PHYSICS Applied Mechanics

pressure increases with depth liquid / gas Pressure in a fluid At sea level, pressure = patm h1 p1 = patm + gh1 pressure increases with depth h2 p2 = patm + gh2 p = gh

Quick Check x container p = gh liquid Which graph shows how the pressure p varies with height x above the base of the container? A B C D p p p p x x x x

Quick Check x container p = gh Liquid Liquid of twice density Which graph shows how the pressure p varies with height x above the base of the container? A B C D p p p p x x x x

pressure increases with depth Upthrust At sea level, pressure = patm h1 low pressure p1 = patm + gh1 pressure increases with depth h2 p2 = patm + gh2 p = gh HIGH PRESSURE UPTHRUST

Upthrust UPTHRUST

Fish floats

How to calculate the upthrust? Calculate upthrust How to calculate the upthrust? UPTHRUST

Upthrust = weight of fluid displaced weight of fluid displaced = upthrust

Upthrust = weight of fluid displaced spring balance T = 9 N T = 6 N T = 5 N 9 N 9 N W = 9 N U = 3 N U = 4 N weighing machine

Upthrust = weight of fluid displaced patm+ patm+ gh2

Upthrust = weight of fluid displaced Quick Check 2

Principle of flotation

Principle of flotation

Principle of flotation

Principle of flotation When upthrust = weight, object floats

Principle of flotation Object may float totally immersed

Principle of flotation But what if the object is totally immersed and the upthrust is still less than the weight?

Principle of flotation upthrust = weight When upthrust = weight, object floats

Principle of flotation What if the object is pushed down underwater and let go … What will happen? upthrust > weight

Principle of flotation

Principle of flotation upthrust = weight When upthrust becomes equal to weight, object floats

Principle of flotation Upthrust depends on how much volume is immersed / displaced When upthrust = weight, object floats in equilibrium

Quick Check Three objects of equal volume are in equilibrium A UA > WA UB = WB UC < WC B UC = WC C UA = WA D

When object is not moving, the friction is called static friction. When object is moving, the friction is called kinetic friction.

Static Friction > Kinetic Friction

Viscous force When object is moving inside a fluid, it experiences viscous force e.g. air resistance, water resistance water air As water is denser than air, object will hit more water molecules than air molecules, so water resistance > air resistance

Viscous force increases with speed The faster the object moving, the greater the force in hitting the molecules, the greater the resistance. water air

Terminal Velocity (object falling in air) Object released from rest: v = 0 m s-1 a = g = 9.81 m s-2 mg t v Fv v = 3 m s-1 a = 4 m s-2 mg

Terminal Velocity (object falling in air) Object released from rest: v = 0 m s-1 a = g = 9.81 m s-2 mg v Fv v = 3 m s-1 a = 4 m s-2 mg Fv t v = 4 m s-1 a = 2 m s-2 mg

Terminal Velocity (object falling in air) Object released from rest: v = 0 m s-1 a = g = 9.81 m s-2 mg v Fv terminal velocity v = 3 m s-1 a = 4 m s-2 mg Fv t v = 4 m s-1 a = 2 m s-2 mg Fv v = 5 m s-1 a = 0 m s-2 mg

Object released and falling After fallen distance x Quick Check Object released and falling in air in vacuum After fallen distance x tair vair aair t0 v0 a0 time taken velocity acceleration A tair < t0 vair < v0 aair < a0 B tair = t0 aair = a0 C tair > t0 D

Falling vs moving up in air falling in air moving up in air Fv Fv v v mg mg viscous force opposite to weight viscous force and weight same direction  lesser accelerating force  greater decelerating force

object thrown up with same speed at same height Quick Check a = initial deceleration t = time to reach the top s = maximum height u u in air in vacuum object thrown up with same speed at same height initial decn time to top max. height A aair > a0 tair < t0 sair < s0 B aair = a0 tair = t0 C tair > t0 D

Quick Check 3

Projectile Motion u

Projectile Motion t = 1 s 50 m s-1 When t = 1 s, sx = 50  1 = 50 m

Projectile Motion t = 1 s 50 m s-1 sy = uyt + ½gt2 = 0 + ½g(1)2 = 5 m

Projectile Motion t = 2 s 50 m s-1 sx = uxt = 50  2 = 100 m sy = uyt + ½gt2 = 0 + ½g(2)2 = 20 m 50 m 50 m

Projectile Motion t = 3 s 50 m s-1 sx = uxt = 50  3 = 150 m sy = uyt + ½gt2 = 0 + ½g(3)2 = 45 m 50 m 50 m

Projectile Motion t = 4 s 50 m s-1 sx = uxt = 50  4 = 200 m sy = uyt + ½gt2 = 0 + ½g(4)2 = 80 m 50 m 50 m

Projectile Motion t = 5 s 50 m s-1 sx = uxt = 50  5 = 250 m sy = uyt + ½gt2 = 0 + ½g(5)2 = 125 m 50 m 50 m

Projectile Motion t = 6 s 50 m s-1 sx = uxt = 50  6 = 300 m sy = uyt + ½gt2 = 0 + ½g(6)2 = 180 m 50 m 50 m

Projectile Motion (with air resistance) 50 m s-1 50 m 50 m

Quick Check 4

Quick Check 4

Question to think about… Suppose You have some ice floating in a glass of water. When the ice melts, does the water level A rise B fall C stay the same

Question to think about… Suppose you are on a boat floating in a lake. A large stone is on the boat. You take the stone and drop it into the water. Will the water level A rise B fall C stay the same

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