Open lesson 1: Density and pressure worksheet

Lesson 1: Density and pressure
What you need to know:
1. Understand how to calculate the density of an object.
2. Understand how pressure, force and surface area are related.
3. How the pressure on an object increases as its depth increases.
You may have heard of certain materials being referred to as dense, but what is
density? Density tells us how much mass of a certain material is contained within
a certain volume.
The density of a material can be calculated from the following equation:
Density (kg/m 3 ) = Mass (kg)/Volume(m 3 )
ρ = m/v lllll
This can also be written as an equation triangle:
So for example if we have a piece of copper which has a mass of 400 kg and a
volume of 0.1 m 3 , then the density of this piece of copper will be:
Density = 400 kg/0.1 m 3
Density = 4000 kg/m 3 llll
In your exam you may be asked write out and use this equation to calculate
density, mass of volume of an object
The word pressure is used in everyday language to mean several things, but in
physics pressure tells us the amount of force that is applied over a certain
area.
Pressure is measured in Pascals (Pa), and pressure, force and surface area are
linked through the following equation:
Pressure (Pa) = Force (N)/Surface area (m 2 )
P = F/A lllllllllllllllllll
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This can also be written as an equation triangle:
This means that if we increase the surface area of an object, but keep the force
applied constant, then the pressure will decrease.
This is the reason why people who walk across ice wear snow shoes, which have
large surface areas. The increased surface area means that the person produces
a smaller pressure on the ice and so it is less likely to break. This can be seen in
the example below:
Two people both, with a weight of 1000N are walking across a frozen lake. The
first person is wearing snow shoes which have a surface area of 0.1m 2 and the
second person is wearing normal shoes which have a surface area of 0.025m 2 . If
the pressure they exert on the ice exceeds 35,000 Pa then the ice will break, so
will the two people be safe? To find out we need to calculate the pressure that
each person exerts on the ice:
Person 1:
Person 2:
Pressure = Force/Area
llllllPressure = 1000 N/0.1 m 2
Pressure = 10 000 Palll
Pressure = Force/Area
Lllllll lPressure = 1000 N/0.025 m 2
Pressure = 40 000 Pal l
This means that the second person is exerting a pressure greater than 35,000 Pa
and so they will fall through the ice! This is why it is important to wear snow
shoes. By increasing the surface area, the person 1 has decreased the pressure
they exert, even though they have the same mass as person 2.
If the forces applied on objects are the same then the bigger the surface area
the smaller the pressure exerted.
In your exam you may be asked to make a similar calculation to the example
above. You may also be asked how surface area can affect pressure and vice
versa.
© Studydoctor 2009

If you have ever been diving underwater you will know that the deeper you go
underwater, the more pressure your body will feel. This is because as you go
deeper down in the water you will have more water above you pushing down
upon your body and so your body will feel more pressure.
So how can we calculate the increase in pressure an object will feel as it goes
deeper underwater? To do this we can use the equation:
Pressure = Force/Area
P = F/A
Firstly we need to calculate the force that the water exerts upon the object that
is underwater:
Force = mass × gravitational field strength
F = m × g
and the mass of the water can be calculated from the equation:
Mass = density × volume
m = ρ × v
However since volume = area × height, this equation can be written as
Mass = density × area × height
m = ρ × A × h
This means that the equation for force can be written as:
Force = density × area × height × gravitational field strength
F = ρ × A × h × g
Now to calculate the pressure on an object we need to use the equation:
P = F/A
And so inserting our equation for force, then pressure an object feels is:
P = (ρ × A × h × g)/A
P = ρ × h × g
Pressure = density × height × gravitational field strength
In your exam you may be asked write out and use this equation to calculate how
the pressure on an object increases with depth
© Studydoctor 2009

So what is the pressure difference a diver will feel as they dive from the waters’
surface to a depth of 10m? Well we can use the equation:
P = ρ × h × g
And since we know that water has a density of 1000 kg/m 3 , the depth of the
diver is 10 m and the gravitational field strength is 10 N/kg, then the pressure
difference is:
P = 1000 kg/m 3 × 10 m × 10 N/kg
P = 100, 000 Pa
This means that the pressure on the diver at a depth of 10 m will be 100,000 Pa
greater than at the waters’ surface.
In your exam you may be asked make a similar calculation to work out the
pressure difference on an object as it changes depth.
Recap:
1. The density of an object can be calculated from the equation:
Density (kg/m 3 ) = Mass (kg)/Volume (m 3 )
2. The pressure that an object exerts can be calculated from the equation:
Pressure (Pa) = Force (N)/Surface area (m 2 )
3. If two objects have the same force applied to them, then an object with a large
surface area will exert a smaller pressure than an object with a smaller surface area.
4. As an object goes deeper underwater than the pressure on it will increase. This can
be calculated from the equation:
Pressure = density × height × gravitational field strength
© Studydoctor 2009