# Subject content

## 3.3 FSMQ Dynamics (9995)

### Prior Learning

 Prior learning Candidates will need knowledge of the following. Trigonometry: Use of Sin, Cos and Tan (but not the Sine or Cosine rules) Algebra: Collection of like terms and solution of linear equations such as Solution of a quadratic equation by at least one of the following methods: use of a graphics calculator use of formula (which must be memorised) completing the squareSolution by factorisation will be acceptable where the quadratic factorises.

### Formulae

Formulae   Candidates should learn the following formulae which may be required to answer questions.
Constant Acceleration Formulae
 $v^2 = u^2 + 2as$
Weight $W = mg$
Momentum Momentum = $mv$
Newton's Second Law $F=ma$ or Force = rate of change of momentum
Friction

No knowledge of calculus is required in this unit.

### Mathematical Modelling

 Mathematical Modelling Use of assumptions in simplifying reality. Candidates are expected to use mathematical models to solve problems by making assumptions to create a simple model of a real situation. Candidates are expected to use experimental or investigational methods to explore how the mathematical model used relates to the actual situation. Mathematical analysis of models. Modelling will include the appreciation that: it is appropriate at times to treat relatively large moving bodies as point masses; the friction law is experimental; the force of gravity can be assumed to be constant only under certain circumstances. Interpretation and validity of models. Candidates should be able to comment on the modelling assumptions made when using terms such as particle, light, inextensible string, smooth surface and motion under gravity. Candidates should be familiar with the use of the words; light, smooth, rough, inextensible, thin and uniform. Refinement and extension of models.

### Vectors

 Vectors Understanding of a vector; its magnitude and direction.Addition and subtraction of two vectors.Multiplication of a vector by a scalar.Addition and subtraction of quantities using vectors.Magnitude and direction of quantities represented by a vector.Candidates may work with the i, j notation or column vectors, but questions will be set using the column vector notation.

### Kinematics in One and Two Dimensions

Kinematics in One and Two Dimensions
Displacement, speed, velocity, acceleration. Understanding the difference between displacement and distance.
Understanding the difference between velocity and speed.
Sketching and interpreting kinematics graphs. Use of gradients and area under graphs to solve problems
The use of Calculus is NOT required for this unit.
Knowledge and use of constant acceleration equations.
 $v^2 = u^2 + 2as$
Application of vectors in two dimensions to represent position, velocity or acceleration, including the use of unit vectors i and j. Candidates may work with the i, j notation or column vectors, but questions will be set using the column vector notation.
Vertical motion under gravity.
Average speed and average velocity.
Magnitude and direction of quantities represented by a vector.
Finding position, velocity, speed and acceleration of a particle moving in two dimensions with constant acceleration.

The solution of problems such as when a particle is at a specified position or velocity, or finding position, velocity or acceleration at a specified time

Use of constant acceleration equations in vector form, for example,
$\mathbf{v} = \mathbf{u} + \mathbf{a}t$.

### Forces

 Forces Drawing force diagrams, identifying forces present and clearly labelling diagrams. Candidates should distinguish between forces and other quantities such as velocity, that they might show on a diagram. Force of gravity (Newton's Universal Law not required). The acceleration due to gravity , , will be taken as . Friction, limiting friction, coefficient of friction and the relationship of $F = \mu R$ Tensions in strings and rods. Knowledge that the resultant force is zero if a body is in equilibrium. Find the unknown forces on bodies that are at rest or moving with constant velocity. Candidates will not be expected to resolve forces or find the components of forces.Candidates will not be expected to use the triangle of forces.

### Momentum

 Momentum Concept of momentum Momentum as a vector in one or two dimensions. (Resolving velocities is not required.) Momentum = $mv$ The principle of conservation of momentum applied to two particles for direct impacts in one dimension. Knowledge of Newton's law of restitution is not required.

### Newtonâ€™s Laws of Motion

 Newton's Laws of Motion Newton's three laws of motion. Problems may be set in one or two dimensions and may include the use of vectors. Simple applications of the above to the linear motion of a particle of constant mass. Application of Newton's second law to particles moving with constant acceleration. Candidates will be expected to find the acceleration of a body if the forces acting are specified, or unknown forces if the acceleration is given. Use of as a model for dynamic friction.

### Projectiles

 Projectiles Motion of a particle moving freely under uniform gravity in a vertical plane. Candidates will be expected to state and use equations of the form and . Candidates should be aware of any assumptions they are making. Calculate range, time of flight and maximum height. Formulae for the range, time of flight and maximum height should not be quoted in examinations. Inclined plane and problems involving resistance will not be set. The use of the identity will not be required. Candidates may be expected to find initial speeds or angles of projection. Modification of equations to take account of the height of release.