Forces and Newton's Laws of Motion

Forces

• A force is a push or pull that causes an object to change its motion or shape
• Forces can be classified as:
  • External forces: acting from outside the system (e.g. friction, normal force, tension)
  • Internal forces: acting within the system (e.g. gravity, electromagnetic forces)
• Forces have both magnitude (amount of force) and direction

Newton's Laws of Motion

• First Law (Law of Inertia): an object at rest will remain at rest, and an object in motion will continue to move with a constant velocity, unless acted upon by an external force
• Second Law (F=ma): the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass
• Third Law (Action-Reaction): for every action, there is an equal and opposite reaction

Equilibrium

• Static Equilibrium: a state where the net force acting on an object is zero, resulting in no acceleration
• Translational Equilibrium: a state where the sum of forces in all directions is zero
• Rotational Equilibrium: a state where the sum of torques (rotational forces) is zero

Support Reactions

• Supports: external forces that prevent an object from translating or rotating
• Reactions: forces exerted by supports to maintain equilibrium
• Types of supports:
  • Fixed support: prevents both translation and rotation
  • Hinged support: allows rotation but not translation
  • Sliding support: allows translation but not rotation

Trusses

• A truss is a structure composed of triangular elements connected at joints
• Method of Joints: a method used to analyze trusses by considering the equilibrium of each joint
• Method of Sections: a method used to analyze trusses by considering the equilibrium of each section of the truss

Centers of Gravity

• Center of Gravity (CG): the point where the weight of an object can be considered to act
• Center of Mass (CM): the point where the mass of an object can be considered to act
• For uniform objects, CG and CM are the same point

Moment of a Force

• Moment of a Force: the turning effect of a force around a pivot point or axis
• Calculated by: M = r x F, where M is the moment, r is the distance from the pivot point to the line of action of the force, and F is the force

Forces

• Force is a push or pull that causes an object to change its motion or shape
• Classified into external forces (friction, normal force, tension) and internal forces (gravity, electromagnetic forces)
• Forces have both magnitude (amount of force) and direction

Newton's Laws of Motion

First Law (Law of Inertia)

• An object at rest remains at rest, and an object in motion continues to move with constant velocity unless acted upon by an external force

Second Law (F=ma)

• Acceleration of an object is directly proportional to the force applied and inversely proportional to its mass
• Force (F) equals mass (m) times acceleration (a)

Third Law (Action-Reaction)

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

Equilibrium

Static Equilibrium

• Net force acting on an object is zero, resulting in no acceleration

Translational Equilibrium

• Sum of forces in all directions is zero

Rotational Equilibrium

• Sum of torques (rotational forces) is zero

Support Reactions

• Supports are external forces that prevent an object from translating or rotating
• Reactions are forces exerted by supports to maintain equilibrium
• Fixed support prevents both translation and rotation
• Hinged support allows rotation but not translation
• Sliding support allows translation but not rotation

Trusses

• Truss is a structure composed of triangular elements connected at joints
• Method of Joints analyzes trusses by considering equilibrium of each joint
• Method of Sections analyzes trusses by considering equilibrium of each section of the truss

Centers of Gravity

• Center of Gravity (CG) is the point where an object's weight can be considered to act
• Center of Mass (CM) is the point where an object's mass can be considered to act
• For uniform objects, CG and CM are the same point

Moment of a Force

• Moment of a Force is the turning effect of a force around a pivot point or axis
• Calculated by: M = r x F, where M is the moment, r is the distance from the pivot point to the line of action of the force, and F is the force