Forces in Equilibrium

• A vector is a physical quantity which has a direction as well as the magnitude
• Displacement is the distance between where you start and where you finish (must include direction)
• Vector examples are forces, acceleration and velocity.
• If two vectors are of the same type then they can be added together. Care must be taken however as their direction may differ so it may not work.

• If there is a physical quantity that does not have a value then it is a scalar.
• Adding vectors of different values require an accurate scale drawing.

• Tm -> x10^9 (Tera)
• Mm -> x10^6 (Mega)
• Km -> x10^3 (Kilo)
• m -> 1 (Metre)
• mm -> x10^-3 (milli)
• MM -> x10^-6 (micro)
• nm -> x10^-9 (nano)

• If an object is stationary or undergoing no acceleration (constant velocity) then the total forces acting on it must be zero.
• Horizontal- F= T x Sin(θ), Vertical-F = T x Cos(θ)
• Where θ is the angle between the horizontal or vertical and the given direction
• and T is the length of the line going in that direction

• If an object does not fall over or accelerate rotationally then the clocwise and anticlockwise moments must cancel out
• A turning force is a force which acts in a circular motion about a pivot. This turning force is called a moment.

• W1D1 = W2D2 where W1 and D1 and W2 and D2 and either side of the pivot

• The centre of gravity of an object is a point where the entire weight of an object seems to act
• The centre of mass of an object is a point where the entire mass of the object seems to be concentrated

• Where there is one support weight, the support must must equal the total of the weights.

• If an object in a stable equilirium is displaced then it will, upon release, return to its equilibrium position
• A supported object will always come to rest with its centre of mass under the point of support. If displaced then a moment will be created to make it return to the equilibrium position again
• If something is in an unstable equilibrium then any slight offset will make it move away from the equilibrium position as the weight is offset from the support force creating a moment that turns the body away from the equilibrium position

Tilting

• When an object is pushed from the side it creates a moment about a pivot.
• If this moment is greater than the restoring force (the weight of the object) multiplied by the distance from the pivot then the object will fall over.

Clockwise -> Mc = Fd 

Anticlockwise -> Wa = W x b/2

Box to fall -> Fd > W x b/2

Free body force diagrams only show the forces acting on the object

T

• To give equilbrium, the resultant must be zero (F1 + F2 + F3) as any two forces give a resultant that is equal and opposite to the third force (F1 + F2 = -F3)

Scale Diagram

• 1) Draw one of the known force vectors
• 2) Use a protractor and ruler to draw other known force at the correct side and angle

• An object in equilibrium is either at rest or moving with a constant velocity. The forces acting on it must give zero resultaant and their turning effects must balance out as well
• (For body in equilibrium)- resultant force must be zero (If 3 forces need closed triangle) and principle of moments must apply (moments of forces about same point must balance out).