# PHYA2 - Mechanics

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• Created by: Franklin
• Created on: 02-05-14 22:46

## Vectors

A scalar quantity has only magnitude

Examples:

• Temperature
• Distance
• Speed
• Time

A vector quantity has both magnitude and direction

Examples:

• Acceleration
• Velocity
• Momentum
• Force
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## Vectors (cont.)

Vectors can be added together to find the resultant vector 2 of 11

## Vectors (cont.2) When forces act in a linear fashion like in the image above, the result (resultant force) is just the overall force

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## Moments

The moment of a force about any point is the is defined as the force x perpendicular distance from the line of action of the force to the point

Moment of a force = F x d

• Units are newton metres (Nm)
• The greater the distance, the greater the moment

Principle of moments: Sum of the clockwise moments = sum of anticlockwise moments

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## Moments 2 Taking moments about the pivot: F1 x d1 =  (F2 x d2) +  (F3 x d3)

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## Couples

Couples: a pair of equal and opposite forces acting on a body but along the same line. Moment of a couple = torque Moment of a couple (torque) = F x S

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## Centre of Mass

The centre of mass of a body the point through which a single force on the body has no turning effect 7 of 11

## Stability

• If a body is in stable equilibrium is displaced then released, it returns to its equilibrium position
• When the body is in equilibrium the reaction of the support and the weight are equal and opposite
• The weight returns to the postion in which it is in the line of action of the support
• In unstable equilibrium the object will not return back to its position of equilibrium

Toppling

• Objects with a high centre of mass are not very stable
• For toppling to occur: Fd >Wb/2
• F = force applied, d = perp dist. from line of action to pivot, W = weight of object, b = width of base
• If the line of action of the weight goes past the pivot the object will topple
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## Tilting Diagram If Fd> Wb/2 toppling will occur (b = width of base)

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## Equilibrium Rules

Triangle of forces: Vector sum = 0 10 of 11

## Projectile Motion

When considering projectile motion, air resistance is usually ingnored. Therefore horizontal velocity is unaffected throughout flight; it is only vertical velocity the changes due to gravity. 11 of 11