The Wrecking Ball – mechanics of a mathematical pendulum

Observe the motion of a mathematical pendulum:

A simple pendulum moves in space while suspended on a cord. The forces in action in the video above are represented by the accelerations (F = m x a, thus the force vector will actually have the same direction and orientation as the acceleration vector).

The pendulum is actually moved only by it’s own weight – or the gravitational force (G = m x g; where acceleration of the gravitational force is g = 9.81 m/s^2):

motion of the pendulum propelled by it’s “weight” or gravitational force

 

This force can be divided and observed as two separate components:

  • the component that creates the tension in the cord (m x g x cos0), and
  • the component that propels the pendulum forward (m x g x sin0)

Ignore the trigonometric functions (sin, cos) and just observe the components and their directions: they actually operate in a coordinate system that is centered inside the ball (m) and has two vertical axes.

Gravitational force’s two components

This way, we can isolate and observe the force that moves the pendulum separately and calculate their intensities in regard to mass of the ball (how much force does the ball have at any point of the motion) but also with how much force does it “burden” the cord.

We can apply this principle to many other patterns of motion in order to analyze separate forces of interest (ie: a downward-moving cart)

Downward moving cart and the forces in action

So why should we care? Well, for one, this allows us to calculate the mass of the ball and the strength of the chain required for… A WRECKING BALL!!!

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