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Centre of gravity and beams
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An object's weight acts through one point: its centre of gravity. The principle of moments tells you how forces share out on a beam.
Centre of gravity
The weight of an object acts through its centre of gravity.
For a uniform beam or ruler, it is at the middle.
For a flat irregular shape (lamina), hang it from a point with a plumb line and draw the line; repeat from another point. The centre of gravity is where the lines cross.
For a uniform beam or ruler, it is at the middle.
For a flat irregular shape (lamina), hang it from a point with a plumb line and draw the line; repeat from another point. The centre of gravity is where the lines cross.
Principle of moments
moment = force × perpendicular distance from the pivot (N m)
For a balanced object: sum of clockwise moments = sum of anticlockwise moments.
The upward forces must also add up to the total downward force.
For a balanced object: sum of clockwise moments = sum of anticlockwise moments.
The upward forces must also add up to the total downward force.
A light beam on two supports
A light beam rests on supports A and B. A heavy object sits on it.
The support nearer the object pushes up with the bigger force.
To find the force at B, take moments about A: F_B × (length AB) = weight × (distance of object from A).
Then F_A = weight − F_B.
If the object is in the middle, each support takes half.
The support nearer the object pushes up with the bigger force.
To find the force at B, take moments about A: F_B × (length AB) = weight × (distance of object from A).
Then F_A = weight − F_B.
If the object is in the middle, each support takes half.
A light beam is 2.0 m long, supported at each end (A and B). A 600 N load is 0.5 m from A. Find the force from each support.
- Moments about A: F_B × 2.0 = 600 × 0.5
- F_B = 300 ÷ 2.0 = 150 N
- F_A = 600 − 150 = 450 N
Answer: A: 450 N, B: 150 N
Weight acts through the centre of gravity. Moment = force × perpendicular distance. In balance, clockwise moments = anticlockwise moments and upward forces = downward forces. On a beam with two supports, the support nearer the load takes more of the weight.
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