The bases of a man’s feet have a
total area in contact with the ground of 0.025 meters squared. The man’s weight is 800
newtons. How much is the pressure applied by
his feet to the ground in kilopascals?
Okay, so in this question, we have
a man who is standing on the ground and his feet have a total area of 0.025 meters
squared. In other words, the total area of
contact between the man and the ground is 0.025 meters squared. So let’s say that the contact area,
which we’ll call 𝐴, is 0.025 meters squared. Now as well as this, we’ve been
told that the man’s weight is 800 newtons. Now the man’s weight is going to
act in a downward direction. So we can say that the weight,
which we’ll call 𝑤, is equal to 800 newtons.
But then, this weight is exactly
the force that the man will exert onto the floor. And therefore, if we want to work
out the pressure applied by the man’s feet to the ground, then we can recall that
the pressure applied to in this case the ground is defined as the force applied by
the man in this case to the ground divided by the total area of contact or
specifically the area of the floor over which that force is distributed.
Now since we’re working in base
units — we’ve been given the area of the man’s feet in meters squared and his weight
in newtons — this means that when we calculate the pressure using this equation,
we’ll actually find it in its own base unit which is the pascal. However, there is a catch: we need
to work out this pressure in kilopascals. We’ll come to that later, but it’s
good to be aware of it now.
So we can say that the pressure
exerted by the man on the floor is equal to the force that he exerts which is 800
newtons — that’s his weight — divided by the area over which that force is
distributed. That area is the same as the
contact area between the man’s feet and the floor or in other words the area of the
man’s feet which happens to be 0.025 meters squared. Then, when we evaluate the
right-hand side of this equation, we find that the pressure ends up being 32000
Now we need to convert this
pressure into kilopascals. To do this, we can recall that one
pascal is equivalent to one thousandth of a kilopascal because the prefix kilo means
1000. So one thousandth of 1000 pascals
is the same thing as one pascal. And therefore, what this means is
that 32000 pascals is the same thing as 32 kilopascals. Hence, our final answer is that the
pressure applied by the man’s feet to the ground is 32 kilopascals.