• State Newton's Third Law
• Differentiate between contact and non-contact forces
• Apply Newton's Third Law
• Identify N3 pairs of forces

Momentum

• Define momentum
• Calculate momentum from a moving object using p=mv
• Describe the vector nature of momentum and illustrate with some simple examples.

A net force on an object causes a change in momentum - if there is no net force on an object/system, its momentum will not change (momentum will be conserved)

• State Newton's Second Law (N2) in terms of momentum:
  the net (or resultant) force acting on an object is equal to the rate of change of momentum.
• Express Newton 2 in terms of symbols:
  
• Explain the relationship between net force and change in momentum for a variety of motions.
• Calculate the change in momentum when a resultant force acts on an object and its velocity:
  · increases in the direction of motion (eg. 2nd stage rocket engine fires)
  · decreases (eg. brakes are applied)
  · reverses its direction of motion (eg. soccer ball kicked back in the direction it came from)
• draw vector diagrams to illustrate the relationship between the initial momentum, the final momentum and the change in momentum in each of the above cases
• know that in the absence of an external force acting on a system, momentum is conserved
• apply the conservation of momentum to two objects moving in one dimension (along a straint line)

Momentum Grade 12

• know that the momentum of s system is conserved when no external forces act on it
• know that an external force causes the momentum to change
• define impulse as:
  
  and use the equation in calculations
• solve problems involving impulse and change in momentum when the applied force is in the horizontal or vertical position
• distinguish between elastic and inelastic collisions
• solve problems involving elastic and inelastic collisions for objects moving along the same straight line
• apply the concept of impulse to safety considerations in evryday life
  eg. airbags, seatbelts, arrestor beds

Vertical Projectile Motion
Represented in words, diagrams, equations and graphs
For vertical projectile motion (near the surface of the Earth if air friction is ignored)

• explain that projectiles:
  · fall freely with gravitational acceleration 'g'
  · accelerate downwards with a constant acceleration whether the projectile is moving upward or downward
  · have a zero velocity at their greatest height
  · take the same time to reach their greates height from the point of upward launch as the time they take to fall back to the point of launch
  · can have their motion described by a single set of equations for the upward and downward motions
  
• use equations of motion, for eg, to determine:
  · the greatest height reached given the velocity with which the projectile is launched upward (initial velocity)
  · the time at which a projectile is at a particular height given its initial velocity
  · the height relative to the ground of the position of a projectile shot vertically upward at launch, given the time for the projectile to reach the ground
  
• draw position vs time ( x vs t), velocity vs time (v vs t) and acceleration vs time (a vs t) graphs for projectile motion
• give equations for position versus time and velocity versus time for the graphs of motion of particular projectiles and vice versa
• given the following graphs:
  x vs t
  v vs t or
  a vs t
  determine the
  · position
  · displacement
  · velocity
  · acceleration
  at any time t
• Describe the motion of the object eg. graphs showing a ball:
  · bouncing
  · thrown vertically upwards
  · thrown vertically downwards
  · etc.
  

Frames of Reference
(Relative Velocity)
For motion in one dimension (linear motion) only:

• define a frame of reference
• give examples of the importance of specifying the frame of reference
• define relative velocity
• specify the velocity of an object relative to different frames of reference, eg:
  · for a person walking inside a train give the velocity relative to the train and relative to the ground
• use vectors to find the velocity of an object that moves relative to something else that is itself moving

Work, Power and Energy
When a force exterted on an object causes it to move, work is done on the object.
except if the force and displacement are at right angles t each other)

• define the work done on an object by a force
• give examples of when an applied force does and does not do work on an object
• calculate the work done by an object when a force F applied at an angle to the direction of motion, causes the object to move a distance, using:
  

The work done by an external force on an object/system equals the change in kinetic energy of the object/system

• know that an object with larger potential energy has a greater capacity to do work
• solve problems using the work energy theorm i.e.:
  the work done on an object by a net force is equal to the change in the objects kinetic energy
  
  Examples may include:
  · objects on horizontal surfaces
  · objects moving in a vertical plane
  · objects on inclined planes
  
• Conservation of mechanical energy (prior knowledge from Grade 10)

Power
(rate at which work is done)

• Define power as the rate at which work is done or energy is expended
• Calculate the power involved when work is done
• If a force causes an object to move at a constant velocity, calculate the average power or instantaneous power using:
  P = Fv
• Apply to real life examples, eg:
  · the minimum power required of an electric motor to pump water from a borehole of a particular depth at a particular rate
  · the power of different kinds of cars operating under different conditions