# Forces in Balance

## Vectors and Scalars

- displacement is a distance in a given direction

- a vector quantity is a physical quantity which has magnitude but no direction

- a scalar quantity has magnitude but no direction

- vector quantity can be reperesented by an arrow in the direction of the vector and of length in proportion to the magnitude of the vector

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## Forces Between Objects

- forces can change the shape of an object, or change it's motion or it's state of rest

- the unit of force is the newton (N)

- a contact force is a force that acts on objects only when the objects touch each other

- when 2 objects interact, they always exert equal and opposite forces on each other

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## Resultant Forces

- the resultant force is a single force that has the same effect as all the forces acting on an object

- if the resultant force on an object is:

0, the object stays at rest or at the same speed and direction

greater than 0, the speed or direction of the object will change

- if 2 forces on an object along the same line, the resultant force is:

their sum, if the forces act in the same direction

their difference, if the forces act in opposite differences

- a free body force diagram of an object shows the forces acting on it

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## Moments at Work

- the moment of a force is a meausure of the turning object

- the movement of a force about a pivot is:

M = Fd

(where 'd' is the perpendicular distance from the line of action of the force F to the pivot)

- to increase the moment of a force, increase F or increase 'd'

- levers can be used to exert a force that is greater than the effort

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## More About Levers and Gears

- a lever used as a force multiplier exerts a greater force than the force applied to the lever by the effort

- the pivot of a force multiplier is nearer to line of action of the force it exerts than to the force applied to it

- gears are used to change the moment of a turning effect

- to increase the moment of a turning effect, a small gear wheel needs to drive a larger gear wheel

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## Centre of Mass

- the centre of mass of an object is the point where its mass can be thought of as being concentrated

- the centre of mass of a uniform ruler is at its midpoint

- when an object is freely suspended, it comes to rest with its centre of mass directly underneath the point of suspension

- the centre of mass of a symmetrical object is along the axis of symmetry

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## Moments and Equilibrium

- if an object at rest doesn't turn:

the sum of the anticlockwise moments about any point = the sum of the clockwise moments about that point

- all the forces acting on an object that dont pass throught the fixed point can turn an object about that point

- the direction of the force and the position of the fixed point determines whether the moment acts clockwise or anticlockwise

- to calculate the force needed to stop an object turning we use the equation above, we need to know all the forces that dont act through the pivot and their perpendicular distances from the line of action to the pivot

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## The Parallelogram of Forces

- the parallelogram of forces is a scale diagram of two force vectors

- the parallelogram of 2 forces is used to find the resultant of 2 forces, that do not act along the same line

- the resultant is the diagonal of the parallelogram that starts at the origin of the two forces

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## Resolution of Forces

- resolving a force means finding perpendicular components that have a resultant force that is equal to the force

- to resolve a force in 2 perpendicular directions, draw a rectangle with adjacent sides along the 2 directions so that the diagonal represents the force vector

- for an object in equilibrium, the resultant force is 0

- an object at rest is in equilibrium because the resultant force on it is 0

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