A레벨_Further Mathematics(AS)_Mechanics 1 > A레벨
교재 : edexcel / 수강기간 : 30일
Mechanics 1 is an applied module that concerns the kinematics, dynamics and statics of particles. Basic concepts of motion are introduced, alongside forces, momentum, moments and more. This area relates strongly to the field of Physics, where these concepts are also studied, but here we focus more on the mathematical side of trying to find solutions to the problems presented
Chapter 1: Mathematical Model in Mechanics
The concept of a mathematical model is introduced and how they often apply to mechanical problems. The SI units system of base and derived units is also introduced which allow for a consistent framework to approach the course with.
Chapter 2: Constant Acceleration
Displacement-Time, Velocity-Time and Acceleration-Time graphs are all introduced, including how they relate to each other and how they can be used in problem solving. Next, the standard equations of motion under constant acceleration, sometimes called SUVAT equations, are derived and used. Finally, problems relating to acceleration under gravity are discussed.
Chapter 3: Vectors in Mechanics
The basic algebra of vectors is introduced, and then applied to problems in Mechanics. In particular, we consider constant acceleration in two dimensions, and look at solving problems involving multiple moving objects in the plane.
Chapter 4: Dynamics of a Particle Moving in a Straight line
Force diagrams, forces as vectors and the concept of a resultant force is introduced. Through Newton’s Second Law of Motion, forces are linked to acceleration. Motion in two dimensions is considered, and then problems involving connected particles - connected either directly or through pulleys – are discussed.
Chapter 5: Forces and Friction
Here we start by resolving forces in parallel and perpendicular directions, allowing us to solve problems with objects on inclined slopes. Friction is then introduced as a contact force between two objects, and the differences between limiting and non-limiting friction are discussed.
Chapter 6: Momentum and Impulse
Through Newton’s Second Law, the idea of the Impulse is derived and applied to forces acting on particles. Through Newton’s Third Law we arrive at the principle of ‘Conservation of Momentum’ and problems involving collisions and explosions.
Chapter 7: Statics of a Particle
In contrast with dynamics, statics is the study of things not moving. Here we look at different cases of modelling problems using statics, and the potential problems that can arise. In particular, how to deal with friction in the non-limiting case is discussed.
Chapter 8: Moments
Until this point, we have considered only linear motion. With moments, the study of the rotational effect of forces are introduced. From the definition of a moment we move to the idea of an object in equilibrium in both a linear sense and a rotational sense. Using this, we are then able to solve problems including finding the centre of mass of objects, and understanding the forces on objects where they are on the point of tilting.
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