### Leaving Certificate Physics

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Mechanics
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# Sample: Moments and Equilibrium

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MOMENTS AND LEVERS

A lever is a rigid body that can rotate about a fixed axis at a point called the fulcrum

The moment of a force is that force multiplied by the perpendicular distance to the fulcrum

$$M = F times d$$

d = perpendicular distance from line of force to fulcrum (m),

F = force (N)

M = moment (Nm)

Moments are useful as we can use them to amplify force, a weight of 500N can be lifted by a force of only 100N, provided there is a 5m lever arm between the force and the fulcrum

Moments are vectors, measured in Newton metres (Nm),

A  positive moment denotes one that would tend to rotate the body it acts on clockwise, a negative one would tend to rotate it anticlockwise.

The centre of gravity of a body is the point through which all of its weight appears to act

EQUILIBRIUM

A body is in equilibrium if:

1. The vector sum of the forces acting on the body  in any direction is zero
2. The sum of the moment of the forces about any point on the body is zero

Example: The uniform metre stick below experiences a number of forces, as well as its weight of 7N, is it in equilibrium? Upward forces = $$12+20 = 32N$$

Downward forces = $$10+7+15 = 32N$$

Take the left end as the fulcrum

Clockwise moments = $$(10 times 0.1) + (7times 0.5) + (15times0.86) = 17.4Nm$$

Anticlockwise moments = $$(12 times 0.2) + (20 times 0.75) = 17.4Nm$$

Since the upward forces equal the downward forces and the the clockwise moments equal the anticlockwise moments, the body is in equilibrium