KNES 361 L5

Introduction to Linear Kinetics

• Definition of kinetics: The study of forces associated with motion.

• Distinction from kinematics: Kinematics focuses on the motion itself, while kinetics investigates the forces causing that motion.

Understanding Force

• Definition of force: A push or pull resulting from the interaction between objects.

• Effects of force: Can change the position or shape of an object, depending on the magnitude of force applied and the object's resistance.

• Characteristics of force:

  • Magnitude: Strength of the force (e.g., how much force is applied).

  • Direction: The path along which the force is applied.

  • Point of application: Where the force is applied on the object.

  • Line of action: The straight line along which the force acts.

Categories of Forces

• Contact forces: Forces that occur when two objects are in physical contact with each other.

  • Examples: Applied force, friction.

• Acting at a distance forces: Forces that occur when objects are not in contact.

  • Examples: Gravitational force, magnetic force, electrical force.

Newton's Laws of Motion

First Law of Motion (Law of Inertia)

• Statement: An object at rest stays at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

• Explanation: Objects will maintain their state of motion unless a force causes a change.

• Concept of inertia:

  • Definition: The tendency of an object to resist changes in its state of motion (or rest).

  • Dependency on mass: Heavier objects have more inertia, making them harder to move or stop.

• Examples:

  • A small soccer ball has less inertia than a heavy bowling ball due to its lower mass.

Second Law of Motion

• Statement: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

• Formula: $F = m imes a$ (Force equals mass times acceleration).

• Explanation:

  • Increasing force leads to increased acceleration; increasing mass leads to decreased acceleration.

• Driving analogy: Pressing the gas pedal of a car increases the force exerted, causing the car to accelerate.

• Unit of force: Newton (N) is defined as kg·m/s².

• Derivation of units: The unit of force stems from its calculation: $1 ext{ Newton} = 1 ext{ kg} imes 1 ext{ m/s²}$.

Calculation of Acceleration

• Two methods of calculating acceleration:

  1. Using the kinematic equation: $a = \frac{\Delta v}{\Delta t}$ (change in velocity over change in time).

  2. Using Newton's second law: $a = \frac{F}{m}$ (force divided by mass).

Application of Newton's Laws through Problem Solving

Problem Example

• Given: 60 kg sprinter accelerates from 3 m/s to 9 m/s in 4.5 seconds.

• Determine: Average force required to produce acceleration.

1. Find acceleration using kinematics:

   • $a = \frac{9 \, \text{m/s} - 3 \, \text{m/s}}{4.5 \, \text{s}} = 1.33 \, \text{m/s²}$.

2. Calculate force using $F = m imes a$:

   • $F = 60 \, \text{kg} imes 1.33 \, \text{m/s²} ≈ 80 \, \text{N}$.

Weight

• Definition: Weight is the force acting on an object due to gravity.

• Weight formula: $W = m imes g$, where $g$ is the acceleration due to gravity (9.8 m/s² on Earth).

• Mass vs. Weight: Mass remains constant; weight changes based on gravitational pull.

• Gravitational differences on other celestial bodies (e.g., Moon: $g ext{ is approximately } 1.62 \, \text{m/s²}$ providing different weights).

Newton's Third Law of Motion

• Statement: For every action, there is an equal and opposite reaction.

• Explanation: Forces always occur in equal and opposite pairs.

• Example:

  • In a space shuttle launch: The shuttle exerts a downward force on the Earth while the Earth exerts an equal upward force on the shuttle, facilitating its ascent.

• Application in jumping: When a person jumps, they push down on the ground, which pushes them up with an equal force (ground reaction force).

Ground Reaction Forces in Sports

• Importance in biomechanics: Analyzes the interaction between a person's movement and the ground.

• Example in high jump:

  • During jump preparation, ground reaction force is lower, then increases during the propulsion phase to allow take-off.

Review and Real World Applications

• Importance of understanding the three laws in sports and daily activities.

• Reinforcement of concepts through examples and problem-solving.

• Encouragement for students to think about real-world examples that illustrate the application of Newton's laws.

Conclusion

• Recap of Newton's laws, their definitions, formulas, and significance in understanding linear kinetics.

• Reminder to apply these concepts in practical scenarios to deepen understanding of the principles of biomechanics.