【#文档大全网# 导语】以下是®文档大全网的小编为您整理的《alevel Notes for solving rigid body equilibrium》，欢迎阅读！
Some notes on how to do rigid body equilibrium problems:
1. Have confidence! The information must be there, available, to solve the problem. Since the only
physical laws we apply are the laws of static equilibrium: total force is zero, total moment is zero, and the laws of static friction, there are only two types of equation + plus one type of inequality that can possibly apply:
∑Fi=0 ∑Fi×di=0
Fi ≤ μRi for each friction force fi
This means that the problems cannot be complicated. In almost all cases, you will only need to solve linear simultaneous equations; calculus or series are not required. Please do remember to
use inequalities rather than equations for the friction forces - this is probably the most common mistake.
2. Search for a pivot.
The principle here is that, in static equilibrium the sum of the clockwise moments about ANY PIVOT INSIDE OR OUTSIDE THE BODY is zero. Since the moment of a force depends on the perpendicular distance from the pivot to the line of action of the force, you are looking for a pivot through which as many as possible of the lines of action of the individual forces pass. Pay attention to corners, centres of bodies and in general to any point which has a high degree of symmetry on the diagram. You need to learn this skill yourself, the examiner will rarely if ever tell you what to do!
3. Make a good free body diagram of the body you're analysing.
In these questions, the examiners will almost always provide you with a diagram. Sometimes they mark on the forces themselves, other times they don't - you can't rely on it. In any cases, it is 100% hopeless to try and solve problems of this complexity without a good quality diagram to look at, so make at least one good quality diagram with a ruler which marks all forces acting on the body you're analysing. It is quite common that you will need to draw more than one diagram - such as two free body diagrams of two connected objects, or sometimes make a diagram of one section of the system to help you analyse the geometry correctly.
4. Unambiguous labelling is a necessity.
It doesn't matter if you choose the letter N or the letter R to represent normal contact forces, but what is EXTREMELY important is to make clear which force you are talking about in your equations. Use subscripts like this:
F1 ≤μN1 F2≤μN2 N1+F2=X
and of course just as important is that these labels match what's on your diagram, otherwise the examiner cannot follow your arguments.
5. Remember the main property of the frictional and normal contact forces.
Friction between two surfaces opposes the relative motion between the surfaces of contact. This will tell you the direction of the force. The normal contact force is always perpendicular to the surface of contact. If the surface is not flat, the direction of the contact will be in the direction of the normal line at the point of contact. The normal contact force between flat surfaces will not always act through the centre of mass of the object concerned - see 6.
6. Toppling and Lami's Theorem.
It can be proved (you don't need to learn how if you're not concerned) that if exactly three forces act on a body, then it will be in equilibrium (neither move nor rotate) if and only if (a) the three forces as vectors form a complete triangle and (b) the line of action of the three forces all pass through the same point.
When trying to find the point at which an object, resting on a surface, is about to topple we can use Lami's Theorem. The lines of action of the normal contact force and the weight must cross at the surface of
contact. This will be possible as long as the line of action of the weight (which is a vertical line through the centre of gravity, by definition) passes through the joint surface of contact. The normal contact force can (effectively) act through any point on the contact surface (it is best to think of it as a weighted average of lots of little contact forces between all the atoms in contact). Once this point crosses outside the surface of contact, static equilibrium is impossible and the body will rotate. This is called toppling.
See the diagram below to help you think about this:
In more complicated, more general cases, it will still be true that on the point of toppling (just about to topple), the normal contact force will act at the corner which is the pivot of the potential rotation.
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2022-05-18
