Contents for this page | Related topics | |
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1. The moment of a force 2. Conditions for equilibrium 3. Levers 4. Mechanical advantage 5. Additional questions |
First law of motion Second law of motion Third law of motion Conservation of momentum Law of universal gravitation |
Data Glossary |

Learning Outcomes | ||

After studying this section, you will (a) know what is meant by the "moment of a force", (b) know the conditions for equilibrium a body subjected to a number of forces, (c) understand how levers work, and (d), be able to calculate the mechanical advantage of a lever. | ||

Helpful background knowledge | ||

Introduction to vectors Addition of vectors Mass and weight |
Units and measurement Dimensions |
Scientific notation Significant Figures |

1. The moment of a force

If a force is applied to the end of an object whose other end is attached to a pivot or hinge, the force will tend to rotate the object about the pivot, called the *FULCRUM*, Thus, a force can, in certain circumstances, have a turning effect. We call this effect the *MOMENT OF THE FORCE* ().

The moment depends on the size of the force, **F**, and the perpendicular distance, **d**, from the fulcrum to a line along the direction of the force vector (). Moments are expressed in units of *NEWTON METRES (N·m)*. The direction of the rotation resulting from a moment is either clockwise or anticlockwise. Clockwise moments are regarded as positive, while anticlockwise moments are negative.

2. Levers

Levers are simple machines () that utilise the moment of a force.

Referring to the diagram on the left, the applied force, **F** (sometimes called the "effort") applies a clockwise moment **Fy** at a distance **y** from the fulcrum. Placed at a distance **x** on the left hand side of the fulcrum, we have a mass **m**, applying a force **mg** (the "load") having an anticlockwise moment **mgx**, where **g** is the acceleration due to gravity. This system will be in equilibrium, that is, there will be no motion, when the clockwise and anticlockwise moments have the same magnitude (numerical value): **Fy = mgx**. This is simply a specific example of the *LAW OF MOMENTS*.

The distance **y** is called the *LEVER ARM* of the force **F** about the fulcrum. Similarly, the distance **x** is the lever arm of the load **mg** about that fulcrum.

The photo on the left, below, shows three kitchen gadgets that operate on the principle of levers (top: pincers, middle: tongs, bottom: garlic press), each operating on a different arrangement of fulcrum, load and effort.

2. Conditions for equilibrium

A body will be in mechanical equilibrium if (a) it does not change its state of lateral motion and, (b), it does not rotate.

In order for a body not to rotate, the law of moments applies:

Law of Moments |
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"A body will be in equilibrium if the algebraical sum of the moments about any point is zero." |

Note that the law of moments is not sufficient for defining the equilibrium of a body, as *TWO* conditions must apply:

- The vector sum of all forces acting on the body must be zero; and
- the algebraic sum of the moments about any point must be zero (law of moments).

3. Mechanical advantage

The *MECHANICAL ADVANTAGE, MA,* of a machine is the ratio of the load and the applied force (effort). In the case of the lever described above, the mechanical advantage is **mg/F**. It is also the ratio of the lever arms of the effort and load respectively, that is, **y/x**.

The mechanical advantage is therefore a factor which tells us how much the input force is multiplied by the machine.

4. Additional questions