PHYA2 - Mechanics

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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

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Vectors (cont.2)

vector2 (http://physicsnet.co.uk/wp-content/uploads/2010/08/vector2.jpg)

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

(http://physicsnet.co.uk/wp-content/uploads/2010/08/moment3.jpg)

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

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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 

(http://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Cremona_triangle_simple_polygones_forces.svg/287px-Cremona_triangle_simple_polygones_forces.svg.png)

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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.

(http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0012/projectile.gif)

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