P2.2 - Newton's Laws

• The gravitational interaction between an object and the earth produces the same magnitude force on the object and the earth.
• Pairs of forces arise when objects interact. In an interaction pair:

  • Each force acts on a different object.
  • The forces are of the same size and type (e.g: gravitational).
  • The forces act in opposite directions.
• Interaction pairs are from Newton's Third Law:

  • "For every action there is an equal and opposite reaction."
  • In other words, forces always come in pairs.
• Non-contact forces can happen between objects that are not touching each other, examples are:

  • Electrostatics.
  • Magnetism.
  • Gravity.
• Charges, magnets, and masses interact at distances.
• A field is an area where an electrical charge, a magnetic material, or a mass experiences a force.
• Forces are vectors, so you can represent them with force arrows.
• Force arrows for non-contact forces start at the centre of an object.
• On a diving board, the Earth pulls you towards it. You exert a force on the earth, but it is so large the earth does not move towards you by a measurable amount.
• Contact force arrows are drawn from the point of contact (e.g: a diving board onto a person's legs).
• Bonds between atoms behave like springs. An object will deform a surface until the normal contact force balances the weight.
• Contact force: Friction

  • Interaction pair: force of object on surface and force of surface on object.
  • Caused by: atoms on the surfaces interact when rough surfaces slide over each other.
• Contact force: Drag (air or water resistance)

  • Interaction pair: force of (falling) object on air and force of air on the object.
  • Caused by: particles of the liquid or gas collide with the object, and the object pushes them away.
• Normal contact force: (e.g: on an elephant)

  • Interaction pair: force of elephant on the ground and force of the ground on the elephant.
  • Caused by: solid objects deforming when force is exerted onto them. Bonds in its particles compress.
• Contact force: upthrust (e.g: on a boat)

  • Interaction pair: the force of the boat on water and the force of water on the boat.
  • Caused by: gravity producing pressure differences in a fluid, the pressure produces a net upwards force.
• Contact force: tension (between a cord and a bungee jumper)

  • Interaction pair: the force of the jumper on the cord and the force of the cord on the jumper
  • Caused by: deformities in a solid when a force is exerted onto them. Bonds condense.
• Weight is the gravitational force of one object to another.
• A free body diagram shows the forces acting on a single object. The object is represented as a single dot or box, and the forces acting upon it are shown with arrows. These diagrams can predict or explain the motion of an object, or to do calculations.
• To draw a free body diagram:

  • Identify non-contact pairs.
  • Identify contact pairs.
  • Focus on a single object.

  
• Free body diagrams can help find the resultant / net force.

  
• Pythagoras' theorem can be used to calculate the resultant force of two forces acting at 90$^{\circ}$to each other.
• To work out which two forces at right angles add up to make right angles by resolving the force in two directions.

  
• Newton's First Law:

  • "An object is either stationary or moving at a constant velocity unless a force acts upon it"
• Inertia is a measure of how difficult it is to change an object's velocity.
• If the resultant force is zero, then the speed or direction of an object will not change.
• If the resultant force is zero, the object is in equilibrium.
• A resultant force can:

  • change the speed of an object.
  • change the direction of an object.
  • Do both of the above at the same time.
• Newton's Second Law: Force (N) = Mass (kg) * Acceleration (m/s^2)

  • The acceleration a resultant force produces on an object relies on: its size, and the mass (inertia) of the object.
• 1 N = 1 kg m/s$^2$
• An object moving in a circle at a constant speed is still accelerating even though its speed does not change. It is changing direction constantly, subsequently changing its velocity. To do this, a force directed towards the centre of a circle acts on the object.
• Terminal velocity is when the force of the air equals the force on the earth towards an object, and your motion no longer changes.

  
• Momentum is a vector quantity that relies on an object's mass and velocity:

  • Momentum (kg m/s$^2$) = mass (kg) * velocity (m/s)
• Law of Conservation of Momentum:

  • In any collision, momentum is conserved the momentum before is equal to the momentum afterwards.
• In an elastic collision, no energy is transferred into other stores. The energy in a kinetic store stays the same. In inelastic collisions, sometimes energy can be transferred to a thermal store.
• An example of inelastic collisions is when the combined velocity of two objects is less than the original objects.
• As mass increases, velocity decreases for momentum to be conserved.
• Doing work is when forces are used to transfer energy between stores.
• Work done (J) = Force (N) * Distance (m)
• 1 Nm = 1 kg m$^2$/s$^2$
• 1 Nm = 1 Joule