A Physics book has a height of 26 cm, a width of 22 cm, and a thickness of 4 cm.
Find the pressure that the Physics book exerts on a desktop when the book lies face up and when the book is balanced on its spine.
I know that P=F/A, I am just not sure which dimensions of the book to use for area. Initially, I used P=density*g*height and got it wrong. I used .26 m for the height, so I think that I used the wrong value for height.
Face up, the area in contact with the desktop is 26 x 22 cm^2.
On the "spine" (binding, where the title is embossed, the area is 26 x 4 cm^2.
You are correct that the density (or weight) of the book will be needed, and pressure = F/A. The weight is M g or (density)*g*volume
To find the pressure exerted by the Physics book on a desktop, we need to determine the area on which the book's weight acts. Let's consider both scenarios separately:
1. Book lies face up:
In this case, the weight of the book is distributed over the entire base, given by the height and width dimensions. Therefore, the area of contact is the product of height and width: A = height * width = 26 cm * 22 cm.
2. Book is balanced on its spine:
When the book is balanced on its spine, only a small portion of the base is in contact with the desktop. In this scenario, the area of contact is simply the thickness of the book. Therefore, A = thickness = 4 cm.
Now, let's calculate the pressure in each case:
1. Book lies face up:
Using the given dimensions, convert them to meters:
height = 26 cm = 0.26 m
width = 22 cm = 0.22 m
The pressure (P) exerted by the book lying face up can be calculated using the formula P = F/A, where F is the weight of the book. Assuming the book's weight is W, we can write:
P = W / A
To determine the weight, we need to use the formula for weight: W = m * g, where m is the mass of the book and g is the acceleration due to gravity (9.8 m/s^2).
Since we have the density (ρ) of the book, which is not provided in the question, we can find the mass using the formula m = ρ * V, where V is the volume.
To find the volume, it is a rectangular solid, so V = height * width * thickness.
Substituting the values into the formulas:
V = 0.26 m * 0.22 m * 0.04 m
= 0.00288 m^3
Let's assume the density of the book, ρ, is 1000 kg/m^3.
m = 1000 kg/m^3 * 0.00288 m^3
= 2.88 kg
W = m * g
= 2.88 kg * 9.8 m/s^2
= 28.224 N
Now, substitute the calculated values for W and A into the pressure formula:
P = W / A
= 28.224 N / (0.26 m * 0.22 m)
≈ 505.05 Pa
Therefore, the pressure exerted by the Physics book lying face up is approximately 505.05 Pascal.
2. Book is balanced on its spine:
In this scenario, the area of contact is the thickness of the book, which is 4 cm = 0.04 m.
Using the same weight and pressure formulas as before, with the calculated weight of 28.224 N and the area of contact of 0.04 m, we can calculate the pressure:
P = W / A
= 28.224 N / 0.04 m
= 705.6 Pa
Therefore, the pressure exerted by the Physics book when it is balanced on its spine is approximately 705.6 Pascal.
To find the pressure that the Physics book exerts on a desktop, we need to determine the area over which the force is distributed. In this case, the force will be the weight of the book, which is given by the formula:
Force (F) = mass (m) * acceleration due to gravity (g)
The given dimensions of the book are:
Height (h) = 26 cm = 0.26 m
Width (w) = 22 cm = 0.22 m
Thickness (t) = 4 cm = 0.04 m
First, let's calculate the weight of the book. The weight can be obtained by multiplying the mass of the book (which we don't have) by the acceleration due to gravity (g = 9.8 m/s^2). However, since we are only interested in the pressure, we can ignore the mass and work directly with the weight.
Now, let's consider the two scenarios:
1. When the book lies face up:
In this case, the entire surface area of the book is in contact with the desktop. The area (A) will be the product of the width and the length of the book. Therefore, we have:
A = w * h
2. When the book is balanced on its spine:
Only the thickness of the book is in contact with the desktop. So, the area of contact (A) will be the product of the width and the thickness of the book:
A = w * t
Now, let's calculate the pressure exerted by the book in each scenario.
1. When the book lies face up:
Pressure (P1) = Force (F) / Area (A)
= F / (w * h)
2. When the book is balanced on its spine:
Pressure (P2) = Force (F) / Area (A)
= F / (w * t)
Since we are given the height, width, and thickness of the book, we can substitute these values and calculate the pressures in each case.