Biomechanics 3
Composition of Forces
Projekt: Cizí jazyky v kinantropologii - CZ.1.07/2.2.00/15.0199
Daniel Jandačka, PhD.

The net force is a vector produced when two or more forces act on a single object. It is calculated
by vector addition of the force vectors acting on the object.
Resultant (Net) Force = Blue Rreaction – Red Gravitational
Squat Jump of Shot Putter with barbell
 Measured at Human Motion Diagnostic Center  University of Ostrava

Forces acting in one line can be added by algebraic sum.
100 N
200 N
400 N
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Example
A coach is assisting his charge in bench press with a barbell of 100 kg. The coach is acting on the
barbell with the force of 70 N and the athlete with the force of 920 N in upward direction. Will
they manage to lift the barbell? What is the resultant force acting on the barbell?
Solution
Weight force of the barbell can be calculated as:
FG = mg = 100 ⋅ 9,81 = 981 N. Let us assume that upward direction of the force is a positive
direction, therefore:
F = 70 N + 920 N + (−981 N) = 9 N.
The resultant force F is 9 N and the athlete, with a little help from his coach, will manage to
lift the barbell.
Measured at Human Motion Diagnostic Center  University of Ostrava

Concurrent Forces
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Resultant force vector is the diagonal of the rectangle created by both horizontal and vertical
force and their parallel lines.
Přesněji můžeme popsat působení síly úhlem mezi výslednou silou a vertikální nebo horizontální
přímkou.

Trigonometric Technique
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Example
Vertical reaction force of the Earth (normal contact force), acting on a runner’s foot, has the
magnitude of FRA = 2200 N; friction force is acting backward and its magnitude is FRB = 500 N. What
is the direction and the magnitude of the resultant force FRC
Figure Landing in running. The blue arrow represents the resultant reaction force FRC. Black arrows
represent friction component of the reaction force FRB and vertical component of the reaction force
FRA, respectively, both acting on the foot.
Solution
To calculate the resultant force, we will use the Pythagoras’ theorem:
FRA2 + FRB2 = FRC2
FRC2 = 22002 + 5002
FRC = 2256 N. And arctangent function (arctg FRC / FRB) to calculate the angle between the
resultant and the horizontal force:
The magnitude of the resultant force FRC is 2256 N and its angle with horizontal plane is α =
77,5°.

The magnitude of the resultant force from two perpendicular forces can be calculated with the use
of the Pythagoras’ theorem, its direction can be calculated with the use of trigonometry.


Resolution of Forces
Resolution of forces allows us to analyze causes of motion separately in vertical, mediolateral,
and anteroposterior directions.
Figure Resolution of reaction force, acting on human foot when walking, into three component
forces. Solid line represents components of the reaction force acting on left foot; dashed line
represents components of the reaction force acting on right foot. Vertical component forces are
marked with blue, anteroposterior component forces are marked with black and mediolateral component
forces are marked with grey.
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Resolution of Forces allows to better understand human neuromuscular functions in many motor tasks.

Equilibrium
Statics is the branch of mechanics studying forces that act on bodies in static or dynamic
equilibrium.
Static equilibrium is a state where bodies are at rest
Dynamic equilibrium is a state where bodies are moving at a constant velocity (rectilinear motion)
In both cases the sum of the forces acting on them is zero.

Free body diagram pictures a body of interest (athlete) and external forces acting on it.
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Figure Free body diagram. FR is the sum of reaction forces acting on both legs and FG is
gravitational force acting on athlete’s body.
Note
In reality reaction forces originate in the place of contact between the feet and the ground.
However, for the sake of this free body diagram we can plot the resultant reaction force whose
point of application is in so called „centre of pressure”, i.e. away from the place of contact
between the feet and the ground.

Static Analysis
If only two forces act on a body in the state of either static or dynamic equilibrium, they have
equal magnitude but opposite direction.
Example
Weightlifter with the weight of 70 kg has lifted a barbell with the weight of 90 kg and is holding
it above his head. As long as he is holding the barbell, both bodies (weightlifter and barbell) are
in static equilibrium. What is the force that must act on the weightlifter’s feet to keep him in
static equilibrium?
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Thank you for your attention
Projekt: Cizí jazyky v kinantropologii - CZ.1.07/2.2.00/15.0199