One way to increase pressure is to increase force. If you press a
wall with your finger, the harder you press, the more pressure you put
on the wall. But you can also increase the pressure by decreasing the
area. When you push a thumbtack into a wall, you apply a force to
the thumbtack. The small area of the sharp point of the thumbtack
produces a much larger pressure on the wall than the area of your
finger does. The greater pressure from the thumbtack can pierce the
wall, while the pressure from your finger alone cannot.
Notice that when a unit,
such as pascal or newton, is
named for a person, the
unit is not capitalized but its
abbreviation is.
The following formula shows exactly how pressure depends on
force and area:
Force
F
Pressure = P = Area
A
In this formula, P is the pressure, F is the force in newtons, and A
is the area over which the force is exerted, measured in square meters
(m2). The unit for pressure is the pascal (Pa). One pascal is the pressure exerted by one newton (1 N) of force on an area of one square
meter (1 m2). That is, one pascal is equivalent to one N/m2.
Sometimes knowing pressure is more useful than knowing force.
For example, many surfaces will break or crack if the pressure on
them is too great. A person with snowshoes can walk on top
of snow, while a person in hiking boots will sink into the snow.
COMPARE How does the
pressure from her snowshoes compare to the
pressure from her boots?
Calculating Pressure
Sample Problem
A winter hiker weighing 500 N is wearing snowshoes that cover
an area of 0.2 m2. What pressure does the hiker exert on the snow?
What do you know? Area = 0.2 m2, Force = 500 N
What do you want to find out? Pressure
F
Write the formula: P = A
Substitute into the formula: P =
500 N
2
0.2 m
Calculate and simplify: P = 2500
N
2 = 2500 N/m2
m
Check that your units agree: Unit is N/m2.
Unit of pressure is Pa, which is also N/m2.
Units agree.
Answer: P = 2500 Pa
Practice the Math
1. If a winter hiker weighing 500 N is wearing boots that have an area of
0.075 m2, how much pressure is exerted on the snow?
2. A pressure of 2000 Pa is exerted on a surface with an area of 20 m2. What
is the total force exerted on the surface?
412 Unit 3: Motion and Forces