Example 1

A block of wood that weighs 30N and measures 5m by 10m by 4m. If it was placed on a table with the largest possible area (5mx10m) in contact with table, exerts less pressure than it would when placed with its smallest possible area (5mx4m) in contact with table.

Solution
Data:
Force = 30N
Largest base area = ?
AL = 10mx5m = 50m2 P = F/A = 30N = 0.6N/30m2 Pressure = 0.6N/m2
Force (F) = 30N.

Small base are = ?
As = 5mx4m
As = 20m2
P= F/A = 30N/20M2 = 1.5 N/M2
Pressure = 1.5 N/M2


Example 2

A tip of needle has a cross- sectional area of 1x106m2. If doctor applies a force of 2N to a syringe that is connected to the needle, what is pressure is exerted at the tip of the needle? 

Soln:
Data:
Area (A) = 1x106m2
Force (F) = 20N
Pressure =?
P = F/A
P = 20 = 2.0x107 N/M2
The pressure extended by the needle lip is 2.0x107N/m2


Example 3

A rectangle metal block with sides 105m by 1.0m by 1.2m rests on a horizontal surface. If the density of the metal is 7000 kg/m3. Calculate the maximum and minimum pressure that the block can exerts on the surface.
(Take the weight of 1 kg mass to be 10N)

Solution:
Data:
Dimension = 1.2m,1.5m,1.0m.
Density = 7000 kg/m3
Maximum pressure (Pmx) = ?
Minimum pressure (Pmn) = ?
Volume = 1.2x1.5x1=18m3

Density = mass/ Volume
7000 kg/m3 = mass/18
Mass = 7000x18 = 126000Kg
1kg = 10N
126000Kg = ?
F = 1260000 = 1.26 x 106

Force of metal = 1.26 x 106
A1 = 1.2 x 1.5= 18m2
A2= 1.2m2= 1.2mx1m=1.2m2
A3= 1.5 x 1m= 1.5m2

Amax = 18m2
Amin = 102m2
Pmn = F/Amx =1.26 x 106N/18M2 = 1.26X106/1.8 X101
Maximum pressure = 1.05x106N/m2/maximum pressure= 0.7x105N/m2


Example 4

A cube of side 2cm is completely submerged in water so that the bottom of the cube is at a depth of 10cm. use g=10m/s2 and s=1000 kg/m3
1. What is different between the pressure on the bottom of the cable and the pressure on its tap?
2. Determine the difference in the force on the top and bottom.
3. What is the weight of the water displaced by the cube?

Solution;
Data.
Depth = 10cm = 0.1m s = 1000kg/m3
g = 10m/s
h= 8cm= 0.08
formular
p= sgh
p=1000 kg/m3x10m/s2x0.1m=1000 N/m2
At the h= 0.08m p= 1000x10x0.08= 800 N/m2
Change in pressure = 1000N/m =200 N/m2

So that different in pressure between the bottom the top is 200N/m2

Pressure = Force/Area = P= F/A
Area =L2= (10.02)2= 0.0004 m2
Distance in water 200N/m2x0.0004 m2
This is the upthrust acting on the cube
Water displaced by the cube in weight= volume of the cube
Volume = l3 (2cm) 3 = 8 cm3
For water, 1cm3= 1g 50.8 cm3 = 8g
Weight of displaced water
mass of displaced water/100=8g = 0.08N


Example 5

Calculate the pressure at the bottom of tank of water 15m deep due to the water above it is (s=1000 kg/m3).

Solution: Data:
Height =15m
S=1000 kg/m3
g= 10m/s2
Formula
Pressure in liquid sgh = 1000x10x15=150000N/M2


Example 6

The pistons of a hydraulic press have their areas given as 3.0x10-4m2 and 2x102m2 respectively. If the smaller piston is pushed down with a force of 12N, what is the force required to push the larger piston?

Soln:
Data:
F1 = 120N,
A2= 2X102m2
A2 = 3X104m2