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Mechanics

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Scalars and VectorsA Scalar quantity is one that has magnitude only. Example mass, length, time etc.

A Vector quantity has both magnitude and direction. Example Force, velocity, acceleration etc.

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Adding Vectors

Two ways to add vectors: 1. Scale Drawing The resultant is R N making an angle of x° with the 4 N

force.

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E is the equilibrant. The Equilibrant is that force required to stop the body from moving. It is equal in magnitude but opposite in direction to the resultant force.

Note: Two vectors are equal if, and only if, they have the same magnitude and they have the same direction.

If ha = kb, either a is parallel to b or h = k = 0.

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The equilibrium vector diagram. Notice: the vectors go around the diagram in the same direction.

The resultant vector diagram.

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2. By Calculations

e.g.

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Subtracting Vectors

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Resolution of Vectors

V = R sin α H = R cos α

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Conditions necessary for a body to be in equilibrium:

▪ The net/resultant force on the body must be zero. ΣF = 0 (the sum of all the forces on the body must equate to zero).

▪ The sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about that point (Principle of Moments).

e.g. 1.

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Note: Since T1 is a bit more vertical than T2, T1 is a little greater than

T2.

Worked Example

A 5.0-N box is placed on a slope inclined at 30° to the horizontal. Find

the components of its weight parallel and perpendicular to the slope.

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SOLUTION

Figure 1

The parallel (to the inclined plane) and perpendicular components of the

weight are shown as dotted arrows. (The angle between the weight and its

component perpendicular to the slope is the same as the angle of inclination of

the slope. This can be proven using geometry.)

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Component of the weight parallel to the slope

= 5.0 sin 30°

= 2.5 N

Component of the weight perpendicular to the slope

= 5.0 cos 30 °

= 4.3 N

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Definitions Mass is the amount of matter contained in a body. It is that property of a body

which resists change in momentum (inertia). Mass does not change from place

to place. Mass is measured in kilograms (kg) and it is a scalar quantity.

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The weight of a body is the force of attraction of the body towards the

centre of the planet. Weight is measured in Newtons (N) and it is a vector

quantity. The force (weight) can change from place to place W = mg,

where g is the acceleration due to gravity.

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The centre of gravity of a body is the

point through which the weight of the body

appears to act. The total weight of the body

acts through the centre of gravity of the

body.