The Physics of the Squat
What makes squatting the most effective lift? The answer is the downward
pull of gravity on the lifter. The squatter is essentially pushing directly
against gravity. Gravity is a an attractive force that acts on every thing
that has mass in the universe. Isaac Newton, famous physicist and mathematician,
discovered the laws that govern this force. His law of universal gravitation
states that:
Every particle in the Universe attracts every other particle with
a force that is directly proportional to the product of their masses and
inversely proportional to the square of the distance between them.
From this law, the the acceleration due to this force of gravity near
the surface of the earth is approximately 9.8 meters per second squared.
This means that if two object are dropped from the same height, they will
hit the ground at the same time, regardless of how much they weigh(of
course, one must neglect air resistance). This is how weight is defined.
An objects weight is defined as the acceleration of gravity g multiplied
by its mass m (mg). For example, a person having a mass of 50 kilograms(kg)
would have a weight of 490 kg meters per second squared, or 490 Newtons(N).
The acceleration of gravity constant was found using Newton's famous three
laws of motion:
1. In the absence of external forces, an object at rest remains at
rest and an object in motion remains in motion with a constant velocity.
2. The acceleration of an object is directly proportional to the net
force acting on it and inversely proportional to its mass.(The equation
(F=ma, or Force=mass * acceleration).
3. If two objects interact,the force exerted by the first object on
the second object is equal in magnitude and opposite in direction to the
force by the second object on the first.
The Squat incorporates all of these laws. For example, take the man squatting
in the picture below. Let's say that he has a mass of 100 kg and the weight
has a mass of about 350 kg. What force must he exert on the bar to
stop himself at parallel, the position shown in the picture?
( www.graphics.stanford.edu)
Let's call the mass of the man m and the mass of the weight M. The total
downward force acting is:
F = mg + Mg = (100 kg)(9.8 m/s^2) + (350 kg)(9.8 m/s^2) = 4410 N
Since F = ma and the man, at this instant he is at parallel is not accelerating,
therefore a =0 and the net force acting in the system must equal 0. This
means that the man must exert a force equal and opposite to the force
applied. This force is called a normal force(n). The downward force
exerted on the man is 4410 N, so when he is sitting at parallel, he must
be exerting a force of 4410 N as well. This problem is an example of static
equilibrium, or when an object has no acceleration, making the net
force equal to zero. The man must exert a force greater than 4410 N to
lift the weight from parallel.
What force must the man exert to accelerate the weights up at 1 m/s^2?
Once again, we use Newton's second law, F = ma. The equation for the forces
acting on the object is:
F = ma = n  (M + m)g = n  4410= (450kg)(1 m/s^2)
n = force of man = 450 N + 4410 N = 4860 N
The man must exert a force of 4860 N on the bar to accelerate the weights
at 1 m/s^2.
The man adds 50 kg to the bar. If he is capable of exerting a force
of 5050 N on the bar, will he be able to lift the weights to their initial
position(assuming he can exert that force for a long time)? If so, what
is the acceleration of the bar?
The total downward force of the weights would be (100 kg + 350 kg + 50
kg)(9.8 m/s^2) = 4900 N
Therefore the man will be able to lift the weight, and his acceleration
will be:
a = F/m = (5050  4900)/(500 kg) = .3 m/s^2
