8m/s^2 = 127.4N

Pressure = 127.4N/0.0774m^2 = 1645.99N/m^2


Jon R: thanks for pointing it out, I caught the error as well while rechecking.

Ron B: that's true, atmospheric pressure should also be considered.

In this case, just add it to the book pressure once you figure out which orientation does the book place on the table.

Answer 2

I don't have time to do the calculation for you, but don't forget to consider the atmospheric pressure. The table must withstand that in addition to the books.

Use 101.3 Kpa = 101,300 N/m2 for the atmosphere (1 pascal = 1 N/m2)

Answer 3

ok. ignore the height of the books, it is not important.
calculate the surface area of the books, make sure you switch cm to m's.

Area = .3048*.254 = 0.077419 m^2
Knowing that weight = mg
Weight = 13kg*9.81m/s^2 = 127.53 N

pressure is force(weight) per unit area.
pressure = 127.53 N/0,077419 m^2
pressure = 1647.27 N.m^2

Good luck!

Edit: the above response is right in theory. there is an error in the area calculation