Download Newton`s Laws and Momentum – Script Draft Introduction One value

Newton's Laws and Momentum – Script Draft
Introduction
One value of biomechanics knowledge is that it helps you predict the potential
positive and negative outcomes of the way the athlete is performing a skill. When
you see a jumper reaching for the long jump take-off board you immediately know
how this is going to affect the length of the jump. The jumper's take-off foot will hit
the board well forward of the center of mass. The reaction force from the ground
will cause a braking effect and slow the jumper's horizontal velocity.
We've examined some important principles of kinematics that provide you will
essential analytical knowledge about motion such as position, velocity and
acceleration. In this module we apply the laws of motion developed by Sir Isaac
Newton to gain more insight about the most effective ways to perform a skill and
how incorrect technique can affect overall performance.
Newton asked three questions:
• What causes an object to accelerate? The answer is: a force
• How much does the object accelerate? The answer is: it depends on the
mass and the applied force
• What is providing the force? The answer is: all forces come in pairs.
One of your first tasks when analyzing the way in which your athlete is
performance a skill is to first identify all the forces and then determine if they are
having a positive or negative impact on the goal of that skill.
When you have completed this module you will be able to:
•
•
•
State Newtons three laws of motion
Apply these three laws to performing sport skills
Explain how extension of Newton's three laws – momentum – is related to
the performance of a sport skill
Newtons Laws of motion
•
Newtons First law of motion (Also known as the law of inertia)
Recall that:
• Mass is the amount of matter that makes up an object
• Weight is the force exerted by gravity on an object.
• Velocity measures the rate of positional change of an object. We
described velocity by talking about speed and direction. This soccer
ball currently has a velocity of zero. But when it is kicked we can
measure its speed in m/sec and determine its direction.
1
Newton's Laws and Momentum – Script Draft
•
Force is defined as an action that changes an object's velocity. This
can cause an object to slow down, speed up or change direction
depending on the direction the force acts in relation to the object's
velocity. When two forces of equal magnitude are acting from
opposing directions the forces are said to be balanced. A change in
velocity will only occur when an unbalanced force acts upon the
object.
This brings us to Newton's First law of motion. “A body will remain at rest or in
uniform motion in a straight line until an external unbalanced force acts on that
body to change its state of motion”.
The tendency of an object to maintain its velocity is known as its inertia. The
greater the mass of an object the harder it is to overcome its inertia with an
unbalanced force.
•
Newtons's second law of motion
Recall that:
• Acceleration is a measure of how quickly velocity changes when an
unbalanced force causes an object to move. When the unbalanced
force causes the speed of the object to increase we say that the
acceleration is positive. When the force causes the object to slow
down we say that negative acceleration (or deceleration) is
occurring. Like velocity acceleration has a magnitude and a direction.
This leads us to Newton's second law of motion. The amount of acceleration
produced when an unbalanced force acts on a body is proportional to the size of
that force.
This law is expressed as a mathematical formula: Force = mass x acceleration.
This means that if the same force is applied to two objects the object with the
smallest mass will have the greatest acceleration.
Important! Make sure you know this.
A force applied to a body causes:
• an acceleration of that body of a magnitude proportional to the force,
• in the direction of the force and
• inversely proportional to the body's mass.
If you want to speed up an object by a certain amount you have to adjust your
2
Newton's Laws and Momentum – Script Draft
force based on the object's mass. Bigger athletes need stronger forces
•
Newton's third law of motion
The simplest way to think about Newton's Third law is that forces come in equal
and opposite pairs. The law states that “For each action there is an equal and
opposite reaction”.
That is, whenever an object pushes another object it gets pushed back in the
opposite direction equally hard. You can't push on the ground, for example, without
it having an equal and opposite push on you. The harder you push on the ground
the harder it will push back on you and the higher you will jump, or the faster you
will run.
It you tried to throw a standing shot in roller skates you would see the result of the
shot pushing back against you with the same force you applied to the shot. The
shot would go forward and you would go backwards.
Here are some action-reaction guidelines
Basic rule
Example
Both forces are always there whenever
any force appears
Your foot pushes down against the
ground and the ground pushes back
The forces always have the same
strength
If you push harder against the ground
the ground will push harder against you
The forces always act in the opposite
direction
Your foot force and the ground forces
are opposite to each other
The forces always act on different
objects
Your foot acts on the ground and the
ground acts on your foot
Both are real forces and can cause
change in motion
You move forward when running, or up
into the air when jumping. The earth has
such a large mass its motion backwards
to your force is infinitesimally small
Examples of action-reaction
Remember that ground reaction forces occur in three directions.
•
•
•
3
Up – down – this allows us to jump
Forward (propulsion) – backward (braking) – this allows us to walk and run,
etc
Side to side (lateral forces, cutting or leaning.This allows us to turn, change
Newton's Laws and Momentum – Script Draft
directions or run on a curve.
Here is a comparison between three triathletes – two are running the Olympic
distance and one is running the Ironman.
•
Runner 1 – has a nice step length. His shin is vertical as the foot strikes the
ground so the ground reaction force is driving upwards and forward. This
force here is referred to as the resultant force. There is very little braking
force.
•
Runner 2 also has a nice stride length and foot strike. If we drop a plumb
line down the center look how close his foot is to the center of mass. The
center line is 156 degrees. If we resolve these forces he will have a little bit
of a braking effect, but he retains high vertical and horizontal forces.
•
Runner 3 is running the marathon portion of the Ironman. He's about half
way through so he is quite tired. This runner was the 2012 winner of
Ironman, Lake Placid so he is quite good. As his foot strikes the ground
notice how far out it is compared with his center of mass. This cause quite a
high braking force. He pushes off quite well – we'd like most of his push off
force carrying him this way. However, he straightens his leg out. The
previous runner was at 153 degrees. This runner is around 163 degrees.
This is a 10 degree difference. The previous runner was around here. Less
force is being lost due to braking forces – not to mention the jarring that
occurs back through the knee and hip joints when there is a large braking
force on each stride.
Momentum
•
Concept overview
Momentum is the quantity of motion possessed by a moving body.
The amount of momentum an object has depends upon two variables: how
much stuff is moving (i.e. its mass) and how fast the stuff is moving (i.e. its
velocity). In essence, momentum = mass x velocity and it is an important
concept in sports.
Any object with momentum requires a force stop it. However, you know from
experience that it take a lot more force to stop a massive object than it does
to stop a smaller object. You also know from experience that an object
moving at a very fast velocity will be harder to stop than an object moving at
4
Newton's Laws and Momentum – Script Draft
a slower velocity.
Conservation of Momentum
The momentum of a system does not change unless acted upon by an
external, unbalanced force. This is the Law of Conservation of Momentum
and you will likely recognize this as Newton's FIrst Law. In essence
momentum is always conserved in any collision. Here is an example of the
conservation of momentum – the momentum of the incoming cart loses its
momentum to the second cart in the collision.
You see this in sport whenever a collision occurs. As the bat and ball collide,
for example, most of the momentum of the bat is transferred to the ball,
which flies off into the outfield. The batter is able to manipulate two variables
to impart velocity to the ball– speed of the bat and mass of the bat.
Transfer of momentum
Transfer of momentum is really the application of conservation of
momentum. It's probably the most useful concept for both you and the
athlete to grasp. Momentum may be transferred from part of a system to
another part. Imagine a car traveling at 100 mph. The drivers side door is
not closed correctly. If the driver slams on the brakes and stops the car very
quickly the door will fly open because once the momentum of the car is
stopped by the brakes, the momentum moves into anything that is not
secured. The unsecured door picks up the momentum and violently opens.
In jumping we transfer momentum to the body when a moving body
segment stops. Blocking (quickly stopping) the swing leg transfers its
momentum to the jumper's body. The result is that an additional force is
transferred to the ground, and therefore there is a higher ground reaction
force.
Transfer of momentum through the kinetic chain
Another application of the transfer of momentum is the kinetic chain effect.
You've probably seen this gadget – it's called newton's cradle. It
demonstrates the transfer of momentum through each ball and ultimately to
the ball at the end of the system. You can think of these balls as
representing the transfer of momentum generated from the ground, through
the legs, hips, shoulders, arm and finally to the implement that accelerates
off at the end.
5
Newton's Laws and Momentum – Script Draft
The transfer of momentum through the kinetic chain involves a complex coordination of a moving chain of body parts. There are two main categories of
kinetic chain patterns: push-like and throw-like.
Push like movement pattern uses the kinetic chain simultaneously in a
single movement. Examples include the bench press, leg press, the sprint
start, the squat, and the basketball free throw. Push-like movements are
used to accumulate forces (or torques) generated about each joint to
produce a high overall force. This is why we use push-like movement when
we are moving heavy objects – such as a rugby scrum. It's also a useful
movement pattern to produce high accuracy. The reason a push-like pattern
is used in the basketball free throw is because it allows high accuracy and
high force production. This type of pattern is useful throwing technique for
children who have lower strength. However, while push like movements can
produce high force and accuracy they do not produce very high movement
speeds.
Throw like movements use the kinetic chain sequentially, one after another.
One theory why throw-like movements produce very high velocity is that
they make the best use of highly elastic tendons. The energy stored in the
elastic tendons causes them to recoil rapidly creating a magnet effect.
The magnet effect
Here is an experiment to demonstrate the magnet effect. First, here's the
normal transfer of momentum from one ball through to the end ball. This is
basically what a thrower is trying to do. The ground supplies the initial force
that must be transferred through the body to the implement.
However, the thrower is also trying add the magnet effect.
Take a look what happens when a magnet is added to this system. Notice
how much more velocity the end ball has now. The magnet accelerate the
ball to a very high velocity and it collides with the system with an increased
force. The result is that the end ball rockets off at a very high speed.
In baseball you will hear the term 'momentum pitching', “core torque,” or
“separation.” These terms express the idea of creating the magnet effect to
accelerate the implement off at a much higher velocity. You can think of
“form” or “technique” as the transfer of momentum without the magnet.
Creating a stretch-reflex through 'core torque', and 'separation', is analogous
to adding the magnet.
Momentum transfer is optimally effective when velocity is transferred from
the lower half of the body through a stretch-reflex mechanism to “super
6
Newton's Laws and Momentum – Script Draft
accelerate” the arm and hand. Core torque and separation are important
components in activating the stretch-reflex. As the front foot strikes the
ground the hips are open towards the target while the shoulders remain
closed. This actives the stretch reflex. Once the thrower, a pitcher, in this
case, puts on the brakes during front foot strike momentum travels though
the muscular core into the shoulders. Using the stretch-reflex in the core and
chest (the magnet) additional velocity is imparted to the arm launching the
implement with a very high velocity.
The basketball chest pass is another interesting application of transfer of
momentum. It is a push-like movement and is used because of its high
accuracy. However, it is not possible to produce high speed with a push-like
action. But, the player can incorporate a throw-like pattern to perform a push
pass.
Recall that throw-like patterns use the magnet effect by stimulating the
stretch-reflex. The optimum chest pass is produced by first stepping
forwards to give momentum to the body. The next task is to push the
shoulders forwards rapidly, simultaneously moving the elbows outwards and
forwards while the hands remain close to the chest. This does two things: a
large momentum is given to the system (the upper body and arms) and
there is a forward velocity. The hands and fingers are squashed to the ball
so their tendons are stretch rapidly while the elbows are flexed quickly so
their tendons are also stretched. The second part of the throw requires a full
extension of the elbows. In this part of the throw there is a significant recoil
of the tendons of the elbows. It is this recoil that increases the speed of the
throw.
Conservation of momentum during flight
The transfer of momentum worked in our previous discussion because some
part of the athlete's body was attached to the ground to create and actionreaction effect with the large earth mass. What happens when the athlete is
in flight and one body segment is moved?
Newton's third law of action-reaction still remains in effect. When a body is
free in flight an action in one part of the body will produce a reaction in some
other part. This is the classic illustration you will see to demonstrate this –
the upper body is swung forward and the lower body will also swing forward
in reaction. You will see this referred to as the Law of Ends and Middle. If
one end of the body is moved in any direction, the opposite end will move in
the same direction and the middle of the body will move in the opposite
direction.
Another example of this is seen in the high jump. As the head and shoulders
7
Newton's Laws and Momentum – Script Draft
drop, the hips rise and the lower legs are drawn towards the head. As the
head rises the hips drop and the legs rise.
References
Blazevich, Anthony. Sports Biomechanics: The basics: Optimizing Human,
Performance. A & C Black, London, 2007.
8