David Sang and Darrell Hamilton Solutions for Chapter: Forces and Matter, Exercise 5: Exercise 5.4

State the equation linking pressure in a liquid to the depth of the liquid.

Calculate the pressure in $\mathrm{Pa}$ at the bottom of an oil storage tank of depth $2.50 \mathrm{m}$. The oil has a density of $980 \mathrm{kg} {\mathrm{m}}^{-3}$, and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Estimate the height of the Earth's atmosphere using the following data:

Atmospheric pressure$=1000 \mathrm{kPa}$; density of air$=1.29 \mathrm{kg} {\mathrm{m}}^{-3}$

Explain why the height of the Earth's atmosphere can only be estimated. 

Objects submerged in a liquid appear to have a smaller weight. One way to explain this is that there is a difference in pressure on the top and bottom surfaces. Knowing the relationship between pressure and force. Calculate the difference in the weight of the block in water compared to its weight in the air.

The block is a cuboid, with horizontal faces of area$=2 {\mathrm{m}}^2$.

The depth of the block is$=1 \mathrm{m}$.

It is submerged in water, of density$=1000 \mathrm{kg} {\mathrm{m}}^{-3}$.

The bottom of the block is at a depth of $6 \mathrm{m}$.