CIE iGCSE Co-ordinated Sciences-P1.5.3 Centre of gravity- Study Notes- New Syllabus

Determining the Centre of Gravity of an Irregular Plane Lamina (Plumb-line Method)

• Aim: To find the position of the centre of gravity (CG) of an irregular flat lamina.
• Apparatus: the irregular lamina (cardboard/metal), retort stand with clamp, pin or drawing pins, plumb line (string + small weight), set square/ruler, pencil, tracing paper (or thin paper), marker, scissors, tape.
• Principle: When a lamina is freely suspended from any point, its CG lies vertically below the suspension point. By suspending from two (or more) different points and drawing the verticals through the suspension points, the intersection of these verticals locates the CG.

Procedure (step-by-step):

1. Cut out the lamina and, if available, place it on tracing paper and trace its outline so you have a copy to mark on.
2. Choose a convenient point near the edge of the lamina and fix a pin (or drawing pin) through this point so the lamina can hang freely when suspended. Attach the pin to the clamp on the stand so the lamina hangs without touching other surfaces.
3. Hang a plumb line from the same clamp so that the string can hang freely next to the lamina. Allow the plumb line to come to rest (no swinging).
4. Carefully mark a line on the tracing paper along the string — this gives the vertical line (line of action) through the suspension point. Use a pencil and ruler to extend the line across the traced outline.
5. Remove the pin and choose a different suspension point on the lamina (preferably not collinear with the first). Repeat steps 2–4 and draw a second vertical line on the tracing paper.
6. The intersection point of the two (or better, three) vertical lines is the position of the centre of gravity of the lamina. Mark that point clearly as the CG.
7. As a check, you may suspend from a third point; its vertical should pass through (or very near) the same intersection point if the experiment is accurate.

Why this works (brief explanation):

• When suspended, the lamina rotates until its weight acts directly below the suspension point. The plumb line shows the direction of the weight (vertical). The CG must lie somewhere on that vertical line. Two different suspension points give two verticals; their intersection is the unique point that lies on both lines the CG.

Precautions / Tips:

• Make sure the lamina hangs freely and does not touch the clamp, stand or nearby surfaces when suspended.
• Let the plumb line stop swinging before drawing the line — wait for steady equilibrium.
• Use sharp pins and a fine pencil to reduce uncertainty in the marked lines.
• Choose suspension points well apart (not very close together) to improve accuracy of intersection location.
• If lines do not meet at a single point (due to small errors), take the area common to the crossing lines as an uncertainty region and estimate the CG as the centre of that region.

Sources of error and how to reduce them:

• Poorly fixed pin or bent pin — use a straight, firm pin and secure clamp to avoid wobble.
• Parallax when marking the line — view the plumb line and tracing paper directly from above when marking.
• Wind or drafts causing the plumb line to swing — perform experiment in a draught-free area.
• Imprecise tracing or drawing — use fine pencils and a ruler; repeat suspensions from a third point as a check.

Optional alternative method (balancing method):

• Place the lamina on a narrow pointed support (knife-edge) and move the support until the lamina balances. Mark that support position as a line of possible CG positions. Repeat with the lamina rotated and balance again. The intersection of the lines gives the CG. This method is less used than plumb-line for irregular laminas but can confirm results.