The normal force and the magic table
27/02/08 15:31 Filed in: Physics
The normal force is a force exerted by a surface onto
an object. There is some really cool things about
this force, almost like it is magic.
For statics, Newton's second law is pretty easy. It
says 
. The total force on an object is
zero. Suppose that there is book on a table
(just sitting there).
In this case, the normal force
and the gravitational force must be equal in
magnitude. If they were not, then the net
force would not be zero. Suppose that the book
has a mass of 1 kg, in this case the
gravitational force would be:
This means that the magnitude of
the normal force must also be 9.8 Newtons. No
problems, right? Everyone is happy.
What if I add another book on top of that book? It would look like this:
If this other book is also 1 kg
in mass, I can represent the forces on both
books. The top (green book) would have the
following forces:
This is the same as the one book
by itself on the table except that the "normal"
force is the force the bottom book pushes on the
top book, not the force the table pushes on the
top book. The table doesn't even touch the top
book. Its still a "normal" force because it is a
contact force and it is perpendicular to the
surface. For the bottom book, it will look like
this:
Where the "top book" force is
the force the top book pushes down on the
bottom book. The magnitude of this top book
force is 9.8 Newtons because the bottom book
pushes up on the top book with 9.8 Newtons.
(this is because of Newton's 3rd law - maybe
there will be more discussion on this later).
The key thing in the second force diagram is
that the normal force has increased from 9.8
Newtons to 19.6 Newtons. This force HAD to
increase, if it did not, there would be more
force pushing down than pushing up and the
forces would not add up to zero.So, where is
the problem. Here is the problem, how does the
table know EXACTLY how much to push up on the
book? If the table pushed MORE than 19.6
Newtons, the book would accelerate upwards. If
the table pushed LESS than 19.6 Newtons, the
book would accelerate downward. That is one
smart table. In fact it seems ALL the tables
are smart since I never see a book exploding
upwards when it is sitting on a table.The
answer to this puzzle lies in the structure of
the table (and all matter). Think of the table
as though it were a spring. The more you
compress a spring, the more force it exerts.
The same is true for a table. When the second
book is added on top of the bottom book, the
table becomes compressed more and exerts more
force. No way you say. I say yes way. The
compression does not have to be much but it is
there.To see this, take a laser pointer and
put a mirror on a table or desk. Shine the
laser at the mirror so that it reflects onto a
far wall. As you push down on the table the
laser will move (because the table is moving).
In this video, I placed some weights on my desk next to a mirror. The desktop bent a little causing a change in the reflected beam.
. The total force on an object is
zero. Suppose that there is book on a table
(just sitting there).
In this case, the normal force
and the gravitational force must be equal in
magnitude. If they were not, then the net
force would not be zero. Suppose that the book
has a mass of 1 kg, in this case the
gravitational force would be:
This means that the magnitude of
the normal force must also be 9.8 Newtons. No
problems, right? Everyone is happy.
What if I add another book on top of that book? It would look like this:
If this other book is also 1 kg
in mass, I can represent the forces on both
books. The top (green book) would have the
following forces:
This is the same as the one book
by itself on the table except that the "normal"
force is the force the bottom book pushes on the
top book, not the force the table pushes on the
top book. The table doesn't even touch the top
book. Its still a "normal" force because it is a
contact force and it is perpendicular to the
surface. For the bottom book, it will look like
this:
Where the "top book" force is
the force the top book pushes down on the
bottom book. The magnitude of this top book
force is 9.8 Newtons because the bottom book
pushes up on the top book with 9.8 Newtons.
(this is because of Newton's 3rd law - maybe
there will be more discussion on this later).
The key thing in the second force diagram is
that the normal force has increased from 9.8
Newtons to 19.6 Newtons. This force HAD to
increase, if it did not, there would be more
force pushing down than pushing up and the
forces would not add up to zero.So, where is
the problem. Here is the problem, how does the
table know EXACTLY how much to push up on the
book? If the table pushed MORE than 19.6
Newtons, the book would accelerate upwards. If
the table pushed LESS than 19.6 Newtons, the
book would accelerate downward. That is one
smart table. In fact it seems ALL the tables
are smart since I never see a book exploding
upwards when it is sitting on a table.The
answer to this puzzle lies in the structure of
the table (and all matter). Think of the table
as though it were a spring. The more you
compress a spring, the more force it exerts.
The same is true for a table. When the second
book is added on top of the bottom book, the
table becomes compressed more and exerts more
force. No way you say. I say yes way. The
compression does not have to be much but it is
there.To see this, take a laser pointer and
put a mirror on a table or desk. Shine the
laser at the mirror so that it reflects onto a
far wall. As you push down on the table the
laser will move (because the table is moving).
In this video, I placed some weights on my desk next to a mirror. The desktop bent a little causing a change in the reflected beam.
