Introduction to Kinetics

MEE1008: Mechanics of Materials - Lecture 15

Kinematics

Study of motion without reference to the forces which cause the motion.

Kinetics

Relates the action of forces on bodies to the resulting motion.

Inertia

The resistance to the rate of change of velocity

m = F/a

Direction of acceleration

Always in the direction of the applied force.

Force unit

Newton (kg m/s²)

Weight equation

mass x gravity

Choice of coordinate system

Depends on the type of motion

Vector sum of ΣF

ΣF = ma

Rectilinear motion of particle

Curvilinear motion of particle

Law of sines

Law of cosines

Force of a spring

A compressed spring exerts a pushing force and a stretched spring exerts a pulling force.

Hooke’s Law

Used to calculate force of spring

F = kx

where F is the spring force, k is the spring constant and x is the distance displaced.

Friction

Occurs when the unlubricated surfaces of two solids are in contact under a condition of sliding or a tendency to slide.

Static friction

No motion

F_max = μ_sN and F < μ_sN

where μ_s is the coefficient of static friction and N is the normal force.

Kinetic friction

Motion

F_k = μ_kN

where μ_k is the coefficient of kinetic friction and N is the normal force.

Steps to construct a free body diagram

1. Decide which system to isolate.

2. Isolate the system and draw its external boundary.

3. Identify all forces acting on the system.

4. Add the coordinate system on the diagram.