Friction is both a boon and a bane in
our daily lives. Friction causes wear and
tear in many of our mechanical systems.
But it is also something that we take
for granted. We need friction to keep
things from falling. I'm sure you don't
want your phone falling off your desk
and getting a cracked screen, right?
But what really is friction? Friction is
a resistive force that an object
experiences when it moves, or tries to
move, relative to another object. Static
friction plays significant role in
preventing objects from, say, falling off
your desk. Every object in contact with
another experiences some degree of
static friction, as long as they are not
moving with respect to each other. When
forces from the surroundings cause an
object to want to move, the surface the
object is on exerts an equal, but
opposite, force called static friction, which
causes it to stay. Exceeding the
particular threshold, however, will cause
the object to move, where instead of
static friction, we would have kinetic
friction. This is the equation for static
friction, where F is the amount of frictional
force, μ is the coefficient of friction,
which depends on the properties of the
surfaces in contact, and N is the amount of
normal force. From this we see that the
amount of frictional force depends on
the coefficient of friction and the
normal force exerted by the two bodies.
Increasing the amount of normal force
with the same coefficient of friction,
increases the amount of frictional force.
The same applies when it is done for the
coefficient of friction. But how about
changing the contact surface area? Why is
that not in the equation? Let's find out!
In this experiment, we examine if the
contact surface area affects the amount
of frictional force. When we place a
brick on concrete, the brick will exert
its weight onto the concrete. This, by
Newton's Third Law of Motion, will exert
the same magnitude of force back onto
the brick, otherwise known as the normal
force. First, we tie a brick to a string
with a load attached to the other end,
which exerts a tensional force on the
brick. The amount of tensional force
depends on the weight of the load
attached to the string. We keep
increasing the load until the brick
starts moving. At that point, the tensional
force of the brick equals the
critical threshold value for static
friction. Then, we investigate if changing
the orientation of the brick affects the
critical threshold value for static
friction.
This allows us to find out if changing
the amount of surface area would have an
effect on the amount of frictional force.
On the first trial, the brick moves when
we have about 2.43 litres of water. This
is equal to "23.8 N" of force
acting on the brick. We repeat this two
more times for consistency,
and average the results.
Now, let's change the orientation of the
brick, therefore, changing the contact
surface area, and see what happens.
What a surprise! The amount of force
required to make the block move is still quite
similar to the first orientation.
So, why did this happen? Since we only
changed the orientation of the block, the
weight of the block remains the same.
Hence, the amount of normal force exerted
by the concrete onto the brick will also
remain the same. Likewise, the surfaces
themselves do not change, so the
coefficient of friction has to remain
the same. And according to the equation
for static friction, if the normal force
remains the same, and the coefficient of
friction remains the same, the force of
friction must also remain the same.
However, this did not occur and all three
orientations. In the third orientation, the lowest surface area, we see that
the amount of force required to make the
block move was a bit lower than for the
other two orientations. This could have
been due to the fact that the roughness
of the wood block was different, because
of the grain of the wood, therefore,
resulting in a different coefficient of
friction. Another explanation for this
could be that, since the block was
standing up, the block actually tilted
when the force was applied,
and fell rather than sliding across the
concrete. If this did occur, then a lower
amount of force would be required to
make the block move. From the roof over
our head, to the bridges we drive our cars
on, we are surrounded by trusses. These
trusses have become essential for
almost all of our buildings and structures.
Without them, we wouldn't have been able
to build some of our most amazing
structures, like the Burj Khalifa. So, what
exactly is a truss? A truss is a
structure which consists of straight
members connected together to make a
framework. Trusses are generally made up
of small triangles which allow for rigid
and strong structures. The use of
triangles in a truss has been proven to
be much stronger than other shapes due to
the low amount of elements, because
unlike polygons with four or more sides,
triangles do not collapse onto
themselves. Even though trusses are very
strong and able to withstand large
forces, there are still some points where
they can fail. These points of potential
failure occur at the members that
experience the greatest amount of force.
This is why we need engineers, like us, to
calculate the force that act on each
member and find out where the potential
points of failures are, to prevent
catastrophic failures. But, how do we
calculate the forces acting on each
member? There are two ways to do this.
First is involving the method of joints.
In brief, the method of joints involves
taking the force at a single joint,
resolving them into their vertical and
horizontal components and making the sum
of the forces in each direction equal to
zero, therefore, giving us the force on
each member at a particular joint. The
second is using method of sections. In
the method of sections, we take a part or
a section of a truss and find the forces
for the members that we split from the
original truss. We can use the standard
rules for static equilibrium, like the
sum of the forces in the vertical
horizontal direction must be equal to
zero, and the sum of the moments about
any point must also be equal to zero, to
find these forces. The basic principle of both
of these methods is that all members of a
truss and the truss itself is in static
equilibrium. This means that the
resultant force and moment acting
on the truss is equal to zero.
Through the use of one, or both of these
methods combined, we are able to find the
magnitude of the force in a member, as
well as if the force on the member is a
compressional force or a tensional force. So,
you may be wondering, "What happens if the
compression or tension force in the
member is too much?" Well, this is when we
have, CATASTROPHIC FAILURE!
Okay, maybe not so dramatic, but in theory
this is what would happen. Generally, in a
truss, the member or members experiencing
the greatest amount of force are most
likely to be the first one(s) to break.
This is what we set out to prove. For our
second experiment we decided, "Hey, why not
build a truss and keep adding weight to
it until it breaks?" But before we could
create our truss, we have to decide what
material we were going to use. We have
a couple options, such as cotton swabs
pencils, maybe even toothpicks. But we
decided to go with popsicle sticks. We
found that the structural integrity of
cotton swabs and toothpicks was just to
low, as they tend to bend when any force
is applied to them. Pencils require too
much force to break, making it hard for
us to conduct the experiment easily. This
is why we settled for popsicle sticks as
it did not require too much force to
break, but just enough to conduct the
experiment. We then created a truss
using popsicle sticks and hot glue, as these
allowed for the members of the truss to
break, rather than the joints, when under
pressure. Then, we attached a plastic bag
to joints B and C, as seen in the diagram,
and placed the truss structure on two
tables with a gap underneath for the
plastic bags. We thought it'd be best to
use plastic bags to hold water, as the
weight of a plastic bag is quite low.
Therefore, we assumed it to be weightless.
We then slowly added water into the
plastic bags, until one of the members
broke.
Here, we can see a bit of bending in the
truss structure. This could mean that for
the weight distribution, the water is no
longer even, which may affect our final
results.
Due to the significant leaning of the
truss structure, we have placed an extra
support next to the truss to prevent it
from having a large unbalanced force,
which could alter the amount of force on
each member. At this point we have about
8 litres of water in the plastic bag,
which amounts to 19.6 N
of force acting downwards at
joints B and C each, and the total weight
force on the structure is about
78.5 N.
We can now see that there is significant
leaning of the truss structure, due to
the incredible amount of force on the
truss. At this point we have about 12.5 litres
of water with one bag containing
6 litres of water and the other
containing 6.5 litres of water. This
provides a force acting downwards of
29.4 N on joint B, and
31.9 N acting on joint C.
Due to the large amount of weight
attached to the truss, the box that the
truss is sitting on starts to deform a
bit. This causes some of the popsicle
sticks to bend, therefore making the
truss lean even more until member DG
finally breaks, causing the whole
structure to fall. The weight force on the
structure at the point of failure, was
about 122.6 N. At the point where
member DG broke, it was
experiencing about 34.7 N
of compression force. This was the
largest force in the truss structure, which
was experienced by member DG as a
compression force and CG as a tension
force. However, we suspect that due to the
leaning of the structure, member DG
could have experienced a bit more force
than calculated, causing it to break
first.
After conducting the experiment, we found
that what we expected to happen is what
happened.
Remember, the member experiencing the largest
amount of force was the first one break?
However, we realized that due to the
structure of a popsicle stick, the truss
is most likely to break at the member
experiencing the greatest amount of
compression force. This is due to the
fact that the tensile stress capacity of
a popsicle stick is larger than the
compressive stress capacity. This means
that the popsicle stick is most likely
to break under compression, rather than
tension, which is what happened in the
experiment. Two members were experiencing
the same force, except, one was
compression and the other was tension,
and the member experiencing the
compression force was the first to break.
There were also some limitations to this
experiment. Since we were using hot glue
to stick popsicle sticks together, it is
possible that there was more hot glue at
one of the joints compared to another.
This would affect the forces acting
at a specific joint, therefore, slightly
exaggerating or understating the force
in a member. However, we had no way of
calculating this. It was also difficult
to find supports that would be stable
enough to hold the truss in place, while
also being tall enough to prevent the
plastic bags from touching the ground.
This is why we had to stack multiple
items on top of each other,
which may have ended up affecting our
results, as one of the items deformed
a bit, which means it is possible that
the truss may have been able to handle
more weight.
However, our final outcome was still the
same as what we were expecting. This
means that in a truss, the member
experiencing the largest amount of force
will most likely be the first one to
break. Whether the member breaks under
the largest amount of compression force
or tension force is dependent on the
material of the member.
Thanks for watching!
We hope you enjoyed our experiments!
