Pascal, des & Bernoulli

8/6/2019 Pascal, des & Bernoulli

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TOPIC: FORCE AND PRESURE

CONTENT (30 minutes):

A) PASCAL’S PRINCIPLE

B) ARCHIMEDES’ PRINCIPLEC) BERNOULLI’S PRINCIPLE

A. PASCAL’S PRINCIPLE (10 MINUTES)

i. Pascal’s principle states that pressure applied to an enclosed fluid istransmitted uniformly to every part of the fluid and to the walls of the container.

Water is ejected out in all directions with the same magnitude showing thatwater pressure is acting with the same magnitude in all directions.

ii. Mathematically, Pascal’s principle can be represented by the equation :

F1 = F2

A1 A2

With F1 = input force,A1 = cross-sectional area of the input cylinder,F2 = output force,A2 = cross sectional area of the output cylinder.

APPLICATIONS :

A hydraulic jack is used to lift a car.



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Assume, AI = 0.01m and A2 = 1m

Explanation:Applied pressure, p = F1 /A1 = F1/ 0.01Transmitted pressure, p = F2 / A2 = F2 / 1By Pascal’s principle, F2/ 1 = F1/ 0.01

Hence, F2 = 100 F1.

Hydraulic system in car brake

A small force acting on the pedal can transmit a large force to stop the wheel.

ACTIVITY A:

1. Figure shows a 10N weight balancing a X N weight placed on a bigger syringe. What is the value of X ?



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2. Figure shows a glass barrel fitted with a plunger. The other end of the barrelis with holes of uniform size.a) State your observation when the plunger is pushed towards the bulbous end.b) State one inference concerning pressure applied on the water by the plunger.

3. A boy invented a machine to compress old newspaper. The machine consistsof a hydraulic system with two pistons as shown in figure. Piston A has a smaller cross-sectional area compared to piston B.

a) The function of this machine is based on a principle in physics. Name theprinciple.b) Explain why a small force exerted by the boy can result in a much bigger

force acting on the old newspaper.

B. ARCHIMEDES’ PRINCIPLE (10 minutes)

1. Archimedes principle states that for a body immersed wholly or partially in afluid, the upward buoyant force acting on the body is equal to the weight of thefluid it displaces.



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2. The spring balance reading in (b)F2 , is less than the spring balance in (a), F1,due to the buoyant force of water on the stone.Buoyant force = Weight of liquid displaced

F1 – F2 = mg= hpg

APPLICATIONSa. Buoyant force = weight of submarine.

The depth of a submarine in the sea depends on the magnitude of the buoyantforce.

b. The rising and falling of the hot air balloon depends on the weight of air displaced.



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c. Buoyant Force = weight of the ship.

d. How deep the ship sinks below the sea level depends on the density of seawater. It indicates whether the ship has entered a tropical ocean or an ocean inthe temperate region.

e. A hydrometer helps to determine the density of the liquid tested.

ACTIVITY B ( minutes) :

1. Experiment:To find the relationship between weight of water displaced and the buoyant force.

Statement of problem:



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Since the density of iron is much higher than the density of sea water, why doesa ship made of iron still float on the surface of the sea?

Hypothesis:

Variables:a) Manipulated: ___________________________________________________

b) Responding: ___________________________________________________

c) Fixed: ________________________________________________________

Operational Definition:Buoyant force = weight of the object in air – the apparent weight of the object in

water.

= ______________

Weight of water displaced = weight of beaker with displaced water – weight of empty beaker.

= W1 – W2

Weight of water displaced = weight of beaker with displaced water – weight of empty beaker.

= B2 – B1

Apparatus:

________________________________________________________________

Procedure:1. Weight of an empty beaker is recorded as B1.2. A stone is suspended by a spring balance in air as shown in Figure.3. The reading of the spring balance W1 is recorded.4. The stone is immersed completely in water in the eureka can.5. The apparent weight W2 is taken.6. The water displaced is collected in a beaker as shown in Figure.



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7. Weight of beaker with the displaced water, B2 is recorded.

Observation:

Weight of stone in air = W1 Weight of stone in water = W2 Buoyant force = ____________ Weight of empty beaker = B1 Weight of beaker with displaced water = B2 Weight of water displaced = ___________ It is found that W1 – W2 = _____________

Conclusion:The weight of water displaced is equal to the __________________________.

2. An object of density 20 g cm

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and mass 400 g is immersed in a liquid of density 1.5 g cm-3

. CalculateTake g = 10 m s-2.a) the volume of the liquid displaced.

b) the mass of the liquid displaced.

c) the buoyant force experienced by the object.

C. BERNOULLI’S PRINCIPLE ( minutes)

Bernoulli’s principle states that when the velocity of a fluid is high, the pressure islow and when the velocity is low, the pressure is high.



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The height of the water column shows the magnitude of the water pressure.The dotted line is the pressure gradient showing how the water pressure isdecreasing gradually.

The velocity of water is highest when it is flowing through the narrowest part of the horizontal glass tube. Hence, its water pressure is the lowest.

APPLICATIONS1. Aerofoil

An aeroplane, with an aerofoil shape, experiences a lifting force which balancesits weight.



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2. Bunsen burner.

Air rushes in due to the lower pressure in a Bunsen burner. Air supports burning.

3. Carburettor

Air rushes in due to the lower pressure in a near the jet of the car engine. Themixture of air and petrol helps in burning.

ACTIVITY C: ( minutes)

1. A horizontal tube AB with both ends closed with rubber stoppers is fixed with

three vertical tubes P, Q and R as shown in figure. Water of density 1 000 kg m-3

is poured into tube P until water reaches level W.



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a) i. What are the heights of water levels for tube Q and tube R respectively?

ii. By neglecting atmospheric pressure, calculate the pressure caused bywater column at point X.

iii. If the cross-sectional area of tube P is 4 x 10-5 m2, calculate the force actedby the column of water in tube P.

b) If the rubber stoppers at both ends of tube AB are taken away so that water

can flow uniformly from end A to end B, then water at tube P rises until level Y asshown in figure.i. Mark on the figure above, the possible water levels for tube Q and tube R.

ii. Give reasons for your answer in (b) (i).

c) The apparatus is modified so that the middle part of the horizontal tubebecomes narrower as shown in figure. Water flows uniformly from end A to endB of the tube and it is found that the water level of tube and it is found that thewater level of tube P is at Z.



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i. Mark on the figure above, the possible water levels of tube Q and tube R.

ii. Compare the velocity of water at E and F.

iii. State the principle which relates velocity and pressure of water along the

horizontal tube.

ASSESTMENT

1. Which of the following does not make use of Pascal’s principle?A Hydraulic jackB Bicycle pumpC Hydraulic brakeD Syringe

2. Which of the following statements is not true?A Pressure of liquid acts in all direction.B When a pressure is applied to a liquid in an enclosed container, the

pressure is transmitted throughout the liquid.C When pressure is transmitted in a liquid, the further the transmission, the

lower the pressure.D The pressure transmitted in a liquid can result in a bigger output force

compared with input force

3. The figure 1 shows a simple hydraulic system.Push

Figure 1

What are the force and pressure at Y compared to the force and pressure atX?

Force at Y compared to X Pressure at Y comparedto X

A Smaller Smaller

B Equal Equal

C Larger Equal

D Larger Larger



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4. Which of the following does not function based on Archimedes’ principle?

A A submarineB A race car C A hydrometer

D An ocean liner

5. A block of wood 10-3 m3 is half immersed in water. If the density of water is

1000 kg m-3

and the acceleration due to gravity is 10 kg-1

, what is the weightof the block of the wooden air?A 0 NB 0.5 NC 1.0 N

D 5.0 NE 10.0 N

6. Which of the following does not operate based on Bernoulli’s principle?A A Bunsen burner B A submarineC Wind surfingD A whistle with ball- bearing

Structured QuestionQuestion 1 and 2 are based on Figure 2

Figure 2

1. Figure 2 shows the structure of a simple hydraulic jack where a smallforce F1 is used to produce a bigger force F2, A1 and A2 are the cross-sectional areas of the pistons.

(a) A force of 1000 N is applied to smaller piston.(i) What is the pressure exerted on the piston? [1 mark]



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(ii) What is the force multiplier of this hydraulic jack? [1 mark]

(iii) How much force is exerted on the larger piston? [1 mark]

(iv) What is the principle been applied in (a)(iii)? [1 mark]

2. The smaller piston is pushed down a distance of d1 = 100 cm and thishas resulted in the larger piston moving up a bit.

(i) How much has larger piston moved? [2 marks]

(ii) What is the assumption made in obtaining the answer in (b)(ii)?[1 mark]

3. Figures 3 and 4 show a same ship sailing in two different locations.



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Figure 3 Figure 4

(a) What is meant by buoyant force? [1 mark]

(b) Using figures above, compare the buoyant forces acting of the ship atthe two different locations.State the relationship between density and the volume of the water displaced. [ 5 marks]

(c) Figure 5 shows a concrete cylinder attached to a spring balance. It islowered into a beaker so that it is partially immersed.

Figure 5

Explain what happens to the reading of the spring balance if the concrete cylinder is raised slightly. [2 marks]



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Answer (Assesment)

Objective questions1. D

2. D3. C4. B5. E6. B

Structured question1. (a) (i) Pressure , P = F = 1000 = 200 Ncm-2

A 5

(ii) Force multiplier = F2 = A2 = 100 = 20 times

F1 A1 5

(iii) Force F2 = 20 F1 = 20 (1000) = 20000 N

(iv) Pascal’s principle

2. (i) Volume, A1d1 = A2 d2 5(100) = 100d2

d2 = 5000 = 5 cm100

(ii) The pressure from the smaller piston is fully transferred to the larger piston.

3. (a) Buoyant force is an upward force resulting from an object being wholly or partially immersed in a fluid.

(b)

• The buoyant forces at both the locations are the same

• This is because the buoyant force is of equal magnitude with the weightof the ship which is unchanged

• The density of water is higher than fresh water

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The buoyant force of a floating ship is equal to the weight of the water displaced.

• The higher the density of the water, the smaller the volume of water displaced.

(c)

• The readings becomes bigger

• This is because the buoyant force is reduced as less water is displaced byconcrete cylinder.

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Pascal, des & Bernoulli