Find the pressure exerted by a waterbed with dimensions of 2 m x 2 m which is 30 cm thick. (hint: use density of water)
To find the pressure exerted by a waterbed, we need to use the formula for pressure:
Pressure = Force / Area
In this case, the force is the weight of the waterbed and the area is the surface area on which the force is exerted.
To find the force, we need to calculate the weight of the waterbed. We can do that by multiplying the mass of the water in the waterbed by the acceleration due to gravity. The mass can be calculated using the volume of the water in the waterbed and the density of water.
The volume of the waterbed can be calculated by multiplying its length, width, and height (thickness).
Given:
Length (L) = 2 m
Width (W) = 2 m
Height (H) = 30 cm = 0.3 m
Density of water (ρ) = 1000 kg/m³ (at average room temperature and pressure)
First, let's calculate the volume of the waterbed:
Volume = Length x Width x Height
= L x W x H
= 2 m x 2 m x 0.3 m
Next, let's calculate the mass of the water in the waterbed:
Mass = Density x Volume
= ρ x V
Finally, let's calculate the force exerted by the waterbed:
Force = Mass x Acceleration due to gravity
= m x g
Substituting the values into the formula, we get:
Force = (ρ x V) x g
Now that we have the force, we can calculate the pressure.
Pressure = Force / Area
The area is simply the surface area of the waterbed, which is the product of the length and width:
Area = Length x Width
Let's calculate the pressure:
Pressure = Force / Area