Chapter 6 - Forces in equilibrium (6.5 Stability (Stable and unstable…
Chapter 6 - Forces in equilibrium
6.1 Vectors and scalars
is any physical quantity that has a direction as well as a magnitude
is distance in a given direction
is speed in a given direction
Force and acceleration
are both vector quantities.
is any physical quantity that is not directional
Examples of scalar quantities are distance, mass, density, volume and energy
6.2 Balanced forces
Equilibrium of a point object
act on a point object, the object is in equilibrium, where it is either at rest or moving at a constant velocity. This occurs when the resultant force is 0 so the two forces are said to be balanced.
act on point object, their combined effect is zero only if the resultant of two of the forces is equal/opposite to that of the third force
6.3 The principle of moments
The moment of any force about a point is defined as the force x the perpendicular distance from the line of action of the force to the point,
the moment of the force = F x d
The principle of moments
For any object in equilibrium the
sum of the clockwise moments = the sum of the anticlockwise moments
Centre of mass
centre of mass
of a body is the point through which a single force on the body has no turning effect.
6.4 More on moments
- support problems, When an object in equilibrium is supported at one point only, the support force on it is equal and opposite to the total downward force acting on the object
- support problems, Where a beam is supported by two pillars the weight of the beam is shared based on the proportion of the distance that the centre of mass of the beam is from both pillars. If the centre of mass is equal distances from each pillar then the weight of the beam is shared equally between each pillar.
is a pair of equal and opposite forces acting on a body, but not along the same line.
The moment of a couple = force x perpendicular distance between the lines of actions of the force
Stable and unstable equilibrium
If a body in stable equilibrium is displaced then released, it returns to its equilibrium position. This is because the centre of mass of the object is directly below the point of support when the object is at rest.
The reason that skittles are easily toppled over is because they have a high centre of mass and a narrow base so the centre of mass is easily displaced away from the support force.
Tilting is where an object at rest on a surface is acted on by a force that raises it up on one side.
A tilted object will topple over if it is tilted too far. If an object on a flat surface is tilted more and more, the line of action of its weight passes closer and closer to the pivot. I the object is tilted so much that the line of action of its weight passes beyond the pivot, the object will topple over of allowed t.
6.6 Equilibrium rules
Free body force diagrams
When two objects interact they always exert equal and opposite forces on one another. A free body force diagram shows only the forces acting on the object.
The triangle of forces
For a point object acted on by three forces to be in equilibrium, the three forces must give an overall resultant of zero. The three forces vectors should form a triangle.