Forces

Force

A vector quantity that describes the interactions between objects.


  • Measured in newtons (N)
  • Terminology to describe forces: force is applied, acts on, or is exerted on or by the object
  • For forces to take effect, two or more bodies must be involved (forces cannot be experienced by an isolated object)
  • Resolving and adding forces: use the same concept from the kinematics section for vector arithmetic

Newton's Laws of Motion

    Newton's First Law

  • A body that experiences zero net force will remain at rest or continue to move at a constant velocity (also called "inertia")
  • Hence, a body is in equilibrium when the net force is 0 (while there may be forces acting the body, the sum of these forces or the resultant force is 0)

    Newton's Second Law

  • The acceleration of an object is dependent on the net forces acting on the object and the mass of the object
  • Hence, F = ma, where F is the net force (N), m is the mass (kg), and a is the acceleration (m⋅s-2)
  • For objects in freefall, F = Fg = mg, as the only force acting upon the object is the gravitational force (therefore ma = mg → a = g)

    Newton's Third Law

  • "For every action, there is an equal and opposite reaction"
  • The "action" and "reaction" refer to forces; if Object A exerts a force on Object B, then Object B exerts an equal amount of force on Object A in the opposite direction.
  • All forces occur in such equal and opposite pairs
  • Fa on b = -Fb on a

Field Forces

Forces which act at a distance without needing physical contact between objects.


  • Gravitational Force (Fg): force of attraction between two masses. At the surface of the Earth, Fg = mg (mass times the gravitational constant), where the direction is towards the center of the Earth
  • Electric Force (Fe): interaction between charged bodies, where like-charges repel, and opposite charges attract
  • Magnetic Force (Fm): interaction between bodies that behave as magnets

Contact Forces

Forces which result from physical contact between objects.


    Normal Force (FN):

  • Force perpendicular and pointing away from a contact point
  • Note: students often confuse this force with the paired force acting opposite to gravity, which is wrong

    Frictional Force (Ff):

  • Resisting force which prevents objects from moving or slows them down while in motion
  • The force's direction points in the opposite direction of the object's motion along the contact surface
    • Static Friction: acts between bodies at rest, Ff ≤ μsFN (normal force times coefficient of static friction)
    • Dynamic/Kinetic Friction: acts between bodies moving relative to each other, Ff = μdFN (normal force times the coefficient of dynamic friction)

    Tension Force (FT):

  • Force often involved in ropes or strings which acts along the object's length
  • The force has the same magnitude but opposite direction of the applied force on the object

    Elastic Restoring Force (FH):

  • Force exerted by a stretchable object (often a spring) that tries to bring itself back to its natural length
  • Hooke's Law: the force acting to return a spring to its unstretched length is proportional and opposite in direction to the extension of the spring
  • FH = -kx, where k is the spring constant (N⋅m-1), and x is the extension/compression displacement of the object (m)

    Viscous Drag Force (Fd):

  • Force exerted by a fluid that opposes a body's motion within it (e.g. air resistance)
  • Dependent on viscosity (a fluid's resistance to flow)
  • IB only expects students to know the viscous drag force experienced by a small spherical body moving with a relatively small velocity in a fluid (Stoke's Law)
  • Fd = 6πηrv, where η is the fluid viscosity (kg⋅m-1⋅s-1), r is the radius of the sphere (m), and v is the velocity of the sphere

    Buoyancy Force (Fb):

  • Force pushing an object up when it is submerged in a fluid, due to differences in pressure
  • Fb = ρVg, where ρ is the density of the fluid (kg⋅m-3), V is volume of the fluid displaced (m3), and g is the gravitational constant