1. PHYSICS
Applied Mechanics

2. 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

3. 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

4. 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

5. 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

6. Upthrust
UPTHRUST

7. Fish floats

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

11. Upthrust = weight of fluid displaced
weight of fluid displaced = upthrust

12. 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

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

14. Upthrust = weight of fluid displaced
Quick Check 2

15. Principle of flotation

16. Principle of flotation

17. Principle of flotation

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

19. Principle of flotation
Object may float totally immersed

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

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

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

23. Principle of flotation

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

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

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

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

28. Static Friction > Kinetic Friction

29. 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

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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. Quick Check 3

38. Projectile Motion u

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

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

41. 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

42. 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

43. 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

44. 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

45. 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

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

47. Quick Check 4

48. Quick Check 4

49. 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

50. 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

51. THE END