Physics 11: Dynamics

2.1 Force and Motion

• Kinematics describes velocity and acceleration without their causes.
• Dynamics examines the causes of acceleration, specifically unbalanced forces.
• Newton's First Law (Law of Inertia):
  • Objects remain at rest or maintain velocity unless acted upon by an unbalanced force.
  • Inertia refers to the resistance of an object to change its state of motion.

Types of Forces

• Thrust (F_thrust): Force causing motion; ceases when contact ends.
• Tension (F_T or T): Force in a string/cable, acting away from an object.
• Spring Force (F_sp): Restores a spring to rest position; proportional to displacement.
• Normal Force (F_N): Perpendicular contact force from a surface.
• Friction Force (F_f): Parallel contact force opposing motion or potential motion.
• Gravitational Force (F_g): Field force directed toward Earth’s center.

Free Body Diagrams (FBD)

• Illustrate all acting forces as vectors, labeled by magnitude and direction.

Example Problems

• FBDs for various scenarios (e.g., sitting student, moving car).

2.2 Newton's Second Law

• Formula: F_net = ma (net force equals mass times acceleration).
• Problem-solving steps:
  • Draw a reference frame.
  • Create an FBD.
  • Determine contributing forces.
• Example calculations for net force and resistive forces.
• Gravitational force on Earth's surface: F_g = mg.

2.3 Vertical Acceleration

• Weight is the gravitational force.
• Apparent weight includes normal forces from surfaces.
• Example calculations of apparent weight in different scenarios (e.g., elevator).

2.4 Friction

• Friction opposes motion and is modeled as F_f = μF_N.
  • Kinetic Friction: When surfaces slide.
  • Static Friction: Prevents movement until a threshold.
• Example scenarios involving static and kinetic friction calculations.

2.5 Hooke’s Law

• Hooke's Law: F = -kx, where k is the spring constant and x is displacement.
• Terminal velocity occurs when drag equals gravitational force.
• Examples: Predict terminal velocities based on object setups.

2.6 Newton’s Third Law

• Law: Forces appear in pairs; action and reaction forces are equal and opposite.
• Examples include boat-ball system and tension in ropes.

2.7 Universal Gravitation

• Gravity is a force between masses proportional to their masses and inversely proportional to the square of the distance.
  • Formula: F = G(m1m2/r²)
• Example problems calculating gravitational forces between objects and determining gravitational field strengths at various locations.

Additional Notes

• Practice problems and exercises are referenced throughout the notes to reinforce each concept.