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Forces: Maintaining Equilibrium or Changing Motion
Objectives:
- Define force
- Classify forces
- Define friction force
- Define normal force
-
Understand the
difference between mass and weight
- Determine the resultant of two or more forces
using vector addition/composition
- Resolve a force into component forces acting at right angles to each other
using vector resolution
- Determine whether an object is in static equilibrium, if the forces acting on the object are known
- Detemine an unknown force acting on an object, if all the other forces acting on the object are known and the object is in static equilbrium
Introduction to Forces
A force is a push or a pull.
A force is something that has the ability to accelerate an object.
Forces are described in units of Newtons (N) or pounds (lb)
1 N will accelerate 1 kg at 1 m/s/s (F = m · a)
Also,
1N = 0.225lb and 1lb = 4.45N
How much do you weigh?
Classification of Forces
Internal forces:
forces that act
within the object or system whose motion is being investigated.
Alone, these forces cannot change the
motion
of the body center of mass.
External forces: forces that act on an object as a result of its interaction with the environment surrounding it.
These forces can change the
motion
of the body center of mass. Many sport
biomechanists are only concerned with external
forces.
Contact forces:
forces that occur from contacting objects
including solids and fluids. These forces
are subdivided into two primary categories.
Friction
force: the component contact
force that acts parallel to the surfaces in
contact (due to the
interactions of surface molecules). There is
static and dynamic friction, and static
friction > dynamic friction. The
mathematical description of friction is:
Friction Force = μ × Normal Force. Friction opposes motion, yet is also responsible for all horizontal motion.
With the aforementioned equation in mind,
how can you increase friction for any given
circumstance?
An interesting
discussion on race car tires...
Normal Contact Force: the component of a
contact force that acts perpendicular to the
surfaces in contact; both the normal and
friction forces are essential to human
movement.
Contact forces in running
Practice Problem: If the ground exerts a
vertical force on a runner that has a
magnitude of 2000 N and the coefficient of static friction between the shoe and the ground is 0.5, what is the maximum horizontal force he can generate under his shoe
before slipping?
Non-contact forces:
forces that
do not require contact between two objects;
the non-contact force of primary concern
here is gravity, which
causes
an acceleration of -9.81 m/s/s, no matter how
large or small the object is. With this in mind, how many N
does one kg of mass weigh? (remember Newton's
Second Law)
The Analysis of Multiple,
Simultaneous Forces
Usually, such
as in the aforementioned practice problem, there
are more than one force involved in a
physiological situation. A
free body diagram is
a tool for simultaneously analyzing multiple forces; it is a drawing of
the analysis object with all external forces
acting upon the object represented as arrows
showing their points of application and
directions.
Colinear forces: two or
more forces that have the same line of action,
but not necessarily the same direction; when
adding these types of forces, one can
use simple algebra.
Colinear
Forces Practice Problem: A weight lifter (mass =
100 kg) lifts a weight (100 N). The vertical
ground reaction force is 1000 N. What is the net
force acting on the weight lifter? How will the
center of mass be affected?
Non-colinear forces: if the forces are not colinear, you cannot algebraically sum each of the
forces. You must use vector addition, or this if
often called vector composition.
Vector addition, or
composition: the
addition of two or more non-colinear vectors, resulting in a
resultant force.
Non-colinear Forces
Practice Problem: The peak normal
contact force for a runner is 1800 N and the
simultaneous frictional contact force is 200 N.
What does the
resultant ground reaction force equal? Also, at
what angle, in relation to the horizontal axis,
is this resultant ground reaction force applied?
Vector resolution
allows you to resolve one resultant force into
perpendicular components; this might be thought
of as the opposite of vector composition.
Another
practice problem.
Static Equilibrium
(ΣF = 0)
When an object is at rest and the forces acting on the object are in equilibrium, they result in a net force of zero.
Weightlifter example: The
acceleration of this weightlifter is zero. If this
person's mass = 80kg, and the mass of the barbell =
70kg, what must the ground reaction force equal?
Fgrf
+ Fbw + Fbb = 0
What
would occur if the ground reaction force applied to
the weightlifter = 2000 N?
How might this occur?
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Additional Practice
Problems:
- Using vector addition,
calculate the resultant force acting on this
gymnast
- Calculate the reaction
forces applied to the
child on a swing,
assuming that the child is in static
equilibrium (ΣF = 0). Calculate the resultant
reaction force (FR), the two separate components
of the resultant reaction force (FRX
& FRY), and the
orientation of the reaction force in
relation to the horizontal (θ).
- The quadriceps
pulls on the patella with a force of 1000 N. The
patellar tendon also pulls on the patella with a force of 1000 N. A force from the femoral condyles is the
only other significant force acting on the
patella. If the patella is in static
equilibrium and the knee is flexed to 120
degrees, what must the magnitude of the force
that is applied to the patella by the femur be?
Chapter One Summary
- Forces are pushes or
pulls that can be represented by vector
quantities.
- External forces can cause
changes in the motion of the center of mass;
the most common are gravity and contact
forces.
- Friction and normal
forces constitute contact forces.
- Vector composition and
resolution are important tools in the
analysis of forces.
- Static equilibrium
indicates that the sum of all external
forces equals zero (ΣFx
= 0 and Fy = 0).
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