Understanding Pressure - Example 2

Example 2:
A block of wood 3 m long, 5 m wide and 1 m thick is placed on a table. If the density of the wood is 900 kgm^-3, find

1. the lowest pressure
2. the highest pressure

on the table due to the block.

Answer:
a.
Step 1: Finding the weight of the block
The volume of the block = 3 x 5 x 1 = 15m³.

Mass = Density x Volume

Mass of the block, m = (900)(15)= 13500 kg

Weight of the block = mg = 13500 x 10 = 135,000N

Step 2: Determine the surface area
The pressure exerted on a surface is inversely proportional to the area of the surface. The bigger the surface, the lower the pressure.

For the wooden block, the biggest surface, A = 5 x 3 = 15m²

Step 3: Finding pressure
  $$\begin{array}{l}P=\frac{F}{A}\\ P=\frac{(135,000)}{(15)}=9000N{m}^{-2}or9000Pa\end{array}$$

b.
The pressure is the highest when the surface area is the smallest.

The smallest surface area of the block = 1 x 3 = 3m²

The highest pressure,
$$\begin{array}{l}P=\frac{F}{A}\\ P=\frac{(135,000)}{(3)}=45,000Pa\end{array}$$