Edexcel IGCSE Physics · Spec 1.33P
Support Forces on a Loaded Beam (Paper 2)
Covers draw the forces on a supported beam, Use vertical force balance and Use moments to find how support forces change.
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Support Forces on a Loaded Beam (Paper 2)
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Explained
A beam on two supports, and the trick that makes it solvable
A plank rests on two supports with a load somewhere along it. Each support pushes upwards, and the question is how much each one pushes.
Two unknowns, so you need two equations, and the topic gives you exactly two.
The two conditions
The beam is not accelerating upwards or downwards, so the upward forces balance the downward ones. The two support forces added together equal the total weight resting on the beam, including the weight of the beam itself if you are given it.
The beam is not rotating either, so the total clockwise moment about any point equals the total anticlockwise moment about that point. That is the principle of moments.
The first equation is easy to write and does not tell you how the load is shared. The second does, and it is where the thinking is.
The trick
Take moments about one of the supports.
The force at that support acts at zero distance from the point you are turning about, so its moment is zero and it disappears from the equation entirely. You are left with one unknown, the force at the other support, and you can solve for it directly.
Then put that answer into the vertical balance to get the first support force, by subtracting it from the total weight.
Choosing the pivot is the whole method. Any point would work mathematically, but choosing a support removes an unknown for free, and choosing anywhere else leaves you with two unknowns and one equation.
A worked example
A uniform beam 4.0 m long rests on supports A and B at its two ends and weighs 200 N. A 600 N load sits 1.0 m from A.
The beam is uniform, so its own weight acts at its centre, 2.0 m from A.
Take moments about A. Clockwise: 600 times 1.0 gives 600, plus 200 times 2.0 gives 400, so 1000 N m in total. Anticlockwise: the force at B times 4.0. Setting them equal, the force at B is 1000 divided by 4.0, which is 250 N.
Vertical balance: the two supports together carry 600 plus 200, which is 800 N. So the force at A is 800 minus 250, which is 550 N.
Check it makes sense. The load is nearer A, so A should carry more, and 550 is more than 250.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards one mark simply for stating the principle: that the sum of the clockwise moments equals the sum of the anticlockwise moments.
One mark, before any numbers, for a sentence. Writing it at the top of a beam question costs a line and earns credit even if the arithmetic afterwards goes wrong.
The calculation that follows is worth three: the substitution into the principle of moments, the rearrangement, and the evaluation. The worked example divides a moment by a distance to find an unknown force, which is exactly the step a support force question needs.
Its notes then allow an error carried forward from the earlier part, and print two acceptable final answers rather than one. An answer rounding to 1.4 newtons is credited if the candidate used the approximate moment printed in the question, and one rounding to 1.6 newtons if they used the more precise value they had calculated themselves.
Both are right, from different starting points, and the mark scheme accepts either. That is worth knowing, because an answer that differs slightly from the one at the back of a book is not necessarily wrong; it may be the same physics carried through from a value rounded earlier.
It also says to ignore units on these marks, and elsewhere in the same question notes that a reverse argument scores one mark at most. Working backwards from a value the question has already given you, to show it is consistent, is not the same as calculating it.
What happens as the load moves
Move the load towards support B and the force at B increases while the force at A decreases, and their sum stays the same because the total weight has not changed.
Directly over a support, that support carries everything except the beam's own share, and the other carries almost none.
Beyond a support, on an overhang, the far support can be pulled downwards rather than pushed upwards, and the beam tips. That is the point of a question asking how far a person can walk along a plank before it topples: the tipping point is where the force at the far support reaches zero.
Spec 1.33P
What you need to know
- Draw the forces on a supported beam
- Use vertical force balance
- Use moments to find how support forces change
Active recall
Quick check
Answer each question before opening the answer.
What equation gives vertical force balance?
RA + RB = W
Why take moments about a support?
Its reaction then has zero moment, simplifying the calculation
What happens to RB as the load moves toward B?
RB increases
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