Forces Unit Flashcards

Fundamentals of Force, Mass, and Motion

• Force:

  • A push or pull acting upon an object.
  • Responsible for causing acceleration.
  • Standard unit: Newtons ($\text{N}$).

• Mass:

  • The quantitative amount of matter contained within an object.
  • Standard unit: Kilograms ($\text{kg}$).
  • Invariant property: Mass remains constant everywhere, even on the Moon.

• Weight ($F_g$):

  • The gravitational force exerted on an object.
  • Formula: $\text{Weight} = \text{mass} \times g$
  • Standard unit: Newtons ($\text{N}$).
  • Variable property: Changes from planet to planet based on the local gravitational field.

• Acceleration of Gravity ($g$):

  • Specifically evaluates to $9.81\,m/s^2$ on the surface of the Earth.

• Inertia:

  • The inherent tendency of an object to resist any change in its state of motion.
  • Determinant: Depends ONLY on mass.
  • Proportionality: A greater mass yields greater inertia ($\text{more mass} = \text{more inertia}$).

• Acceleration:

  • Defined as a change in velocity over time.
  • Manifestations: Speeding up, slowing down, or changing direction.
  • Standard unit: Meters per second squared ($m/s^2$).

• Net Force:

  • The overall vector sum of all individual forces acting upon an object, calculated after adding them up and canceling opposite forces.

• Equilibrium:

  • State in which the net force acting on an object equals zero ($\text{Net force} = 0$).
  • Motion state: The object remains either entirely at rest OR continues moving at a constant velocity.

Types and Classifications of Forces

• Contact Force:

  • Any force that requires physical touching between objects to act.
  • Examples include: friction, tension, normal force, push, and pull.

• Field Force:

  • Any force that acts across a distance without requiring physical touching.
  • Examples include: gravity, magnetism, and electrical force.

• Normal Force ($F_n$):

  • The supporting force exerted by a surface pushing back on an object.
  • Acts perpendicularly at a right angle ($90^\circ$) relative to the surface.
  • Surface condition: On a flat horizontal floor, the normal force exactly equals the object's weight.

• Friction ($F_f$):

  • A resistive force that directly opposes motion between surfaces that are touching.

• Tension ($F_t$):

  • The pulling force transmitted and carried through a rope, cable, or string.

• Applied Force:

  • A push or pull applied directly to an object by an external person or thing.

• Air Resistance:

  • A specific form of friction exerted by air that pushes against an object moving through it.

Newton's Laws of Motion

• Newton's First Law (Law of Inertia):

  • An object maintains its state of rest, or continues moving at a constant velocity, unless acted upon by an unbalanced net force.
  • Real-world example: A person lurching forward when an automobile suddenly applies its brakes.

• Newton's Second Law:

  • Governed by the relation $F = ma$.
  • Force relationship: More force results in more acceleration ($\text{more force} = \text{more acceleration}$).
  • Mass relationship: More mass results in less acceleration ($\text{more mass} = \text{less acceleration}$).
  • Real-world example: A train requires significantly more force to speed up than an automobile due to its substantially larger mass.

• Newton's Third Law:

  • Every action has an equal and opposite reaction.
  • Real-world example: A rocket engine forcefully pushes exhaust gas downward, which simultaneously causes the gas to push the rocket upward.

Mathematical Equations and Calculations

• Newton's Second Law Formula:

  • $F = ma$
  • Meaning: $\text{Net force} = \text{mass} \times \text{acceleration}$

• Acceleration Formula:

  • $a = \frac{F}{m}$
  • Used specifically to calculate acceleration when net force and mass are known.

• Weight Calculation:

  • $F_g = mg$
  • Explicit calculation on Earth: $\text{Weight} = \text{mass} \times 9.81$

• Net Force in Two Dimensions (2D):

  • Step 1: Add all forces acting along the $x$-axis ($x$ forces).
  • Step 2: Add all forces acting along the $y$-axis ($y$ forces).
  • Step 3: Determine total resultant magnitude using the Pythagorean theorem:
  • $\sqrt{x^2 + y^2}$

Standard Units of Measurement

• Newton ($\text{N}$):

  • The universal derived unit used for ANY force, encompassing:
  • Weight
  • Friction
  • Normal force
  • Tension
  • Net force

• Kilogram ($\text{kg}$):

  • The fundamental unit used for mass.

• Meters per Second Squared ($m/s^2$):

  • The standard unit for acceleration, including the acceleration of gravity ($g$).