Chapter 6, Problem 63A

What is the pressure on a table when a 20-N book with a $0.05\text{-}{m}^2$ cover lies flat on it? What is the pressure when the book stands on its end (area $0.01m^2$

)?

To determine

Pressure exerted on the table for both the cases.

Answer to Problem 63A

When book lies flat on the table, the pressure is $P_1=400{\text{N/m}}^2$ and when book stands on its end, the pressure is $P_2=2\times {10}^3{\text{N/m}}^2$ .

Explanation of Solution

Given:

Weight of book, $F_g=20\text{N}$

Area of flat book, $A_1=0.05{\text{m}}^{\text{2}}$

Area of book’s end, $A_2=0.01{\text{m}}^2$

Formula Used:

The pressure is given as,

  $P=\frac{F}{A}$

Where, $F$ is the applied force and $A$ is the area in contact.

Calculation:

When book lies flat on the table, the pressure on table is

  $\begin{array}{l}{P}_1=\frac{F_g}{A_1}=\frac{20}{0.05}\\ \Rightarrow P_1=400{\text{N/m}}^2\end{array}$

When book stands on its end, the pressure on table is

  $\begin{array}{l}{P}_2=\frac{F_g}{A_2}=\frac{20}{0.01}\\ \Rightarrow P_2=2\times {10}^3{\text{N/m}}^2\end{array}$

Conclusion:

Therefore, when book lies flat on the table, the pressure on table is $P_1=400{\text{N/m}}^2$ and when book stands on its end, the pressure on table is $P_2=2\times {10}^3{\text{N/m}}^2$ .