Archimedes 1

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3.5 ARCHIMEDES’ PRINCIPLE

Buoyant Force and Floatation

1. An object immersed in water is subjected to two forces, the ________ of the object which acts

downwards and an _________ or buoyant force which acts upwards.

2. A buoyant force is the ________ force resulting from an object being wholly or partially immersed

in fluid.3. An object which has a _________ less than the liquid in which it is submerged, will be subjected to

_________ force which causes the object to __________ on the surface of the liquid.

4. Conversely, an object which has a density _________ than the liquid in which it is submerge, will

_________ to the bottom as the buoyant force is not sufficiently strong enough to support the

__________ of the object.

When an object is immersed in a

fluid, the object will ____________

a certain volume of the fluid.



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Archimedes’ Principle

1. Figure above shows an object attached to a spring balance. The ________ of the object in air, W1 is

__________ than its weight when immersed in water, W2. The different in weight is due to an

upward _________ force acting on an object by the water.

2. Consider the weight of an object in an air as its _________ weight and the measured when the object

is immersed in a fluid is its _________ weight. Hence:

a) In air, a load of mass 8 kg has a real weight, W1 = ___ N (reading on spring balance).

b) When the object is fully immersed in water, the reading on the spring balance, W2 = ___ N

(apparent weight)

c) Buoyant force is equal to the apparent _______in weight.

Buoyant Force = Apparent loss in weight= Actual weight - Apparent weight

= 80 N - 70 N

= 10 N

3. Archimedes’ Principle states that for a body immersed wholly or partially in a fluid, the upward

_________ force acting on the body is equal to the _________ of the fluid it _____________.

Buoyant force = Actual weight, W1 – Apparent weight, W2



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4.

Figure above shows a rectangular block submerged in a liquid of density, ρρρρ. The pressure of the

liquid on the lower surface of the block, P2 is _________ than the pressure on the upper surface of

the block P1

Resultant force = Buoyant force

= F2 - F1= h2ρgA - h1ρgA

= ρgA (h2 – h1)

= ρgV

= mg

= _________ of liquid displaced

Submerged Object

Weight of the object > ______________

ρobject > ρfluid

V fluid displaced = ___________

Upthrust = Weight of the fluid displaced

= V fluid displaced x ρfluid x g

= V object x ρfluid x g

apparent loss in weight = Upthrust

object

liquid



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Floating Object

Weight of the object = ________________

(only for a floating object and not for a sinking object)

Vfluid displaced = Vobject (for a sinking object Vfluid displaced = V object)

But,

Vfluid displaced V object in the fluid

APPLICATION OF ARCHIMEDES’S PRINCIPLE

Submarine

1. A submarine applies the principle to enable it to _______ and _______. The _________ tanks are

special compartments in a submarine.

2. The submarine_______, when the ballast tank is filled with _____ so that the buoyant force is greater

than the _________ of the submarine.3. The submarine______, when a ballast tanks are filled with ________ so that the buoyant force is

________ than the weight of submarine.



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Hot Air Balloon

1. A hot-air balloon __________ a large volume of _____________

2. The balloon ________ when the buoyant force is less than its _______.

3. When its weight is equal to the buoyant force, it remains _________ in the air.

4. Weather balloons use a light gas such as ________or__________.

5. In Sport and recreation, balloon is filled with hot air which has a lower density than cold air. The

weight of the balloon can be varied by controlling the quantity of ___________ in the balloon.

Hydrometer

1. A hydrometer is an instrument used to measure the ________ of liquids such as _______ in a battery.

2. It consists of a tube with a bulb at one end. ______ shots are placed in the bulb to ________in down

and enable the hydrometer ________ vertically in the liquids.

3. In a liquid of lesser density, a greater ________ of liquid must be __________ for the buoyant force

to equal the weight and so the more the hydrometer is submerged. The hydrometer floats ________

in a liquid of higher density.



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EXERCISE

1. What is the buoyant force acting on the

nut when immersed in water?

2. A stone weight 2.5 N. When it is fully submerged in a solution, its apparent weight is 2.2 N. Calculate the

density of the solution if its volume displaced by the stone is 25 cm3. ( g = 9.8 N kg

-1)

3. Figure below shows the cross-section of a submarine. The volume of the submarine is 240 m3

. When theballast tank is empty, the submarine floats at the surface of the sea with 3/4 of its volume below the surface

of the sea. The density of sea water is 1200 kg m-3

.

(a) (i) On figure above mark and label two vertical forces acting on the submarine.

(ii) State the relationship between the two forces in (a) (i).

(b) (i) Calculate the magnitude of one of the two forces in (a) (i).

(ii) Name the principle used in b (i).

(c) The captain of the submarine observed that the submarine is not strong enough to dive safely to the

bottom of the sea. Suggest modifications that can be made to the submarine to make it safer. Justify

your suggestions.



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3.4 Applying Pascal’s Principle

The idea of Change of Pressure in a fluid

Diagram 1

1. Diagram 1 show that air is shot out from the holes in the glass flask with the same speed

when the piston is pushed into the flask.

2. This is because the pressure acting on the water is transferred uniformly through the

water.



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PASCAL’S PRINCIPLE

1. Pascal’s Principle state that pressure applied to an enclosed liquid is transmitted equally

to every part of the liquid.

2. A basic hydraulic system is operating on Pascal’s principle.3. As stated in Pascal’s principle,

pressure is transmitteduniformly throughout anenclosed liquid. Figure 2 shows

pressure transmitted equally

from a smaller piston to a largerone.

P1 = pressure applied onsmall piston

P2 = pressure applied on big

pistonF1 = input forceF2 = output forceA1 = small piston area

A2 = large piston areaFigure 2

Application of Pascal’s Principle

1. One pratical device that

makes use of Pascal’sprinciple is the hydraulic lift.

Since the input pressure, Pin is equal to the output

pressure, Pout, we have.

in

in

A

F =

out

out

A

F

Fout =in

out

A

A x Fin

Since Aout is much bigger than Ain, the resulting force multiplier effect enables a heavy

object like a car to be lifted by much smaller input force.



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2. In a hydraulic brake, when the brake pedal is pressed, pressure will be transferredthrough the pedal brake liquid to the car’s tyres.

3. In a drum brake, the pressure transferred will

(a)

move the small piston(b) cause the brake drum to be pressed by the brake pedal.

4. The frictional forces between these brake components cause the car to slow down andstop.

5. When the brake pedal is released, a spring pulls the brake disc to their original positions.



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EXERCISES

1. Figure 1 shows a 10 N weight

balancing a X N weight placed on a

bigger syringe.

What is the value of X?

2.

Figure 2 shows a garage hydraulic lift

with two pistons. The smaller piston has

a cross-sectional area, A1 = 4.0 cm2. The

bigger piston has a cross-sectional area,

A2 = 240 cm2.

If the maximum force that can be

applied on the smaller piston is 600 N.

What is the maximum weight of a car

that can be lifted by the bigger piston?

3. Diagram 1 shows a simple hydraulic

press. The cross-sectional area of piston

A and B are 0.08 m2 and 1.2 m2

respectively.

(a)

What is the force which acts on

piston A?

(b)

Calculate the pressure exerted on

piston B.

(c) Calculate the mass of load Y

which can be lifted by the piston

B.

(d) If the piston A moves down by 6

cm, calculate the distance moved

by the piston B.



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3.6 UNDERSTANDING BERNOULLI’S PRINCIPLE

Have you ever wondered how a massive object like an aeroplane can fly? When an aeroplane moves fast

enough on a runway, it experiences an upward lift that enables it to take off.

To understand how an aeroplane can fly, we need to understand an important principle in physics called

Bernoulli’s Principle.

1. Bernoulli’s Principle states that when the velocity of fluid is high, the pressure is low, and when the

velocity is low, the pressure is high.

2. Diagram below shows our daily activities which show the principle of Bernoulli.

-

When the air is blown in the surface of a piece of a paper as shown, it is observed that the papermoves up.

- This happened because the air moved at a very high velocity on the surface of the paper. In this case,

the air pressure on the surface of the paper will decrease.

-

So the paper is pushed up by the higher atmospheric pressure which acts at the bottom of the paper.

-

The filter funnel is inverted and a ping-pong ball is held below it.

- When the air blows harder as shown in the diagram, it is observed that the ball is not falling down.

- This phenomenon is caused by low pressure above the ball.

- The bottom of the ball has the higher atmospheric pressure which can hold the ball from fallingdown.



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- When the air is blown harder through the straw as shown. The two ping-pong balls will move closely

to each other.

- The faster the movement of air will cause the lower the pressure between the balls.

- So the ping-pong balls get closer.

- The ping-pong ball will be pushed closer to each other if there is higher atmospheric pressure whichacts on them.

Bernoulli’s Principle Applied to Fluid Flow in Tubes.

1. When water is not flow, the water levels A, B and C at the vertical tubes are the same.

2. When water is flowing at a steady rate, water levels at the vertical tubes are decreasing.

3. When water is not flowing, pressure at A, B and C are the same.

4. When water is flowing at a steady rate, it flows from higher pressure to lower pressure. The pressure at

A is higher that at B and the pressure at B is higher than at C.

5. When a fluid passes through a tube that narrows section, E, its speed increase, hence at E the water

flows at a higher velocity and its pressure is the lowest.



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Application of Bernoulli’s Principle

Aerofoil

1.

The flight of an airplane is based on the principle regarding the effect of the flow of air around itswings, which are in the form of an aerofoil.

2. Figure below shows that the upper region of the aerofoil has higher air velocity than the lower region

of the aerofoil. By Bernoulli’s principle, the lower region has a higher pressure than the upper region

of the aerofoil. This causes a lifting force on the aerofoil.

Bunsen burner

1.

When gas flows out through the jet, the velocity of the gas is high and by Bernoulli’s principle, its

pressure is low.

2.

Hence, atmospheric pressure will force the surroundings air into the burner. The mixture of the gas andair allows a complete combustion.



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Carburettor

1. Carburettor is a device which controls the speed of a car engine. It works by regulating the quantity of

petrol and air that enters the engine.

2. The air flows past a choke valve, which controls the quantity of air, into a narrow section of the

carburettor where the air velocity increases.

3.

In accordance to Bernoulli’s principle, the high velocity of the air in the narrow section creates a

region of low pressure. The higher atmospheric pressure force the petrol to go up to the jet and is

ejected to form a spray.



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Exercise

1. Diagram shows an experiment. The tube is inverted into a basin of water.

(a) The air flows in the tube from A to B;

- Compare the velocity of air at K, L, and M,

- Mark the water levels in tubes P, Q, and R.

- Compare the pressure in tubes P, Q and R.

- Name the principle used. Explain the principle.

2. Diagram shows an insecticide sprayer.

(a) When the piston is pushed inwards, what happens to the pressure at P?

(b) Explain your answer in (a)

(c)

Which of the following areas P, Q and R has the lowest pressure?

(d)

Explain your answer in (c).

(e) Explain briefly how the insecticide can be sprayed out of the spray.



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Objective Questions

1. The figure shows two polystyrene spheres are hungby a string respectively.

When the air is blown harder through the straw, the

balls will

A remain stationaryB move closely to each other

C move far apart to each other

2 The figure shows the flow a liquid through aBernoulli tube. The smallest pressure of the liquid is

at point……

3 The figure shows water flows through a Venturitubes from point P to point Q.

In which vertical tubes A ,B,C or D the pressure ofwater is very low?

4 The figure shows an arrangement of apparatus

which is used to show the Bernoulli’s Principle.

When the air is blown, the level of water in tube

A X will the highest

B Y will the highest

C Z will the highest

D X,Y and Z will the same

5 The figure shows water rising up the tubes X,Y andZ if the air is blown.

Which of the following is true regarding the water

level in tube X,Y and Z?

A Water level in X < Water level in Y < Waterlevel in Z

B Water level in X < Water level in Z < Waterlevel in Y

C Water level in Z < Water level in Y < Water

level in XD Water level in Y < Water level in Z < Water

level in X

6 The figure shows the wing of an aeroplane which is

moving with a uniform acceleration in the directionshown by the arrow.

Which of the following is true?

A The uplift force is higher than the weight of

objectB The resultant force in direction of the motion

of the object is zeroC The pressure in region P is higher than in

region QD The velocity of air in region P is higher than in

region Q.

7 Which of the following is based on Bernoulli’s

Principle?

A SyringeB Drinking strawC Bunsen burner

8 The figure shows a water spray that is

produced when the air flows through the jet.



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Which of the following is true?

A According to Pascal’s Principle, the above

system produces a water spray.B The air pressure at Q is higher than that at P

C The velocity of air at Q is higher than that at P

9 The figure shows a motion a ball when it is kicked

by a player.

The motion of the ball can beexplained by

A Principle of conservation of momentumB Principle of conservation of energy

C Archimedes’ principleD Bernoulli’s principle

10 A ball which is thrown forward in a spin moves in a

curve , as shown in the figure.

The curved path taken by the ball is due to

A equilibrium of forcesB Bernoulli’s principleC Archimedes’ principle

D principle of conservation of momentum

11 The figure shows a ping-pong ball that does not fall

when the water flows.

Which principle explains the figure?

A Pascal’s principle

B Bernoulli’s principleC Archimedes’ principle

12 Which of the following instruments is not based on

Bernoulli’s principle?

A Filter pump

B Car carburettorC Rubber plunger

D Wing of aeroplane

Archimedes 1

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