Biomech Theory Review (Final)

What is linear kinetics?

• The study of the forces that cause motion in straight lines

What is linear momentum?

• The product (multiplication) of a system’s (object/ person of group or world) mass and velocity

• Quantifies the motion and inertia of a system

• Momentum is directly proportional to an object or system’s mass and velocity

  • The greater an object’s mass or the greater an object’s velocity, the greater it’s momentum

• As an equation it is represented as P = mass x velocity

  • P is a vector quantity that has magnitude and direction

What is conversation of momentum?

• The idea that moment in a system at it’s initial time (Ti) is equal to it’s final time (Tf)

  • There is no change (no gain / loss) of momentum as collisions or movements progress

  • If a car rear ended someone, the trailing car would slow down while the leading car would speed up while the changes in motion would be proportional to each other, the momentum of the cars have a system that both cars will nor have change

  • Ppre = Ppost (m1v1 + m2v2 = m1’v2 + m2’v2)

What are perfect collisions?

• 2 major scenarios where observing the perfect collision can be used to solve for post collision velocities

  • Collision where 2 objects have the same mass AND one object is stationary and the collision is perfectly head on (A perfect transfer of momentum)

    • Where V1 = V2’

  • Collision where objects of a same or different mass have the same post collision velocity as each other

    • Where V1’ = V2’

What are non perfect collisions?

• A scenario where we need a measure to represent bounciness so that we can solve for non perfect collisions

• We use e (coefficient of resistitution) to represent bounciness

Perfect Elastic (e = 1)

• No loss of energy (where the ball bounces to the same height it was dropped)

Perfectly Inelastic Collisions (no bounciness) (e = 0)

• All energy is lost ( ball doesn’t bounce)

Not perfectly elastic collisions (E is b/w 0 and1)

• Some energy is lost but the ball bounces somewhat)

What directions would objects go depending on the mass of collisions?

Lower mass colliding with a stationary object of a higher mass: Big mass moves positive, small mass moves negative.

Higher mass collides with a moving object of a lower mass: Big mass becomes stationary while small mass moves positive.

Object with a lower mass collides with a lower mass moving in the same direction: Both masses move positively in the same direction.

Where does e (coefficient of restitution) come from?

e comes from the post bounce velocity being divided by the drop height velocity.

When a golf ball is dropped from the waist it will bounce back to the same height.

• There is tons of energy upon bounce and so it doesn’t have the same amount of energy to bounce back to the height the ball was dropped from

• when dropped from a height the ball will hit the ground with the same Vf, but the

• new Vi as it leaves the ground will be less than the pre bounce Vf.

E is the relationship between pre collision or pre bounce velocity and post collision or post bounce velocity.

How does static equilibrium change in linear kinetics and kinematics?

• Fw remains the same, however Fma is added onto the equation which is the extra force imposed by the scenario such as a forced imposed by the elevator

What happens during a pullup or deadlift?

Pullup

• Fn against your hands will be equal and opposite to your Fw when you’re at the bottom or top of the bar

  • Pulling up from the bottom position will increase and will be felt as if the body got heavier

Deadlift

• The bar is stationary against the floor, pulling it up slightly, normal force of the barbell will go down while the normal force of the the floor against the feet will go up but the sum of Fnp and Fnb will be the same as if you aren’t touching the bar

• As soon as you lift the bar from the ground, you produce an acceleration and therefore a force causing your Fn p to be greater than the previous sum of Fnp + Fnb

• Force decreases when you reach maximal speed, trading off strength for speed

What happens when you land from a jump?

• When landing, there is an initial downward impact velocity (Vi) that is followed by a stop velocity (Vf = 0m/s) when the COM slows down to a rest.

  • The change in velocity occurs over some amount of time and requires an acceleration in the opposite direction ( deceleration)

  • Vi dictates deceleration since Vf is 0, therefore it will be a negative velocity over the change in time

  • Stopping faster means Vf - Vi occurs over a shorter time (small delta t), but this requires that acceleration is much larger

  • Stopping slower means having a longer time and a smaller acceleration

• The total vertical component of the reaction force (Fn) must therefore equal the sum of BW and the force produced by the body’s mass decelerating

What is impulse?

• (J) represents the cumulative effect of a force acting for a time

• J = F (delta t)

• Impulse is therefore measured in Newton seconds (Ns) which are equivalent to momentum units

• 10 Ns = 10 kgm/s x s = 10 kgm / s

What are the 2 things we can do with impulse momentum?

• Keep the change in momentum fixed (delta p)

  • We can manipulate F by changing the duration of its effect either increasing or decreasing

  • An object with a Vi not equal to 0m/s comes to rest where Vf = 0m/s

• We manipulate velocity, changing momentum

  • An object at rest Vi = 0m/s has it’s Vf not = 0m/s (slow / fast)

    • We can manipulate (increase / 2x increase) Vf by changing the delta t duration of applied K

What is angular kinetics?

• Investigation of the causes of rotational motion with respect to the forces that cause the rotational motion

• Includes moment of inertia and angular momentum

• Also includes torque or moment of force

What is torque or moment of force?

• Crucial for understanding all human movement

• Calculating torque is necessary to explain strength, understanding that we need to calculate moment arms which describe how torque allows us to lift heavier and safer

• Torque: the tendency of a force to produce a rotation

• Moment: used to express a physical quantity acting at ( multiplied by) a distance

  • Moment of Force is the force acting at a distance

• T = F x r or M = F xd

What is a moment arm?

• The perpendicular distance from the line of action to the axis of rotation (AoR)

What is the line of action and axis of rotation?

LoA: Imaginary line through which force is applied and acts

• It extends infinitely in both directions of the applied forces orientation

AoR: A point which rotation occurs

• Fulcrum

  • Force is measured in N, MA is measured in Meters

  • Torque is measured in Nm (newton meters)

  • Changes to either force will cause a proportional change in Torque.

Considering static equilibrium: T = 0Nm

What can be said about torque as a vector quantity?

• + rotation: counter clockwise

• - rotation: clockwise

How does limb orientation dictate moment arms?

• Moment arms due to weight will change only with changes in limb orientation relative to gravity

What are the resistance types?

Changes in the type of resistance when imposed a force will change the directions of the LoA and therefore the lengths of the moment arm.

• Free Weights (LoA: up +down): Force proportional to mass and gravity which always produce LoA’s that go up and down.

• Manual resistance (LoA: any direction): Push / pull in therapy can result in LoA’s of any direction as the force can be directed in any direction

• Cables (LoA: any direction): Force is proportional to the mass and gravity that is modified by pulleys or cams to change the direction of the cab;e’s pulling force

• Elastics (LoA: any direction): Force is proportional to the stiffness and stretch distance of the elastic and the LoA’s can be in any direction

What are levers?

• fundamental type of simple machine where input work is modified at output, the modification may mean that the output work has changes with respect to magnitude and / or distance of force

• Have 3 constituent parts:

  • Fulcrum: AoR

  • Load: Force to be moved at some distance

  • Effort: Forced to be applied at some distance

• The relative position of the fulcrum, load and effort differentiates and defines a lever into a lever class

  • Their relative positions also change the general mechanical advantage inherent to each lever class

What is mechanical advantage?

M load / M effort = 1

• We can split these across the equal sign and perform the same total work (moment of force) at input and output but with a different force and / or distance

• If a mechanical advantage is 2, the Feffort will move an Fload that is of 2x it’s magnitude, but can also mean that the effort force must be at 2x as far from the fulcrum, compared to the distance of the load force

What should we know in general about Mechanical Advantages?

• MA > 1 means that a smaller Feffort moves a magnitude that is greater than the Feffort applied, and that this is accomplished by a Deffort that is longer than the Dload

  • Feffort is amplified to its multiple by MA

• Having an MA < 1 means that a larger Feffort moves a magnitude that is lesser than the Feffort applied and that is accomplished by a deffort that is shorter than the dload

  • Feffort is attracted to its multiple by MA

What are the classes of Levers?

1st: Fulcrum is b/w the load and effort

• Teeter totter

• MA can be <1 or >1

2nd: Load is b/w effort and fulcrum

• Wheelbarrow

• MA is always >1

3rd: Effort is b/w fulcrum and load

• Tongs

• Ma <1 always

What can be said about the mechanical advantages of levers?

• First class levers have a neutral or ambigouous mechanical advantage

• Second class levers have a mechanical advantage for the force of effort based on the distance of effort always being larger than the Dload

• Third class levers have no MA for force of effort, based on distance of effort being shorter always than Dload, which have a Fload that is <1

Why have human joint muscles evolve to function primarily as 3rd class levers with inherent MA < 1?

• 2nd class levers while allowing force amplification allow lifting of heavier loads have a trade off / deficit of requiring that the effort force moves a large distance relative to the shorter distance that the load force moves

• 3rd class levers. while having a mechanical disadvantage where it always takes more force to lift the load that is produced, have the benefit of the effort force moving a relatively shorter distance than the load force

• Muscle excursion is the total amount of distance a muscle can shorten or lengthen (ranges from 3 - 6 cm) total displacement depending on the muscle

  • Most of our muscle joints evolved in preference trading force for distance and consequently speed (ROM and Ang. Vel.)

What 2 muscle joints act as both 2nd and 3rd class levers?

• The Jaw

• Plantar Flexion at the Talocrural Joint

What are internal moment arms and resultant joint moments?

• Our joints allow our muscles to produce linear pulling forces against the insertion points of respective limb segments to rotate those limb segments

• Muscle insertions tend to be within a few cm of their operating joint

  • Internal moment arms of muscle joints can maximally only be as long as this distance

  • TO counter external torques that are produced by forces that generally act along much longer external moment arm distances the muscles are required to produce force enough so that the Minternal = -Mexternal

  • However joints don’t only have a single muscle producing force via a single moment arm

  • RJM, is the net rotary tendency of all tissues spanning a joint

    • All torques that arise from all the pulling forces of all muscles, ligament, skin, etc. that span a joint

How can we use biceps as an example for RJM and internal moment arms?

• Bicep curl requires that the biceps etc. lifts the forearm, but the triceps will also be pulling on the forearm in the other direction

• Biceps need to counter the weight of the forearm and dumbbell (Mexternal) but also the pulling force of triceps going in the other direction (Minternal / RJM)