Wire framework consisting of a rectangle and triangle

Wire Framework Consisting of a Rectangle and Triangle

Introduction to Wire Frameworks

• In Further Mechanics, a wire framework is a structure composed of thin, uniform wires arranged to form a shape.
• These frameworks have negligible thickness and can be treated as line segments.
• This section will look at a simple wire framework composed of a rectangular and triangular segment.

Wire Frameworks - Finding the Centre of Mass

• The centre of mass of a wire framework is found by breaking it down into its simpler components - in this case, a rectangle and a triangle.
• With these individual components, we find their individual centres of mass and their individual moments about a common axis.
• This is essentially treating each segment of the wire framework as its own separate system, and then combining these at the end.

Centre of Mass in a Rectangle

• For a rectangle, the centre of mass is simply at the geometric centre - where the diagonals intersect.
• The distance to the chosen axis is the perpendicular distance from the centre of mass to the line of the axis.

Centre of Mass in a Triangle

• For a triangle, the centre of mass is located where all the medians intersect, also known as the centroid.
• The distance to the chosen axis is the perpendicular distance from the centroid to the line of the axis.

Combining the Centres of Mass

• The moment of each shape about the chosen axis is found by multiplying its mass by its distance from the axis.
• Add up all the moments to give the total moment and add up all the masses to give the total mass.
• Finally, divde the total moment by the total mass. The resulting value gives the position of the centre of mass of the entire wire framework.

Practical Application

• Understanding the centre of mass of a wire framework is useful in various fields, such as physics, engineering, and product design, where creating balanced, stable structures is imperative for successful outcomes.