CH - 8
Seesaws and Balance
Everyone enjoys a seesaw, although small
children seem to enjoy them the most. However,
maybe the only reason “grown-ups” don’t often
use them is because they feel “seesaws are for
kids.” But I suspect that on many occasions, older
people do use
them- after
dark, for
example, when
other people
can’t see them,
or when
“showing a kid”
how to use
one!
The physics of a seesaw is beautiful. A seesaw
consists of two masses, one at each end of a long
beam; the beam rotates about an axis, stops, then
rotates the other way. While they are turning at a
constant speed, all the torques of a seesaw are
balanced. When the foot of the rider touches the
ground, an extra torque is exerted and angular
acceleration occurs. You probably never thought
of seesaws in quite this way, but you have been
applying physics every time you have ever ridden
one!
Torques are required to analyze the motion of a
seesaw. A torque is caused by a force exerted at
a distance from an axis and is the product of the
force times the distance. (   rF ) An unbalanced
torque will cause a change in rotation, or an
angular acceleration. Balanced torques will
produce no change in the rotation rate. An object
which is stationary will remain so; if it is turning,
then it will continue to do so.
If all the torques of a seesaw are balanced, no
change in the motion will occur. This can be
expressed as:

clockwise
=

counterclockwise
On the left side of the equation, all the torques
tending to make the seesaw move clockwise are
added together. On the right side, all the torques
tending to make the seesaw move
counterclockwise are added together.
If two people of equal mass get on a seesaw, each
at the same distances from the axis, no unbalanced
torques exist ( rF  rF ) and the seesaw will not
change its rotational motion. The seesaw will
continue its constant rotational motion until one
person puts a foot on the ground and pushes up.
This causes a torque, and angular acceleration. This
seesaw will start turning in the opposite direction.
When a seesaw is used normally, much of the time,
there are no unbalanced torques. This only causes
problems if no one is touching the ground and the
seesaw is not turning. Then, you need help=
somebody else must exert a torque on the seesaw.
Without an unbalanced torque, the seesaw will not
change its motion, and both people will be stuck up
in the air!
But how does a seesaw work with people of unequal
mass? As an example, we will use a seesaw that is 3
meters long and has a very small mass (which can
be ignored). If both people sit equal distances from
the support, one person will tend to stay on the
ground and the other will never touch the ground.
This no fun, so you must seat each rider at a
different distance from the support. In our example,
Mark has a mass of 30 kg and John has a mass of
60 kg, and we must find how far from the support
each should sit.
Any axis of rotation can be used, but for the sake of
convenience, let us choose the axis where the first
force is exerted, going from left to right. Once the
axis is chosen, all measurements are made from that
axis. If John, with his 60 kg is on the left end, his
gravitational force of 600 N (F = mg) will exert no
torque. His distance from our chosen axis is 0
meters, so when the force is multiplied by the
distance, the result is zero.
The support exerts a 900 N force upward equal to
the total downward force from John and Mark. (600
N + 300 N = 900 N) This is force is exerted at an
unknown distance, X. Mark exerts a 300 N force at a
distance of 3 meters from the axis. (See figure 1)
The support’s force tends to make the seesaw turn
counterclockwise and Mike’s force tend to make the
seesaw turn clockwise. No other torques exist. In
equation form we have:
Questions and Problems
1. What is required for equilibrium to exist?
2. Two people are sitting on a seesaw that is
2.5 meters long. One has a mass of 40 kg
and the other has a mass of 60 kg. Draw a
diagram of this and put the size (or
magnitude) of all involved forces on your
diagram.
Figure 1
So the distance that John must sit from the
support is 1 meter. Mark must sit 2 meters from
the support (3m -1m= 2m). The person with half
the mass must sit twice as far away from the
support. This result agrees with our experience.
It may seem strange, but the physics of seesaws
is similar to the physics of standing on your feet.
Two people on a seesaw cause two downward
gravitational forces. The center support of the
seesaw provides an upward force. In the case of a
person standing, the ground exerts two upward
forces, one against each foot, while gravity exerts
a downward force at the center of one’s mass. If
you stand with equal weight on both feet, your
center of the mass is over a point midway
between your feet. (The center of mass is the
place where all the mass could be considered to
be concentrated.) Gravity pulls straight down from
the center of mass. (See Figure 2) Using your left
foot as the axis, the torque from gravity is your full
weight times ½ the distance between your feet.
3. Using the left end of the seesaw in the
diagram from problem 2 as an axis, write an
equation for balancing the torques and find
where the center support should be placed
for the seesaw in problem 2.
4. When a seesaw is used normally, a force is
exerted by one person and then the other as
their feet touch the ground. Describe this in
terms of torques and the rotation of the
seesaw about its axis.
5. A girl stands with 1/3 of her weight on one
foot, and 2/3 of her weight on the other. Over
what point is her center of mass? (Explain
your reasoning.)
6. Your foot is longer than it is wide. Explain
why it is easier to fall to one side rather than
forward or backward when you are standing
on one foot (the answer is related to torques).
7. A seesaw is set up so that one side is twice
as long as the other side. A 30 kg child wants
to use this seesaw. Find the two possible
masses that the other child could have and
still have a balanced seesaw.
The torque from your right foot is ½ your weight
times the total distance between your feet. These
torques are equal in size with one clockwise and
the other counterclockwise. Half the force needs
twice the distance from the axis to make you
balance.
If you are standing on one foot, where must your
center of mass be? In order for no torques to
cause you to tip, the center of mass must be right
over the one foot on the ground. In this case, no
torques are exerted because all forces are acting
at zero distance from the axis. With no torques,
you don’t tip over.
Figure 2.