Biomechanical Concepts of Linear Kinetics

Newton's Laws of Motion

• First Law - Law of Inertia: A body will maintain a state of rest or constant velocity unless acted upon by an external force that changes its state.

  • An object at rest will remain at rest unless a net force acts on it.
  • An object in motion will remain in motion unless a net force acts on it.

• Requires a force in order to acceleration depending on mass.

• Third Law - Action-Reaction: When one body exerts a force on a second, the second body exerts a reaction that is equal in magnitude and opposite in direction on the first body.

  • Action: You pushing on the ground.
  • Reaction: Ground pushing on you.

• Newton's Law of Gravitation: All bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the distance between them.

  • F1 = F2 = G \frac{M \times m}{r^2}

    • Where:
      • F1 and F2 are the forces of attraction between two bodies.
      • G is the gravitational constant.
      • M and m are the masses of the two bodies.
      • r is the distance between the centers of the two bodies.

  • The greater the mass, the greater the attraction.

  • The further apart, the less the attraction.

What is Force?

• A push or a pull.
• Basically: the effect of one body on another
• Direct Mechanical Contact.
• While there is no motion occurring, boy and dog are exerting equal and opposite forces on the rope.

How is force calculated?

• Force = mass \times acceleration

  • Mass is expressed in kilograms.
  • Acceleration = \frac{Vf - Vi}{tf - ti} = \frac{\Delta velocity}{\Delta time} = m/s^2
    • Velocity = \frac{displacement}{change \space of \space time} = \frac{position2 - position1}{time2 - time1}
  • 1 N = 1 kg \cdot m/s^2

• Example Calculation:

  • Given weight w = 100N and acceleration a = 2.5 m/s^2, find force F. Since w = mg, m = \frac{w}{g} = \frac{100N}{9.8 m/s^2} = 10.2 kg. Therefore, F = ma = 10.2 kg \times 2.5 m/s^2 = 25.5 N

• Example Calculation using pounds:

  • Given mass M = 8 lbs and acceleration a = 7 m/s^2, find force F. First, convert pounds to kilograms: m = 8 lbs \times 0.453 kg/lbs = 3.62 kg. Therefore, F = ma = 3.62 kg \times 7 m/s^2 = 25.34 N

Forces

• Examples of forces acting on a soccer ball include air resistance, surface friction, ball weight, and the force applied by a foot.

Vector Composition

• Forces can be added as vectors, where the length of the tail represents magnitude and the head represents the direction of force.
• Adding a negative vector to a positive results in a zero force.

Quantitative Example

• Calculate the magnitude and direction of the resultant vector that is formed when taking the sum of the two vectors.
• Given two forces F1 = 200N at 30°and F2 = 300N at 45°
• F{1x} = F1 \cos \theta = 200N \cos(30°) = 173.2 N
• F{1y} = F1 \sin \theta = 200N \sin(30°) = 100 N
• F_1 = 173.2 i + 100 j
• F{2x} = F2 \cos \theta = 300N \cos(135°) = -212.1 N
• F{2y} = F2 \sin \theta = 300N \sin(135°) = 212.1 N
• F_2 = -212.1 i + 212.1 j
• FR = F1 + F_2 = (173.2 - 212.1)i + (100 + 212.1)j = -38.9i + 312.1j
• |F_R| = \sqrt{(-38.9)^2 + (312.1)^2} = 314.5 N
• \theta_R = \tan^{-1}(\frac{312.1}{-38.9}) = -82.9°
• Since F_R is in the second quadrant: \theta = 180° - 82.9° = 97.1°

Qualitative Example

• Given Fx = 30 N and Fy = 60 N, one can qualitatively determine the resultant force vector, but not the magnitude and exact direction.

Finding Vector Components

• Given a vector, one may need to find its components.

Example of Vector Components

• Sue is pushing a table in the northwest direction; thus, the component vectors will be north (Fx) and west (Fy) direction.
• A northwest vector has a northward and westward component.

What is a Net Force?

• The single resultant force derived from the vector composition of all the acting forces.
• The force that determines the net effect of all acting forces on a body.
  • Example: Forces acting on the patella, including the vastus lateralis, vastus medialis, quadriceps tendon, patellar tendon, and fibula.

Practical Applications

• It is not uncommon for two or more forces to act about the point of torque calculation.
• Any force that does not pass through the elbow joint center will cause torque.
  • Example: Forces acting on the elbow joint, including the biceps brachii, brachialis, pronator teres, brachioradialis, forearm, hand, and dumbbell.

WORK, POWER AND ENERGY RELATIONSHIP

Work, Power, and Energy Relationships

• What is mechanical work?

  • The product of a force applied against a resistance and the displacement of the resistance in the direction of the force.
  • W = Fd where:
    • W is work
    • F is force
    • d is distance
  • Units of work are Joules (J).

• What is mechanical power?

  • The rate of work production.
  • Calculated as work divided by the time over which the work was done.
  • Power = \frac{Work}{Time} = Force \times Velocity
  • Units of power are Watts (W).

• What is mechanical energy?

  • The capacity to do some work.

  • Units of energy are Joules (J).

  • There are three forms energy:

    • Kinetic energy
    • Potential energy
    • Thermal energy

• During the pole vault, runners kinetic energy is stored by the pole as potential energy for subsequent release as kinetic energy and thermal energy.

• No velocity, no kinetic energy, in motion typically an inverse relation.

• What is the principle of work and energy?

  • The work of a force is equal to the change in energy that it produces in the object acted upon.

• Energy is the ability to do some work

• W = \Delta KE + \Delta PE + \Delta TE

Friction

• Interaction between two object surfaces (apply force to object that does not move).
• Greater force just before motion.
• Friction in motion will always be less than static & max static.
• Examples of reducing friction: oil, water, surface oil in car air hockey.
• Coefficient of friction is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. coefficient interaction between 2 surfaces

Examples of Altering Normal Reaction Force

• Pushing a desk: R = wt + P_y
• Pulling a desk: R = wt - P_y

Rolling Friction

• Typically less than sliding friction.

Linear Momentum

• Once something is in motion, it will remain constant except with no external force.

What is an impulse?

• The product of force and the time over which that force acts (F \times t).
• Can change an object's momentum.
  • Impulse = Force \times time = \Delta (Mass \times velocity)
• Units = Ns.
• Examples are a gun or a hammer throw

Practical Applications of Impulse

• When two bodies come into contact at one time, it is a moment of impact, and there is a transfer of force from one object to another, and both objects will deform as examples bouncy ball.

• A positive impulse occurs when the force is applied in the same direction as the movement.

  • It typically increases the velocity of the object or body.
  • Example: When a sprinter pushes off the starting blocks, the ground reaction force generates a positive impulse that accelerates them forward.

• A negative impulse occurs when the force is applied in the opposite direction of the movement.

  • It usually decreases the velocity or slows the object down.
  • Example: When a runner lands during gait, the ground exerts a.

Factors that Influence the Outcome when Two Bodies Collide

• Elasticity of the two objects

• Direction of Impact

  • Coefficient of restitution

    • How well they return to original shape.

Direct vs Oblique Impact

• In direct impact, the center of mass is on the line of impact, whereas, in oblique, it is not.
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Oblique Impact with a Fixed Surface

• Horizontal and vertical component
• Role of Friction
• Angle of Incidence
• Angle of Reflection
• When friction is negligible
• Angle of incidence ects ap8ection
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