Marine BASICS of physics with example prblems

Marine

1. BASICS

2. Units of Measurement Measurements inevitably involve units The SI Units are Units can be combined in a variety of ways to form complex units, many of which have their own names/symbols Velocity = dist /time  m/s Acceleration = Velocity/time  m/s/s or m/s2 Force = ma  kg . m/s2 kilogram (kg) Unit of mass metre (m) Unit of Distance second (s) Unit of time ampere (A) Unit of electric current kelvin (K) Unit of thermodynamic temperature

3. Mass Mass is how hard it is to get something to move Intimately related to the idea of inertia Distinct from weight, which relates to gravity the same mass weighs different amounts on different planets Inertia relates to Newton’s first law of motion : an object in motion will remain in that state of motion unless acted on by an outside force Then we have Newton’s Second Law of Motion: F = ma Examples of Force : gravity exerts a downward force on you the floor exerts an upward force on a ball during its bounce a car seat exerts a forward force on your body when you accelerate forward from a stop

4. Newton’s Third Law For every force, there is an equal and opposite force every “action” has a “back-reaction” Force on box by floor (normal force) Force on box by gravity box floor

5. Buoyance Force Buoyance force is the upward force on an object exerted by the surrounding liquid. The pressure at the top of the object, which pushes the object downward is gravitational force. The pressure at the bottom of the object, which pushes the object upward is buoyant force.

6. How do you Calculate Buoyant Force?

7. There are 3 types of Buoyancy Positive Buoyancy When the buoyant force is greater than the weight of the object, then the object floats. Neutral Buoyancy When the buoyant force is equal to the weight of the object, then the object is suspended in the liquid. Negative Buoyancy When the buoyant force is less than the weight of the object, then the object sinks

8. Density Density of a substance is defined as the mass per unit volume of that substance . Units can be found using Density = Mass / Volume i.e Kg/m3, g/ml Relative Density (RD) Relative Density is the ratio of density of substance to the density of water.

9. Relative Density >1  Sinks Relative Density <1  Floats

10. Archimedes Principle The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces. Upward force = weight of the liquid displaced W = m (mass) x g (acceleration due to gravity) Mass = Volume x density i.e. (v x d) Upward force = v x d x g Upward force = loss in weight Loss in weight = real weight (object outside water) – apparent weight (object immersed in water)

11. Q1 Loss in weight of the Object ? Real weight – Apparent Weight 200 g – 170 g = 30 g Buoyant Force on the Object = Loss in Weight of the Object =30 g Q2 Apparent weight of a floating body ? When a substance is floating, the weight of the substance is equal to the upward force. Apparent weight = loss in weight – real weight = 50g – 50g = Zero

12. Q3 Volume of body = Volume of water displaced 1000 cm3 Apparent weight = Real weight – upward force = m x g – v x d x g = 5 x 10 m/s2 - 1000 cm3 x 1 g/cm3 x 10 m/s2 = 50 -10 (kg) = 40 kg

13. Underwater Volume and Displacement Underwater Volume = u/w volume The Volume of water displaced is the underwater volume. Displacement = W The weight of the displaced water is equal to the weight of the body immersed.

14. Basic calculations on Mass, Density and Volume A rectangular tank measures 16 m x 15 m x 6 m. How many tonnes of oil of RD 0.78 can it hold? A cylindrical tank of diameter 8 m is 10 m high. 400 t of oil of RD 0.9 is poured into it. Find the ullage assuming Pi is 3.1416.

15. Q1. A rectangular tank measures 16 m x 15 m x 6 m. How many tonnes of oil of RD 0.78 can it hold? Density = Mass / Volume Mass = Volume x Density =(16 x15 x 6) x 0.78 =1123.2 Note: Volume of rectangle = l x b x h

16. Q2. A cylindrical tank of diameter 8 m is 10 m high. 400 t of oil of RD 0.9 is poured into it. Find the ullage assuming Pi is 3.1416. Volume of Cylinder = ∏r²h = 3.1416 x 4 x 4 x 10 = 502.656 To find Volume of oil filled in the tank Volume = Mass / Density ∏ r²h= 400 / 0.9 3.1416 x 4 x 4 x h = 444.444 h = 8.84 Ullage = 10 – 8.84 = 1.16 m

17. Centre of Buoyancy

18. Denoted by B or COB It is the geometric centre of the water displaced that is the geometric centre of the underwater volume of the ship The position of the COB is indicated by Its height above the keel. This distance is referred to as KB. KB of a box shaped vessel is half the draft, if the vessel is upright and on even keel. KB of a ship shaped vessel is little more than half the draft. KB of a triangular ship shaped vessel is 2/3 rd of draft.

19. A box shape vessel off displacement 1640 t is 50 m long 10 m wide 8 metre height. F ind her KB in sw , if she is on even keel and upright. A triangle shaped vessel floats in sea water her water plane is a rectangle 40 metre into 12 metre if KB is 3.6 meter find her displacement

20. Q1. A box shaped vessel of displacement 1640 t is 50 m long 10 m wide 8 m high. Find her KB in sw , if she is on even keel and upright. W = u/w Volume x density 1640 = 50 x 10 x draft x 1.025 Draft = 1640 /500 x 1.025 = 3.2 m KB of box shaped vessel = ½ of draft = ½ x 3.2 m = 1.6 m

21. Q2. A triangle shaped vessel floats in sea water her water plane is a rectangle 40 metre into 12 metre if KB is 3.6 meter find her displacement KB = 3.6 m 2/3 of draft = KB 2/3 x d = 3.6 D = 5.4 m Area of Triangle = ½ Base x height = ½ x 12 x 5.4 = 32.4 m2 u/w volume = Area x length = 32.4 x 40 = 1296 m3 W = u/w volume x density = 1296 x 1.025 = 1328.4 t

22. Centre of Gravity COG - Weight of the ship acts vertically downward