# Force and Motion

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## Force and Acceleration

- the greater the resultant force on an object, the greater the objects acceleration

- the greater the mass of an object, the smaller its acceleration for a given force

- the resultant force acting on an object is:

resultant force = mass x acceleration

- the inertia of an object is its tendency to stay at rest or in uniform motion

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## Weight and Terminal Velocity

- the weight of an object is the force acting on the object due to gravity, its mass is the quantity of matter in the object

- an object acted on only by gravity accelerates at about 10m/s

- the terminal at velocity of an object is the velocity it eventually reaches when it is falling, the weight of the object is then equal to the frictional force on the object

- when an object is moving at terminal velocity, the resultant force on it is 0

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## Forces and Braking

- friction and air resistance oppose the driving force of a vehicle

- the stopping distance of a vehicle depends on the thinking distance and the braking distance

- high speed, poor weather conditions, and poor vehicle maintenance all increase the braking distance

poor reaction time (due to tiredness, alcohol, drugs or using a mobile phone) and high speed both increase the thinking distance

- F = m a gives the braking force of a vehicle

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## Momentum

- the momentum of a moving object is

p = m v

- the unit of momentum is kg m/s

- a closed system is a system in which the total momentum before an event is the same as the total momentum after the event, this is called conservation of momentum

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## Using Conservation of Momentum

- momentum is defined as mass x velocity, and has both size and direction

- when 2 objects push each other apart, they move with different speeds if they have unequal masses, and with equal and opposite momentum, so their total momentum is 0

- use the equation:

Ma Va + Mb Vb = 0

when 2 objects, A and B recoil from each other

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## Impact Forces

- when vehicles collide, the force of the impact depends on mass, change of velocity and the length of the impact time

- the longer the impact time, the more the impact force is reduced

- when 2 vehicles collide:

they exert equal and opposite forces on each other

their total momentum is unchanged

- impact force = change of momentum / impact time

so the shorter the impact time, the greater the impact force

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## Safety First

- cycle helmets and cushioned surfaces (e.g. playgrounds) reduce impact forces by increasing the impact time

- seat belts and air bags spread the force across the chest and increase the impact time

- side impact bars and crumple zones may give in an impact, and so increase the impact time

- conservation of momentum can be used to find the speed of a car before an impact

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## Forces and Elasticity

- an object is called elastic if it returns to its original shape after removing the force deforming it

- the extension is the difference between the length of the object and its original length

- the extension of a spring is directly proportional to the force applied to it, as long as the limit of proportionality is not exceeded, this relationship is linear

- beyond the limit of proportionality, the extension of a spring is no longer proportional to the applied force, this relationship becomes non-linear

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