9/23 in class Newton's Laws and Forces

Motion and Forces

• Acceleration: Occurs when an object's speed or direction changes. It is the effect of a net force, not a force itself. If an object is moving at constant speed around a curve, it is accelerating due to changing direction.

Newton's Laws

• Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force (i.e., if $F_{net} = 0$, then velocity is constant).
• Newton's Second Law: The net force acting on an object is equal to the product of its mass and acceleration ($F_{net} = ma$). This describes a cause-and-effect relationship where net force (cause) produces acceleration (effect).
  • Forces and acceleration are vector quantities. Newton's Second Law can be split into components: $ΣF<em>x = ma</em>x$ and $ΣF<em>y = ma</em>y$.
• Newton's Third Law: For every action, there is an equal and opposite reaction. Action-reaction pairs are equal in magnitude, opposite in direction, and act on different objects (e.g., force of A on B = - force of B on A).
  • Example: Earth exerts a gravitational force on you, and you exert an equal and opposite gravitational force on Earth.

Types of Forces

• Weight (Gravitational Force, $F<em>w$ or $F</em>g$): The force exerted by a planet (e.g., Earth) on an object, always pointing towards the center of the planet. Measured in Newtons ($N$).
• Normal Force ($F_n$): A contact force exerted by a surface on an object, always perpendicular to the surface.
• Tension Force ($F_t$): The force exerted by a rope, cable, or string when pulled taut.
• Friction Force ($F_f$): A force that opposes the relative motion or tendency of motion between two surfaces in contact. Always parallel to the surface.
  • Static Friction ($F_s$): Opposes the initiation of motion and can vary in magnitude up to a maximum value to maintain equilibrium. It keeps an object stationary.
  • Kinetic Friction ($F_k$): Opposes motion when surfaces are slipping or sliding past each other. It takes over once static friction's maximum value is surpassed and the object is in motion.
• Thrust/Push ($F<em>p$ or $F</em>{thrust}$): A generic force applied to an object, often from an engine or a direct push.

Units of Force

• The SI unit of force is the Newton ($N$). $1 N = 1 \frac{kg \bullet m}{s^2}$.
• A common imperial unit is the pound (lb). The conversion is approximately $1 ext{ lb} hickapprox 4.45 ext{ N}$.

Free Body Diagrams (FBDs)

• Purpose: To visualize all external forces acting on a single object.
• Steps:
  1. Identify the Object: Clearly define the specific object being analyzed.
  2. Represent as Point Particle: Draw the object as a single point, ignoring its size and shape.
  3. Choose Coordinate System: Define a coordinate system (e.g., x-y axes). Often, it's beneficial to tilt the coordinate system so that the acceleration (if any) is along a single axis, simplifying component calculations.
  4. Draw and Label Forces: Draw arrows originating from the point particle, representing each force. Label them based on their type (e.g., $F<em>w$, $F</em>n$, $F_t$). The direction of each force is crucial and must be accurate (e.g., normal force is perpendicular to the surface).
  5. Indicate Acceleration (Optional): If known, denote the direction of acceleration or state if the net force is zero.