Download Conditions of Linear Motion

Conditions of Linear Motion
Nature of Force
Definition of force – push or pull that may or may not be through
direct contact (e.g., diver’s feet pushing against a diving board,
force between two separated magnets)
Aspects of Force – vector quantity with both magnitude, direction, and
point of application
Magnitude – amount of force
e.g., weight is a common force; w=mg (note, f=ma)
Point of application of force – point at which force is applied to an
object; forces with equal magnitude and direction but
different points of application of force will have different
effects on an object
Force through center
of gravity will cause
linear translation.
Eccentric force will
cause translation and
rotation.
Force couple (two
forces with equal
magnitude and
opposite direction
applied equal
distances from the
center of gravity) will
cause rotation.
Resolution of Forces
Angle of pull
e.g., joint compressive and joint turning forces
Defining system
Internal forces – forces that occur within a system (e.g., If
the system is defined as the human body, muscular
contraction is an example of an internal force.
Internal forces do not cause a change in the position
of the center of gravity of the defined system. Kicking
the legs and swinging the arms has no effect on the
parabolic path of the center of gravity of a long
jumper because these are internal forces to the system
of the human body.)
External forces – forces that occur outside a system (e.g., If
the system is defined as the forearm, muscular
contraction of the biceps brachii is an example of a
force that is external to the system. Gravity is
external to the system of the long jumper and causes
the curved parabolic path taken by the center of
gravity.)
Anatomical pulley – tendons that pass over bony projections in
the body can be considered as anatomical pulleys
Composite effects of two or more forces
Linear forces – forces applied in the same direction along the
same line; these forces can be added by placing vectors head
to tail
+
=
Concurrent forces – forces acting at the same point of application,
but at different angles
Parallel forces – forces acting parallel to each other, but at a
different point of application
Orthogonal forces – forces acting perpendicular to each other;
they do not have an influence on each other
fr
fy
fx
fr
=
fx
fy
Newton’s Laws of Motion
Law of Inertia – a body will continue in a state of rest or uniform
motion unless acted upon by an unbalanced force
inertia – property that an object has that causes it to remain in its
state of rest or uniform motion; mass is a measure of inertia
Law of Acceleration (or the Law of Momentum) – the acceleration of
an object is directly proportional to the force causing it, it is in the
same direction as the force and is inversely proportional to the
mass of the object
f=ma (e.g., w=mg)
f=ma ft=m(at) ft=mv or ft=mv
ft= change in impulse
mv= change in momentum
Example of sprinter attempting to get out of the starting blocks:
results from instrumented starting blocks to record horizontal
force while sprinter is in the blocks applying force
Area under the force-time curve represents impulse (the larger
the area under the curve, the greater the change in momentum of
the sprinter in a horizontal direction).
sprinter 1
forcex
sprinter 2
forcex
time (sec.)
sprinter 3
forcex
time (sec.)
time (sec.)
Sprinter 2 gets out of the blocks the fastest. However, the area
under the force-time curve is relatively small. Thus, this
sprinter doesn’t change his/her momentum very much.
Sprinter 1 applies a greater average force than sprinter 2.
However, this sprinter stays in the blocks for a longer time.
Sprinter 3 is in the blocks for a relatively short time and, while in
the blocks, applies the greatest average force. Sprinter 3
has the largest area under the force-time curve (largest
impulse). Therefore, this sprintertakes advantage of getting
out of the blocks quickly and while in the blocks applies
greater force.
Law of Action and Reaction – for every action there is an equal and opposite
reaction
Forces that Modify Motion – In addition to forces that produce motion, there
are forces that act to modify motion.
Weight
An object’s weight is determined by the Law of Gravity which
states that the force of attraction between two objects is directly
proportional to the masses of the two object and inversely
proportional to the square of the distance between their centers of
mass.
F = (constant) m1m2
________
r2
w=mg
Contact forces
Normal reaction forces (equal and opposite forces) – For every
force there is an equal and opposite force. The starting
blocks push back against the sprinter with a force equal and
opposite to the force that the sprinter applies to the blocks.
Ground reaction force is a specific example of a normal
reactive force that we experience when standing, walking,
running, etc..
Friction – This is the force that opposes the effort to slide or role
one body over another.
coefficient of friction =  =P/W or  =P/N, where P is the
force required to move an object and W is the weight
of the object or the normal force (N); P is equal and
opposite to the frictional force (F) and T is the
reactive or normal force which acts perpendicular to
the surface. In this case, T = weight of the object.
W
F
P
T
We can use an incline to evaluate the coefficient of friction. The coefficient of
static friction is the tangent of the angle at which the object begins to slide.
The coefficient of sliding friction is the tangent of the angle at which the object
just continues to slide.
P = w sin


N = cos
mg=w
tan = sin/cos or tan = P/N = 
Static friction – force required to just get the object moving
Sliding friction – force required to just keep an object moving;
sliding friction in less than static friction
Rolling friction – force required to get an object rolling; rolling
friction is less than sliding friction
 Friction is proportional to the force pressing the two surfaces
together.
 Friction is independent of the surface area in contact.
 Friction is overcome by changing either the nature of the two
surfaces or the magnitude of the force applied.
 At slow speeds, friction usually decreases as speed increases.
 At extremely high speeds, friction increases.
Elasticity and rebound
The nature of rebound is governed by:
Elasticity – ability to resist distortion and return to its
original size and shape (the distortion that occurs is
called strain and is proportional to the stress (force
causing it)
Elastic limit – when stress is too large, permanent
distortion occurs
Coefficient of elasticity (or restitution)
e = (height of rebound/height of drop)1/2
Angle of rebound
Angle of
Incidence
Angle of
reflection
Factors influencing the rebound:
Coefficient of rebound (restitution)
Coefficients of rebound are less than 1. Therefore, the magnitude of the
vertical velocity after rebound is less than its magnitude
immediately prior to impact. If friction is assumed to be equal to
zero, the ball will rebound with an angle of reflection greater than
its angle of incidence.
Friction
Because of friction, the horizontal component of velocity after impact
will be less than this component before impact. If e is assumed to
be equal to 1, the angle of reflection will be less than the angle of
incidence.
Spin
If the linear velocity of the perimeter of a ball with top spin is greater
than the relative velocity of the center of mass of the ball and
rebound surface, the horizontal velocity of the center of mass of
the ball will be greater after rebound. This will result in an angle
of reflection greater than the angle of incidence.
The combination of coefficient of rebound, friction, and spin can be
used in various sports to create an advantage in play. Can you name
sports in which one or more of these variables can be manipulated to
create an advantage? Explain your answers.
Fluid Forces – Gasses (e.g., air) and liquids (e.g., water) are fluids.
Objects in these fluids are susceptible to three fluid forces:
buoyancy, drag, and lift.
Buoyancy – According to Archimedes’ Principle, the magnitude
of the upward force on a object immersed in a liquid is
buoyed up by a force equal to the weight of the liquid
displaced. If the upward force is greater than the weight of
the object, it will float; if less than the weight of the object,
it will sink.
Density – is the ratio of the mass of an object to its volume
Specific gravity – is the ratio of the density of a given volume of
material to the same volume of water. The specific gravity
of water is 1. Objects with specific gravity greater than 1
will sink and those with specific gravity less than 1 will
float. The human body is composed of tissues with various
specific gravity (e.g., specific gravity of bone and muscle is
greater than 1, specific gravity of fat is less than 1).
Therefore, people with a lot of adipose tissue float high in
the water. People with a high proportion of lean body mass
may sink.
Drag – is the resistance to the relative movement of an object through a
fluid. It is experienced on the leading edge of the object. There
are two types of drag – surface and form.
Surface drag – is the friction of a fluid passing over the surface of
an object. If the flow of the liquid is smooth and unbroken,
it is referred to as laminar flow. This usually occurs when
fluids slowly pass around objects with smooth surfaces.
Smooth surfaces will cause less surface drag than rough
surfaces.
Form drag – is associated with the area of the object presented to
the fluid. If the area is large and the relative velocity of the
fluid is great, it will create high pressure on the leading
surface of the object and the fluid will not be able to move
in smooth layers around the object. The layers of fluid will
break up causing a turbulent flow and a vacuum on the
back side of the object to retard the forward velocity of the
object. Form drag can be reduced by streamlining an
object. Blunt objects tend to have a high form drag and
streamline objects tend to have low form drag. A discus can
have either a high or low form drag. It depends on the
orientation of the discus to the fluid that is flowing past it.
This orientation of the long axis relative to the direction of
the fluid is called angle of attack.
Lift – an upward force of a fluid on an object associated with a
greater force on the bottom surface of an object. This is
associated with Bernoulli’s Principle, which states that the
pressure in a moving fluid decreases as the speed increases.
Laminar flow – object is streamline with respect to the fluid
passing over its surface and it presents a small cross
sectional area to the direction of flow of the fluid.
Note that the fluid moves around the object in layers
and that the fluid on the top goes the same distance in
the same time as the fluid on the bottom. Therefore,
there is an equal pressure above and below the object.
Therefore, there is no lift.
Turbulent flow -object is not streamline with respect to the
fluid passing over its surface and it presents a large
cross sectional area to the direction of flow of the
fluid. This results in a large drag force associated
with its form. Note that the fluid attempts to move
around the object in layers but breaks away and
demonstrates eddies on the back side of the object.
These eddies are indicative of turbulent flow. The
fluid that moves over the object goes the same
distance in the same time as the fluid that goes under
the object. Therefore, there is an equal pressure
above and below the object, resulting in no lift.
Lift and Drag – Note that the angle of attack causes both a lift and drag force
against the object. Also note that the fluid that passes over the top of the
object travels a greater distance than the fluid that passes below the object in
the same period of time. In accord with Bernoulli’s Principle, there is greater
pressure below the object than above the object. This difference in pressure
causes the lift force. In projectile activities such as discus and javelin
throwing, there is an attempt by the performer to maximize the lift to drag
ratio by throwing the object at an appropriate attack angle.
Lift force
Drag force
Magnus effect – is the explanation behind a curved path taken by a
spinning ball. Basically, it is the application of Bernoulli’s
Principle to a spinning ball.
High pressure - associated with high relative velocity
of ball perimeter and fluid
Top spin
Path of ball
Low pressure - associated with low relative velocity
of ball perimeter and fluid
Low pressure - associated with low relative velocity
of ball perimeter and fluid
Path of ball
Back spin
High pressure - associated with high relative velocity
of ball perimeter and fluid
Work, Power, and Energy
Work = force x distance
Power is the rate of doing work
Power = work/time = (force x distance)/time
Large values of power can be obtained by either having
elements in the numerator (force and/or distance)
with large magnitudes and/or having a small time
value in the denominator of the equation.
“Powerlifting” is a misnomer. Even though
powerlifters lift large loads, they perform the lifts in
relatively long periods of time. Activities such as
vertical jump and standing long jump are more
correctly considered to be power activities because
they involve short duration application of large
muscular forces of the legs.
Energy – is the ability to do work. There are many forms of
energy (e.g., chemical energy, strain energy, kinetic energy
and potential energy). Two forms of energy that are
possessed by freely falling objects and projectiles are
potential energy and kinetic energy.
Potential energy is energy due to position.
PE = mass x gravity x height = weight x height
h By virtue of this object’s height above the
surface, it has energy and the potential to
do work.
Kinetic energy is energy due to motion.
KE – ½ x mass x velocity2
Vy = 0
Ball projected upward
from the ground has
kinetic energy associated
with its vertical velocity.
+vy
position 1
At the highest point,
it has lost its kinetic
energy because vy is
equal to zero. However,
what it has lost in
kinetic energy, it has
gained in potential energy.
position 2
Prior to striking
the ground, the
magnitude of -vy
is equal to +vy.
-vy
position 3
Note that energy was conserved. What was lost in kinetic energy was gained
in potential energy and what was lost in potential energy was gained in
potential energy. Therefore, the total amount of energy of the system from
start to end remained the same. This concept is called the conservation of
energy.
LinearMotion.doc