3.12
Force, Area, and Pressure
Force and Pressure
A thumbtack (Figure 1) is a solid object. A force applied
to one part of a solid—the head of the thumbtack—is
transmitted directly through it to any other solid object it
is in contact with—such as a bulletin board. But there’s
something special about the thumbtack’s design that
makes it so handy. As shown in Figure 2, we see that the
force applied to the large surface area (the head of the
thumbtack) is transmitted through the tiny pointed end.
The magnitude of the force applied by your thumb
hasn’t changed, but its distribution has. Instead of the
force being spread out over a large area, the force
becomes concentrated on the tiny surface area of the
sharp point.
The distribution of force over an area is called
pressure. This can be written as:
Pressure =
Force
Area
Figure 1
Thumbtacks are useful because they have
surfaces that allow us to pierce things easily.
How are they designed so that we don’t
have to use much force to make them work?
The thumbtack works because it has two surface areas:
the first one big, and the second one small. When the
force is applied to the thumbtack on the large surface
the pressure is low. At the point, because the force is
distributed over the tiny surface area, the pressure
becomes very high. The material of the bulletin
board collapses under this pressure.
Figure 2
If there are 2 surface areas, the
distribution of the force, or the
pressure, changes.
The thumb exerts force onto the thumbtack
Force is distributed over large surface area
low pressure
Force is concentrated over small surface area
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Unit 3
high pressure
Reducing Pressure
Snowshoes are also solids, but they work the opposite
way from thumbtacks—they increase surface areas
instead of reducing it.
If you walk in deep snow in your boots, the pressure
from the boots will compress the snow and you will sink
in. However, if you put on a pair of snowshoes, the
pressure on the snow is lower and you can walk on the
surface and sink only a little (Figure 3). The snowshoe
reduces the pressure you exert on the snow because the
snowshoe has a much larger surface area than the
bottom of your boot. Because snowshoes distribute force
in this way, they are a more efficient way to get across
deep snow than regular boots.
Figure 3
Snowshoes lower the pressure on the snow
and prevent the user from sinking in.
Calculating Pressure
As shown below, the equation for pressure is
Pressure =
or P =
Force
Understanding Concepts
Area
1. Using your own words, define
pressure.
F
2. Describe the main feature of an
object that
A
Force is in units of newtons (N), and area is in units of
square metres (m2). Therefore, pressure is in units of
N/m2. One N/m2 is also called 1 pascal (Pa). However,
since 1 Pa is a very small amount of pressure, the
kilopascal (kPa) is a more common unit: 1000 Pa = 1 kPa.
Suppose a student with a mass of 54 kg is walking on
the snow (see Figure 3). When the student places all his
or her weight on one foot, the pressure on the snow can
be calculated as follows:
With Snowshoe
With Boot
weight of student = 540 N
surface area of snowshoe = 0.20
P=
=
F
A
540 N
0.20 m 2
= 2700 N/m2 = 2.7 kPa
weight of student = 540 N
m2
surface area of boot = 0.05 m2
P=
=
F
A
540 N
0.05 m 2
= 10 800 N/m2 = 10.8 kPa
How can the concept of
transmitting force through a
solid and either increasing or
decreasing pressure apply to
the design of your can crusher?
(a) increases pressure;
(b) decreases pressure.
3. A pile of scrap metal with a
weight of 20 000 N is dumped on
a platform with an area of 25 m2.
What is the pressure on the
platform?
Making Connections
4. Which would hurt more: a large
man in running shoes who steps
on your toe, or a small woman in
high heels? Why?
5. A student going on a winter
camping trip with her school will
need to carry a heavy backpack.
She decides to wear skis for the
long trek instead of winter boots.
Is this a good idea? Why or why
not?
6. A person walking across a frozen
lake accidentally breaks through
the ice and falls in the water.
Using what you know about
pressure, explain how a rescue
crew can reach the accident site,
but not break through themselves.
Mechanical Advantage and Efficiency
175