Question

a) How much force is the air exerting on the front cover of a book that is 23.3 cm long and 18.3 cm wide?

b) What mass has a weight equivalent to this force?

Answer 1

a)

Air is exerting a pressure of 1 atm on the front cover of the book normally.

Now, the area of the book is

  A = (23.3 cm)(18.3 cm)

Pressure exerted on the front cover of the book is equal to force acting normally by air divided by area of the front cover of the book.

P = F /A

Here, force acting on the book normally is F.

From the above equation, the force acting on the book is

F = PA

Substitute 1 atm for P and (23.3 cm)(18.3 cm) for A in the above equation,

Rounding off to three significant figures, the force that the air is exerting on the front cover of the book is 4310 N.

b)

Let m be the mass of weight equivalent.

Weight is equal to mass times the acceleration due to gravity.

Thus,

W = mg

Here, acceleration due to gravity is g.

Consider the weight equivalent is equal to the force that the air is exerting on the front cover of the book.

F = W

= mg

m = F/g

Substitute 4310 N for F and 9.8 m/s² for g in the above equation,

Rounding off to three significant figures, the mass equivalent to the force is 4.40 x 10² kg.