L5. Kinematics

Kinematics. Basic Definitions

Kinematics is the part of mechanics that deals with the description of motion regardless of its cause

• Bodies in motion are modelled as particles (no size)

• Displacement (change in the position)

• Traveled distance d and displacement S are different in general case

• Average velocity is the ratio of the displacement to the time

• Average speed is the ratio of the traveled distance to the time

Uniform Motion

• Trajectory is a straight line

• Velocity is constant

• Acceleration is zero

• Displacement is given by S=V t

1D Motion: Constant Acceleration

• Trajectory is a straight line

• Acceleration is constant

• Velocity changes and is given by V(t)=V₀+at

• 

  

  The average velocity can be found as

• Displacement is given by S=S₀+V₀t+at²/2

• Because a=const, displacement is also

t =

SUVAT- Equations of motion (1 dimension)

Projectile’s Laws of Motion

• The horizontal component of the velocity is constant

V_x = V_o cosӨ

• The vertical component is given by

V_y = V_o sinӨ - gt

• The displacement along the x - axis is

X = V_o cosӨ * t

• The displacement in the y - direction is

Y = Vo sinӨ t – gt­²/2

L6. Newton’s Laws

Dynamics is the relationship of motion to the forces that cause it.

Force is a measure of an interaction between two objects. Forces always come in pairs

• Contact forces (e.g. push, pull, friction)

• Long-range forces (e.g. electric, magnetic, gravitational)

Drawing diagrams to show the forces acting on an object—free body diagrams (FBD)—we use arrows to show the relative size and direction.

Need to find a single force—the resultant force through SUPERPOSITION of all forces acting on an object

Newton’s Law of motion:

Newton’s First Law (Law of Inertia)

An object moves with a velocity that is constant in magnitude and direction, unless acted on by a non-zero net force.

Newton’s Second Law

The acceleration (a) of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Newton’s Third Law

“Forces are always in Pairs” (Action – Reaction)

If a body A exerts a force on body B (an ‘action’), then body B exerts a force on body A (a ‘reaction’). These two forces have equal magnitude and opposite direction

Pulley. Assumptions:

• The pulley is frictionless

• The pulley has negligible mass

• The strings connecting pulleys are inextensible and have negligible masses

Terminal Speed. Assumptions:

• Object is falling in gravity (force down = weight)

• The object falls through a fluid (air or liquid) that resists the falling (resistance force is upward)

• The Terminal speed is reached when the forces of resistance equals the weight, and the Net Force = zero

Free Body Diagram

To create a free body diagram:

Step 1 – Identify only ONE object for each FBD.

Step 2 – Draw simplified sketch

Step 3 – Draw vectors to show all external forces acting on that ONE object (weight of a uniform body is downward from center)

Step 4 - If there is a net Force, show it as vector next to the object.