Forces and Momentum

• Free-Body Diagrams


  Representation of forces acting on an object as vector arrows
• Free-Body Diagrams


  • Forces are represented as vector arrows scaled to their magnitude and pointing in their direction
  • Each force is clearly labeled
• Drawing Free-Body Diagrams


  1. Represent the body as a point or shape

  2. Only include forces acting on the body

  3. Forces must be in correct direction and proportional length

  4. All forces must be clearly labeled
• Common forces in Free-Body Diagrams

  • Weight (W)
  • Tension (T)
  • Normal Reaction Force (N)
  • Upthrust (U)
  • Frictional Force (F)
• Free-Body Diagrams can be used to identify forces, resolve net forces, and analyze balanced/unbalanced forces
• Resultant Force


  Single force that describes the combined action of all forces on an object
• Balanced Forces


  • Forces cancel each other out, no resultant force
• Unbalanced Forces


  • Forces do not cancel out completely, there is a resultant force
• Determining Resultant Force in 1D

  Add forces in same direction, subtract forces in opposite direction
• Determining Resultant Force in 2D

  Use Pythagoras or trigonometry to resolve vectors
• Newton's First Law: An object will remain at rest or move at constant velocity unless acted on by a resultant force
• Translational Equilibrium


  When the resultant force on an object is zero
• If the resultant force is zero, the object is either at rest or moving at constant velocity
• Newton's Second Law: The resultant force on an object is directly proportional to its acceleration
• F=ma


  Resultant force (F) is equal to mass (m) times acceleration (a)
• An unbalanced force causes an object to accelerate in the direction of the force
• An object moving at constant velocity has no acceleration, so its forces must be balanced, which means the resultant force is zero. The drag forces are invisible to us, which makes this tricky to see.
• Newton's Second Law


  The resultant force on an object is directly proportional to its acceleration
• F = ma


  F = resultant force (N), m = mass (kg), a = acceleration (m/s^2)
• This relationship means that objects will accelerate if there is a resultant force acting upon them
• An unbalanced force acting on a body means it experiences a resultant force
• If the resultant force is along the direction of motion, it will speed up (accelerate) or slow down (decelerate) the body
• If the resultant force is at an angle, it will change the direction of the body
• Resultant Force


  The vector sum of all the forces acting on the body
• Resultant forces on a body can be positive or negative depending on their direction
• The resultant force could also be at an angle, in which case, the magnitude and direction of the resultant force can be determined using either calculation or scale drawing
• Acceleration


  If the resultant force is in the same direction as the motion of an object, the acceleration is positive. If the resultant force is in the opposite direction to the motion of an object, the acceleration is negative.
• An object may continue in the same direction however with a resultant force in the opposite direction to its motion, which means it will slow down (decelerate) and eventually come to a stop
• If there are no drag forces, or they're negligible, the acceleration is independent of the mass of an object
• Newton's Third Law


  Every action has an equal and opposite reaction
• Forces arise in pairs, where if object A exerts a force on object B, then object B exerts an equal and opposite force on object A</b>
• A Newton's third law force pair must be the same type of force, the same magnitude, and opposite in direction, acting on different objects
• The free-body force diagram in the question is an example of Newton's first law, not Newton's third law
• Contact Forces


  Forces which act between objects that are physically touching, e.g. friction, air resistance, tension, normal (reaction) force
• Non-Contact Forces


  Forces which act at a distance, without any contact between bodies, due to the action of a field, e.g. gravitational force, electrostatic force, magnetic force
• Friction


  A force that opposes motion, occurs when objects rub against each other
• Static Friction


  Friction that occurs when a body is stationary on a surface
• Dynamic Friction


  Friction that occurs when a body is in motion on a surface
• The surface frictional force always acts in a direction parallel to the plane of contact between a body and a surface
• Friction


  The force that slows down an object when it bumps into and rubs up against a surface