# Forces in balance

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## Vectors and Scalars

Displacement distance in a given direction

Vector a quantity that has a magnitude and direction

• Weight
• Velocity
• Acceleration

Scalar a quantity that only has a magnitude

• Temperature
• Speed
• Energy

The direction of the arrow shows the direction of the vector quantity

The length of the arrow represents the magnitude of the vector

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## Forces between objects

Newtons Third Law when 2 objects interact with each other, they exert equal and opposite force on each other

Non-Contact Forces  forces that can be exerted between objects without them being in contact with one another

• Gravity- A gravitational force comes between all masses
• Manets- A magnetic force acts between magnetic poles
• Charges- Exert electrostatic forces on each other at a distance

Contact Forces forces that can be exerted on each other due to them being in contact

Normal force

• acts upwards in opposition to the object

Force of friction

• acts in opposition to the pushing force that is trying to change its motion. Force always acts to slow a moving object down
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## Resultant Forces

Resultant forces  The single force that would have the same effect  as all the other forces acting on the object

Resultant forces determine whether a body will be stationary ,moving at constant speed or accelerating

Newtons First Law the forces acting on an object are balanced, the resulatant force on the object is zero

• if the object is at rest it is stationary
• if the object is moving it keeps moving with the same speed and in the same direction

Unbalaned Forces

When the resultantb force is not zero, the forces acting on the object are not balanced.The movemrnt of the object depends on the size and direction of the resultant force

• Resultant force is equal to the difference between 2 forces
• Resultant forces is in the direction of the larger force

Sometimes forces forces act at right angles to each other.The resultant force can then be found from a scale diagram using pythagorus therom

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## Moments at work

Moment of a force a measure of the turning effect of the force on ana object

Moments can be increased by: increasing the force
using a spanner with a longer handle

Moment,M(Newton meters,Nm) = Force,f(Newtons,N) x Distance,D(Metres,M)

The distance is the perpendicular distance from the line of action of the force x to the pivot

Load  the weight of the object

Effort the force the person applies to the crowbar

Sum of clockwise moments = Sum of anticlockwise moments

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## Levers and gears

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

Gear used to change the moment of a turning effect

When a low gear is chosen:

A small gear wheel driven by the engine shaft is used to turn a large gear wheel on the output shaft. So the output shaft turns slower than the shaft engine

The turning effect of the output shaft is greater than the turning effect of the engine shaft

Low gear gives low spped and a high turning effect

When a high gear is chosen:

A large gear wheel driven by the engine shaft is used to turn a small gear wheel on the poutput shaft. So theoutput shaft turns faster than the engine shaft, so the car can move at a higher speed

But the force of the smaller gear wheel acts nearer to its shaft than the force of the larger gear wheel acting on its shaft. So the turning effect of the output shaft is less than the turning effect of the engine shaft

High gear gives high speed and a low turning effect

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## Centre of mass

Centre of mass of a object 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 mss 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

Point of moments

If an object at rest doesnt turn The sum of clockwise moments about any point = The sum of anticlockwise moments abou that point

All the forces acting on an object that dont pass through a 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 principle of moments. 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

Parallelogram of forces a scale diagram of to vectors

The pallelogram of forces is used to find the resultant of two forces that do not act along the same line

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

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## Resolution of forces

Resolving a force fimding perpendicular components that have a resultant force that is equal to the force

To resolve a force in two perpendicular directions, draw  a rectangle adjacent sides along the two directions so that the diagonal represents the force vector

Key conditions object to be in equilibrium are:

• The resultant force on the object is zero
• The forces acting on the object have no overall turning effect

An object at rest is in equilibrium because the resultant force is zero

To work out if an object is in equilibrium:

• If the liness of action of the forces are parallel, the sum of the forces in one direction must be equal to the sum of forcse in the opposite direction. This means that the resultant force on the object is zero
• If the lines of action of the two forces are not all parallel, the forces can be resoved into two components along the same perpendicular lines. The components along each line must balance out if the resultant force is zero
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