# Fluid Mechanics + Projectile Motion

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## Fluid Mechanics

Study of forces acting on a body travelling through the air or water

Air resistance - body travelling through air

Drag - body travelling through water

Factors affecting air resistance + drag:

• velocity - greater velocity = greater AR + drag
• frontal cross sectional area - larger frontal cross sectional area = greater AR + drag
• streamlining - more streamlined + aerodynamic = lower AR + drag
• surface characteristics - smoother surface = lower AR + drag as less friction
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## Projectile Motion

The movement of a body through the air following a curved flight path under the force of gravity

Projectile - a body that is launched into the air losing contact with the ground surface

Factors affecting distance of projectile:

• speed of release - due to Newtons second law of acceleration, the greater change in momentum results in greater acceleration through air
• angle of release - 45° optimal angle to maximise horizontal distance
• height of release - where release height higher than landing height, optimal angle less than 45° + vice-versa e.g. javelin/bunker
• aerodynamic factors - Bernoulli + Magnus principles
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## Projectiles in Flight

Parabolic flight path:

• if weight is dominant force + AR very small
• flight path symetrical at highest point
• e.g. shot put - high mass + low velocity

Non-parabolic flight path:

• if air resistance dominant force + weight very small
• e.g. badminton shuttle - low mass + high velocity
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## Lift + Bernoulli PRinciple

Bernoulli principle - the creation of an additional lift force on a projectile in flight resulting from Bernoulli's principle that the higher velocity of air flow, the lower the surrounding pressure

Lift force - an additional force created by a pressure gradient forming on opposing surfaces of an aerofoil moving through a fluid

Aerofoil shape:

• curved upper surface, forcing air flow to travel further distance + therefore move at higher velocity
• a flat underneath surface that allows air to travel shorter distances at a lower velocity

Therefore:

• as velocity increases - pressure decreases
• as all fluids move from an area of high to low pressure, a pressure gradient forms + creates additional lift force
• additional lift force increases time projectile hangs in air, extending flight path

Angle of attack - the most favourable angle of release for a projectile to optimise lift force due to Bernoulli principle

Downard lift force - works in downward direction if shape inverted

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## Spin + Magnus Force

Magnus force - a force created from a pressure gradient on opposing surfaces of a spinning body moving through the air

Topspin - eccentric force applied above centre of mass creating downwards magnus force

Backspin - eccentric force applied below centre of mass creating upward magnus force

Sidespin - eccentirc force applied away from centre of mass creating side magnus force

Slice - projectile deviates to right

Hook - projectile deviated to left

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