Published by Patrick Mutisya · 14 days ago
Describe an experiment to determine the position of the centre of gravity of an irregularly shaped plane lamina.
The centre of gravity (CG) of a thin, flat object is the point through which the resultant weight of the object acts. For a uniform lamina the CG coincides with the centre of mass.
Mathematically, if the lamina is divided into small elements of mass \$mi\$ at positions \$(xi, yi)\$, the coordinates of the centre of gravity \$(xG, y_G)\$ are given by
\$xG = \frac{\sum mi xi}{\sum mi}, \qquad yG = \frac{\sum mi yi}{\sum mi}\$
In practice we locate \$G\$ by using the principle that a lamina will balance when supported at its centre of gravity.
| Item | Purpose |
|---|---|
| Irregularly shaped thin lamina (e.g., cardboard cut‑out) | Object whose CG is to be found |
| Two thin, straight supports (e.g., metal rods or wooden strips) | Provide a line of support for the lamina |
| Adjustable mounting board or bench | Holds the supports in a fixed relative position |
| Plumb line (string with a small weight) | Indicates the vertical direction (gravity) |
| Ruler or measuring scale | Measure distances on the lamina |
| Paper and pencil | Record measurements and draw construction lines |
When a lamina is supported at two points, it will balance if the line joining the support points passes through the centre of gravity. By locating two such lines (using different pairs of support points) the intersection of the lines gives the position of \$G\$.
| Trial | Support points (A, B) – coordinates (cm) | Line drawn \$L_i\$ | Intersection point \$G\$ (cm) |
|---|---|---|---|
| 1 | (x₁, y₁) , (x₂, y₂) | Line \$L_1\$ | To be determined after both trials |
| 2 | (x₃, y₃) , (x₄, y₄) | Line \$L_2\$ |
Because each line \$L_i\$ is forced to pass through the centre of gravity, the intersection of any two such lines must be \$G\$. No calculations are required beyond measuring the intersection point, but you may verify the result by checking that the lamina balances when supported at \$G\$.