Mathematics 9709 — specification explorer

1. Forces and equilibrium

• 4.1.1identify the forces acting in a given situation
• 4.1.2understand the vector nature of force, and find and use components and resultants
• 4.1.3use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero
• 4.1.4understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component
• 4.1.5use the model of a ‘smooth’ contact, and understand the limitations of this model
• 4.1.6understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = n R or F G n R , as appropriate
• 4.1.7use Newton’s third law.

2. Kinematics of motion in a straight line

• 4.2.1understand the concepts of distance and speed as scalar quantities, and of displacement, velocity and acceleration as vector quantities
• 4.2.2

  sketch and interpret displacement–time graphs and velocity–time graphs, and in particular appreciate that represents displacement, represents velocity, represents acceleration:

  • the area under a velocity–time graph
  • the gradient of a displacement–time graph
  • the gradient of a velocity–time graph
• 4.2.3use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration
• 4.2.4use appropriate formulae for motion with constant acceleration in a straight line.

3. Momentum

• 4.3.1use the definition of linear momentum and show understanding of its vector nature
• 4.3.2use conservation of linear momentum to solve problems that may be modelled as the direct impact of two bodies.

4. Newton’s laws of motion

• 4.4.1apply Newton’s laws of motion to the linear motion of a particle of constant mass moving under the action of constant forces, which may include friction, tension in an inextensible string and thrust in a connecting rod
• 4.4.2use the relationship between mass and weight numerical, and use of the approximate numerical value 10 (m s
• 4.4.3solve simple problems which may be modelled as Including, for example, motion of a particle on a the motion of a particle moving vertically or on rough plane where the acceleration while moving an inclined plane with constant acceleration up the plane is different from the acceleration while moving down the plane.
• 4.4.4solve simple problems which may be modelled as e.g. particles connected by a light inextensible string the motion of connected particles. passing over a smooth pulley, or a car towing a trailer by means of either a light rope or a light rigid tow- bar.

5. Energy, work and power

• 4.5.1understand the concept of the work done by a W force, and calculate the work done by a constant force when its point of application undergoes a displacement not necessarily parallel to the force
• 4.5.2understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae
• 4.5.3understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in appropriate cases the principle of conservation of energy
• 4.5.4use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion
• 4.5.5solve problems involving, for example, the instantaneous acceleration of a car moving on a hill against a resistance.