Dynamics

What causes motion?

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Dynamics

Starring ...

 Dynamics

    Staring ...

         Force

External forces have the potential to change the state of motion of the system.

Forces :

Representing

interactions

between

systems

A Force is a vector quantity; whose magnitude represents the strength of the interaction.

The SI unit for Force is the Newton [N]

The implication is that there are boundaries that can be placed between systems, and the interaction can be summarized in terms of external forces between the systems.

Remember that "Force" is a concept -- it is one idea that humans use to describe interactions between entities. When we speak of forces, we speak of fictions of our imagination, which we can then use to analyze the situation and predict the outcome.

 Dynamics

    Staring ...

         Mass

The mass of a system

can be defined as a measure of

the system's tendency to resist

any change in its state of motion.

velocity

acceleration

inertia

Mass

is a measure of inertia

  Dynamics

    Staring ...

         Force, Mass, Acceleration

Forces have the potential to cause acceleration

Mass resists acceleration

  • The SI unit of Force is (N) which stands for Newtons.
  • The SI unit of Mass is (kg) which stands for Kilogram.

Dynamics

Types of Forces

 Dynamics

    Types of Forces

         Weight

  • Weight is the label we give to the force of gravity of a planet on an object on or close to its surface.
  • On Earth, g=9.8 m/s^2 downwards, so
    • for example, the weight of a 5kg object that is on (or near) the surface of Earth is
      • ​W=(5kg) (9.8 m/s2)=49N downwards.
\vec{W}=m\vec{g}
  • The weight of any object of mass m is given by:

       where g is the acceleration due to gravity of the planet. 

 Dynamics

    Types of Forces

         Surface Contact

  • The component of the contact force that is perpendicular to the surface.

The Normal Force

When the object of interest is in surface contact with other objects, then the contact force has two components:

  • The component of the contact force that is parallel to the contact-surface.

The Friction Force

  • There are two types of friction forces
    • Static friction force, if the two surfaces in contact are not moving relative to each other.
    • Kinetic friction force, if the two surfaces in contact are moving relative to each other.
\vec{F}_N
\vec{F}_N

ground on ladder

wall

on ladder

\vec{F}_N

ladder

on wall

\vec{F}_N

ladder on ground

 Dynamics

    Types of Forces

         The Tension Force

  • This force is carried by ropes, strings, cables, cords, etc.

The Tension Force

 Dynamics

    Types of Forces

         The Spring Force

  • The force that is applied by springs, elastic bands, bungee cords, etc.

The Spring Force

  • This force is proportional to the strain on the spring (stretch or compression.)
\vec{F}_\text{Spring}=-k\vec{x}

 Dynamics

    Types of Forces

         Other Forces

  • Basically, pull and push forces applied by people or engines etc.

Applied Forces

Dynamics

The Net Force

 Dynamics

    The Net Force

         Free Body Diagram

More on FBD: link to section 5.7

  • A free-body diagram (FBD) is a schematic that indicates all the external forces acting on an object.

 

  • In the previous definition, the word "on" is critical -- the forces that are exerted by the object of interest are not included; only the forces that are exerted on the object of interest are included in a FBD of that object.

 Dynamics

    The Net Force

         Adding Forces (as vectors)

The Net Force is defined as the vector sum of all the external forces acting on an object.

Since Forces are vectors, their sum follows the rules for adding vectors (by components.)

Solved example: link to section 5.1

Dynamics

Laws of motion

Where I grew up there was a long road that had the perfect slope and road conditions, such that if I went down with my bicycle at a certain velocity and avoided all bumps, then I was able to coast down the road without slowing down or speeding up.


It was such a fun feeling being in such perfect equilibrium....

  Dynamics

    Laws ...

         1. Law of Inertia

Later in life, I was fortunate enough to be able to understand on an analytical level the intricate balance of the forces acting on the bike and me to keep us in the same state of motion... each force having the potential to change the state of motion, but somehow the combination of forces balancing out to have no net effect -- as if no forces acted in the first place...

And being able to think this way, and

to see the possibilities of that way of thinking,

was also a fun feeling in a different way...

  Dynamics

    Laws ...

         1. Law of Inertia

  Dynamics

    Laws ...

         1. Law of Inertia

An object tends to maintain its state of motion, unless acted upon by a net external force.

\Sigma\vec{F}
\vec{a}=0
\Sigma\vec{F}=0
\iff
\large 1

  Dynamics

    Laws ...

         2. Newton's second law

A system that is subject to a net external force will accelerate at a rate that is proportional to the external net force and inversely proportional to the mass of the object.

\Sigma\vec{F}\ne0
\iff
\vec{a}=\frac{\Sigma\vec{F}}{m}
\large 2

  Dynamics

    Laws ...

         2. Newton's second law

\Sigma\vec{F}\ne0
\iff
\vec{a}=\frac{\Sigma\vec{F}}{m}
  • Acceleration is directly proportional to and in the same direction as the net (total) external force acting on a system." (i.e. larger net force leads to larger acceleration)
  • Acceleration is inversely proportional to the mass of the system. (In other words, the larger the mass (the inertia), the smaller the acceleration produced by a given net force.)
\large 2

  Dynamics

    Laws ...

         3. Newton's third law

Forces come in pairs -- when objects A and B interact, the force of A on B and the force of B on A are equal in magnitude and opposite in direction.

\vec{F}_\text{A on B} = - \vec{F}_\text{B on A}
\large 3