Newton's Laws of Motion

Newton's Laws of Motion

Introduction to Newton's Laws

  • Isaac Newton: A 17th-century physicist and mathematician whose theories are still widely used.

  • Focus: Three laws of motion.

Newton's First Law: Inertia

  • An object in motion stays in motion (or at rest) unless acted upon by a net force.

  • Essentially: objects resist changes in their state of motion.

  • Net Force: The vector sum of all forces acting on an object.

    • Example: Two people pushing a box in opposite directions. If forces are equal, there is no net force and no motion. If forces are unequal, there's a net force and acceleration.

Newton's Second Law: Force and Acceleration

  • An acceleration is produced if the sum of the forces is nonzero.

  • \sum F = ma where \sum F is the net force, m is the mass, and a is the acceleration.

  • The direction of acceleration is the same as the direction of the net force.

  • Forces are vectors and must be summed accordingly (component-wise).

  • Example: Pushing a car.

    • Car mass: m = 1000 kg

    • Acceleration: a = 0.05 m/s\,^2

    • Force needed: F = ma = (1000 \text{ kg})(0.05 \text{ m/s}^2) = 50 \text{ N}

Newton's Third Law: Action and Reaction

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

  • Examples:

    • Mosquito landing on your arm: The mosquito experiences a force to stop, and you experience an equal and opposite force (though imperceptible).

Inertia, Mass, and Weight

  • Inertia: The tendency of an object to resist changes in its motion. Quantified by mass.

  • Mass: A measure of inertia. A massive object has a high tendency to "do nothing" (resist motion).

  • Units:

    • SI: Kilograms (kg) are units of mass. Newtons (N) are units of force.

    • SAE: Pounds (lbs) are commonly used to denote mass, but they are actually a unit of force. Slugs are the SAE unit of mass.

  • Common Misconception: Saying "I weigh 100 pounds" is technically incorrect; it should be "I have 100 pounds of force."

The Role of Friction

  • In everyday life, friction often obscures Newton's first law.

  • Example: A chair moving in a circle will eventually stop due to friction.

  • Frictionless environments (or nearly so) demonstrate Newton's laws more clearly. Example: Olympic curling.

Application of Newton's Second Law

  • Summing forces in one dimension determines acceleration in that dimension.

  • \sum Fx = max (sum of forces in the x-direction equals mass times acceleration in the x-direction).

Tug of War Example

  • Animation demonstrates balanced and unbalanced forces.

  • Balanced forces: No motion (or constant motion).

  • Unbalanced forces: Acceleration in the direction of the net force.

Considerations for Newton's Laws

  • Forces are applied via ropes: The force applied is the same at the point of attachment, regardless of the distance to the source of the force.

  • Force acting at a distance is a more complex topic.

Examples of Newton's Third Law

  • Normal Force: When you stand on the floor, gravity pulls you down, but the floor exerts an equal and opposite force (the normal force) upward.

  • Gravitational Force: Earth pulls on the moon, and the moon pulls on the Earth with an equal force.

  • Firing a Gun: The bullet accelerates out of the barrel, and the gun recoils due to an equal and opposite force.

  • Rocket Propulsion: Exhaust is expelled from the rocket, and the exhaust pushes back on the rocket, propelling it forward.

Summary

  • Newton's three laws of motion are applicable in everyday life, even with friction.

  • Forces are not directly visible, so vector diagrams (free body diagrams) are helpful for analysis.

  • Free body diagrams will be the focus of the next lecture.