# Forces in balance

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## Vectors and scalars

Displacement is distance in a certain direction (without a change of direction)

Vectors are physical quantities that have magnitude and direction, e.g. acceleration, force,

Scalars are physical quantities that have magnitude but no direction, e.g. mass, temp

The size of a quantity is its magnitude

• The direction of the arrow shows the director of the vector quantity
• The length of the arrow represents the magnitude of the vector quantity

A force is a vector quantity as it has magnitude and direction

Can be reperesented by an arrow

• The force of the hammer on the nail is represented by an arrow.
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## Forces between objects

Forces (N) can change the shape of an object, or change its motion or its state of rest

• A force is a push/pull that acts on an object because of its interaction w/ another objec e.g friction, air resistance.

Contact forces are forces that must touch to interact, e.g friction, air resistance, tension. They occur when an object's supported by or strikes another object

Non-contact forces are forces that don't need to touch to affect each other, e.g. magnetic force, electrostatic forces, force of gravity

Newton's 3rd law states when 2 objects interact w/ each other, they exert equal and opposite forces on each other e.g the weight of an object is the force of gravity on it due to the Earth. The object exerts an equal and opposite force on the Earth.

The driving force on a car is what makes it move,and teh car is pushed fowards becaue there is friction between the ground and the tyres

The forces of friction on roads and tyres are in forwards and reverse directions.

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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

Newton's first law of motion states that an object at rest will remain at rest unless acted on by an unbalanced force and an object in motion will continue in motion w/ the same speed and direction, unless acted on by an unbalanced force.

• When a crate is pushed across a rough floot at a constant spedd, the push force on it is eual in size and acting in the opposite direction,

If the Rf isn't 0, the movement of the object depends on the size and direction of the Rf

• When jet plane takes off, the thrust force of the engines is greater than the force of air resistance.
• The resultant force is equal to the difference between the two forces and in the direction of the larger force,

A free-body force diagram shows forces acting on an object, w/out any other objects drawn. The forces are represented by arrows pointing in the direction of the force

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## Moments at work

• The moment of a force is a measure of the turning effect of the force on an object.

The turning effect can be increased by increasing the size of the force and using a spanner w/ a longer handle

Levers

A crowbar is a lever used to raise one edge of a heavy object. The weight is the load, the force the person applies is the effort, the point the crowbar turns is the pivot. The crowbar enables only a fraction of the effort needed to life the object. The lever's a force multiplier, as the effort moves a bigger load

moment, M (N/m) = force, F (N) x distance from pivot, d (m)

T investigate the turning effect of a force, move a weight along a newton metre and record the distance, increasing the weight each time and use equation to calculate moment

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## More about levers and gears

When a lever's used to increase a force, the force applied to the lever must act further from the pivot than the force it has to overcome,

e.g. bottle opener- the force on the cap is much bigger than the force applied to the opener, so the opener acts as  a force multiplier a the line of action on the force applied is further from the pivot than the edge of the cap.

Gears

• Gears multiply the effect of a turning force. E.g. gears increase the turning effect of the engine, so a bigger force is exerted on the gears
• To increase the moment of a turning effect, a small gear wheel needs to drive a larger gear wheel
• Low gear gives low speed and a high turning effect - small gear wheel driven by engine shaft is used to turn a large gear wheel on the output shaft, so output shaft turns slower than engine shaft
• High gear gives high speed and a low turning effect - larger gear wheel driven by engine shaft is used to turn a small gear wheel on output shaft, so output shaft turns faster than engine shaft, so car moves at higher speed
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## Centre of mass

• The centre of mass of an object is the point at which its mass can be thought of as being concentrated

After suspending and releasing an object, it will come to rest w/ its centre of mass directly below the point of suspension, the object's in equilibrium. Its weight doesn't exert a turning effect on the object as its centre of mass is directly below the point of suspension. An object is freely suspended if it returns to its equilibrium position after the turning force is taken away

• If an object has more that one axis of symmetry, its centre of mass is where the axes meet

If object is irregular, put hole in one corner of card and suspend from rod. Use plumbline (string w/ small weight on end) to draw vertical line on card from rod. Repeat, hanging the card from different corners until you see centre of mass (the point where the two lines meet)

• The centre of mass of a symmetrical object is along the axis of symmetry.
• When an object is freely suspended, it comes to rest with its centre of mass directly underneath the point of suspension
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## Moments and equilibrium

If an object at rest doesn't turn, the sum of the anticlockwise momentd about any point = the sum of clockwise moments about that point

All the forces acting on an object that don't pass through a fixed point can turn an object about that point.

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

To calculate the force needed to stop an object turning, use the equation. We need to know all the forces that don't 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

It is used to find the reultant of two 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

Use weights and pulleys to show parallelogram of forces. The parallelogram of forces is used to find the Rf of 2 forces that don't act along the same line. You'll need a protractor, ruler, sharp pencil and paper. The Rf is the diagonal of the parallelogram that starts at the origin of the 2 forces.

• The tension in each string is is equal to the weight it supports
• The line down the centre of the diagram represents the vertical line through the point where the three strings meet
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## Resolution of forces

Resolving a force means finding perpendicular components that have Rf that's equal to the force

To resolve a force in 2 perpendicular directions, draw a rectangle w/ adjacent sides along the 2 directions so that the diagonal represents the force vector

For an object to be in equilibrium: the Rf must be 0 and the forces acting on the object must have no overall turning effect

To see if an object's in equilibrium:

• If the lines of action of the forces are parallel, the sum of the forces in 1 direction must be equal to the sum of forces in the opposite direction. So Rf = 0
• If the lines of action of the forces aren't parallel, the forces can be resolved into 2 components along the same perpendicular lines. Components must balance out if Rf = 0
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