PRESSURE PRESSURE ON SOLIDS ON SOLIDS AND FLUIDSAND FLUIDS

PRESSURE PRESSURE ON SOLIDS ON SOLIDS AND FLUIDSAND FLUIDS

DENSITY - is a measure of the DENSITY - is a measure of the compactness of a substance.compactness of a substance.

= m/V= m/Vwhere: where:

m = mass in g or kgm = mass in g or kgV = volume in cm3 or m3V = volume in cm3 or m3

= density in g/cm3= density in g/cm3or kg/m3or kg/m3

(See table 9.2 p. 301)(See table 9.2 p. 301)

DENSITY - is a measure of the DENSITY - is a measure of the compactness of a substance.compactness of a substance.

= m/V= m/Vwhere: where:

m = mass in g or kgm = mass in g or kgV = volume in cm3 or m3V = volume in cm3 or m3

= density in g/cm3= density in g/cm3or kg/m3or kg/m3

(See table 9.2 p. 301)(See table 9.2 p. 301)

Question: Question: Question: Question:

1. Why can you carry a 1. Why can you carry a person more easily in a person more easily in a swimming pool than on swimming pool than on land?land?

2. Why is it easier to float 2. Why is it easier to float in sea water than in in sea water than in fresh water?fresh water?

1. Why can you carry a 1. Why can you carry a person more easily in a person more easily in a swimming pool than on swimming pool than on land?land?

2. Why is it easier to float 2. Why is it easier to float in sea water than in in sea water than in fresh water?fresh water?

ObjectivesObjectives1. Explain the pressure-depth1. Explain the pressure-depth

relationshiprelationship

2. State Pascal2. State Pascal’’ss Principle Principle

3. Describe how Pascal3. Describe how Pascal’’ss

principle is used in practicalprinciple is used in practical

applications.applications.

PRESSURE IN SOLIDSPRESSURE IN SOLIDSPRESSURE IN SOLIDSPRESSURE IN SOLIDS

PRESSURE - is a force PRESSURE - is a force per unit area per unit area

P = F/A P = F/A

Unit: N/mUnit: N/m2 2 or Pa (pascal)or Pa (pascal)

PRESSURE - is a force PRESSURE - is a force per unit area per unit area

P = F/A P = F/A

Unit: N/mUnit: N/m2 2 or Pa (pascal)or Pa (pascal)

Question:Question:

•If you push both a pin and a If you push both a pin and a barbecue stick against a cork barbecue stick against a cork board with equal force, which board with equal force, which do you think will cut the cork do you think will cut the cork board first?board first?

•What determines whether What determines whether your skin suffers a cut? Is it your skin suffers a cut? Is it the force or pressure? Justify the force or pressure? Justify your answer. your answer.

Sample ProblemSample Problem•The heel on the woman’s The heel on the woman’s

shoe occupies an area of shoe occupies an area of 1.19 x 101.19 x 10-3-3 m m22 on the floor. on the floor.

How large a compressive How large a compressive stress (pressure) does a 55 stress (pressure) does a 55 kg woman exert on the floor kg woman exert on the floor when balancing on one heel?when balancing on one heel?

•Answer: P = 452,941.18 N/mAnswer: P = 452,941.18 N/m22

QUESTION:QUESTION:

Is there more pressure at Is there more pressure at the bottom of a bathtub the bottom of a bathtub of water 30 cm deep or at of water 30 cm deep or at the bottom of a pitcher the bottom of a pitcher of water 35 cm deep? of water 35 cm deep? Justify your answer.Justify your answer.

PRESSURE and DEPTHPRESSURE and DEPTHPRESSURE and DEPTHPRESSURE and DEPTH The extra The extra pressure at pressure at depth depth hh in a in a liquid is due to liquid is due to the weight of the weight of a liquid above.a liquid above.

P = P = gh gh

The extra The extra pressure at pressure at depth depth hh in a in a liquid is due to liquid is due to the weight of the weight of a liquid above.a liquid above.

P = P = gh gh h

ANSWERANSWER

There is more pressure There is more pressure at the bottom of the at the bottom of the pitcher, because the pitcher, because the water in it is deeper. water in it is deeper. The fact there is more The fact there is more water in the bathtub water in the bathtub does not matter. does not matter.

SAMPLE PROBLEMSAMPLE PROBLEM

•Calculate the pressure Calculate the pressure of water at the bottom of water at the bottom of a swimming pool of a swimming pool which is 1.8m deep.which is 1.8m deep.

•Answer: P =17 640 Pa Answer: P =17 640 Pa

Question:Question: Which Which tube has the tube has the greatest pressure greatest pressure given the same level given the same level of liquid?of liquid?

PRESSURE IN FLUIDSPRESSURE IN FLUIDSPRESSURE IN FLUIDSPRESSURE IN FLUIDS

The pressure of the The pressure of the liquid is the liquid is the samesame at at any given depthany given depth below below the surface, the surface, regardless of the regardless of the shapeshape of the of the container.container.

The pressure of the The pressure of the liquid is the liquid is the samesame at at any given depthany given depth below below the surface, the surface, regardless of the regardless of the shapeshape of the of the container.container.

Total pressure on an open Total pressure on an open container is the sum of container is the sum of pressure above the liquid pressure above the liquid surface and the pressure at surface and the pressure at a deptha depth hh

P = PP = Poo + + gh gh

Example Problem 9.3 p. 302Example Problem 9.3 p. 302

• What is the total pressure on the back of a What is the total pressure on the back of a scuba diver in a lake of 8 m?scuba diver in a lake of 8 m?

• What is the force on the diver’s back due to What is the force on the diver’s back due to the water alone, taking the surface of the the water alone, taking the surface of the back to be a rectangle 60 cm by 50 cm?back to be a rectangle 60 cm by 50 cm?

• Answer: P =1.79 x10Answer: P =1.79 x1055 Pa Pa F = 2.35 x10F = 2.35 x1044 N N

PASCAL’SPASCAL’S PRINCIPLEPRINCIPLE•Changes in pressure Changes in pressure at any point in an at any point in an enclosed fluid at rest enclosed fluid at rest are transmitted are transmitted unchanged to all unchanged to all points in the fluid and points in the fluid and act in all directions.act in all directions.

Pascal’s PrinciplePascal’s PrinciplePascal’s PrinciplePascal’s Principle

P1 = P2

F1/A1 = F2/A2

Wo = Wi

F1d1 = F2d2

QUESTION:QUESTION:•As the car is As the car is

being lifted, being lifted, how does the how does the change in change in fluid level in fluid level in the reservoir the reservoir compare compare with the with the distance the distance the car moves? car moves?

ANSWER:ANSWER:• The car moves The car moves

up a greater up a greater distance than distance than the fluid level the fluid level drops, since drops, since the area of the the area of the piston is piston is smaller than smaller than the surface the surface area of the area of the fluid in the fluid in the reservoir.reservoir.

Cite some practical Cite some practical applications of Pascal’s applications of Pascal’s

PrinciplePrinciple

ARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLEARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLE

A body wholly or partly A body wholly or partly immersed in a fluid is immersed in a fluid is buoyed up by a force buoyed up by a force equal to the weight of equal to the weight of

a fluid it displaces.a fluid it displaces.

A body wholly or partly A body wholly or partly immersed in a fluid is immersed in a fluid is buoyed up by a force buoyed up by a force equal to the weight of equal to the weight of

a fluid it displaces.a fluid it displaces.

ARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLEARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLE•A buoyant force is exerted A buoyant force is exerted

on an object submerged in on an object submerged in a fluid. a fluid.

•The pressure beneath the The pressure beneath the object is larger than the object is larger than the pressure above.pressure above.

•The resultant force on the The resultant force on the object is upward, opposing object is upward, opposing the force of gravity. the force of gravity.

•A buoyant force is exerted A buoyant force is exerted on an object submerged in on an object submerged in a fluid. a fluid.

•The pressure beneath the The pressure beneath the object is larger than the object is larger than the pressure above.pressure above.

•The resultant force on the The resultant force on the object is upward, opposing object is upward, opposing the force of gravity. the force of gravity.

ARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLE

• The apparent change The apparent change in (or loss in) weight of in (or loss in) weight of an object immersed in an object immersed in a liquid is due to the a liquid is due to the buoyant force. buoyant force.

•The apparent weight The apparent weight equals the actual equals the actual weight minus the weight minus the buoyant force.buoyant force.

• The apparent change The apparent change

in (or loss in) weight of in (or loss in) weight of an object immersed in an object immersed in a liquid is due to the a liquid is due to the buoyant force. buoyant force.

•The apparent weight The apparent weight equals the actual equals the actual weight minus the weight minus the buoyant force.buoyant force.

ARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLEARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLE

•If the weight of the If the weight of the submerged object is submerged object is greater than the buoyant greater than the buoyant force, it will SINK. force, it will SINK.

•If it is less, it will FLOAT.If it is less, it will FLOAT.

•If it is the same, it will If it is the same, it will have neutral buoyancy have neutral buoyancy (anywhere in the fluid).(anywhere in the fluid).

•If the weight of the If the weight of the submerged object is submerged object is greater than the buoyant greater than the buoyant force, it will SINK. force, it will SINK.

•If it is less, it will FLOAT.If it is less, it will FLOAT.

•If it is the same, it will If it is the same, it will have neutral buoyancy have neutral buoyancy (anywhere in the fluid).(anywhere in the fluid).

ARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLEARCHIMEDES’ ARCHIMEDES’ PRINCIPLEPRINCIPLE

Where:m = the mass of liquid displaced g = the acceleration due to gravity

FFBB = mg = mgFFBB = = liquidliquid v v liquidliquid g g

FFBB = mg = mgFFBB = = liquidliquid v v liquidliquid g g

ARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLE

QUESTION:QUESTION:

A stone is thrown into A stone is thrown into a deep lake. As it sinks a deep lake. As it sinks

deeper and deeper deeper and deeper into the water, does into the water, does

the buoyant force on it the buoyant force on it increase, decrease, or increase, decrease, or

remain unchanged?remain unchanged?

ANSWER:ANSWER:•The volume of displaced water The volume of displaced water

at any depth is the same in at any depth is the same in each at any depth. Water is each at any depth. Water is practically incompressible, so practically incompressible, so its density is the same at any its density is the same at any depth, and equal volumes of depth, and equal volumes of water weigh the same. The water weigh the same. The buoyant force on the stone buoyant force on the stone remains unchangedremains unchanged as it sinks as it sinks deeper and deeper.deeper and deeper.

QUESTION:QUESTION:

•We know that if a fish We know that if a fish make itself more dense, make itself more dense, it will sink; if it makes it will sink; if it makes itself less dense , it will itself less dense , it will rise. In terms of buoyant rise. In terms of buoyant force, why is this so?force, why is this so?

ANSWER:ANSWER:•When the fish increases its When the fish increases its density by decreasing its density by decreasing its volume, it displaces less volume, it displaces less water, so the buoyant force water, so the buoyant force decreases. When the fish decreases. When the fish decreases its density by decreases its density by expanding, it displaces more, expanding, it displaces more, and the buoyant force and the buoyant force increases.increases.

TriviaTrivia•The people who can’t The people who can’t float, 9 times out of float, 9 times out of 10, are males. Why?10, are males. Why?

•More males are more More males are more muscular and slightly muscular and slightly denser than females.denser than females.

QUESTIONS:QUESTIONS:1.1.The volume of a submerged The volume of a submerged

object is equal to the _____ of object is equal to the _____ of liquid displaced.liquid displaced.

volumevolume2. The weight of a floating object 2. The weight of a floating object

is equal to the ______ of liquid is equal to the ______ of liquid displaced.displaced. weightweight

This is generally applicable for all This is generally applicable for all fluids.fluids.

Bernoulli’s Principle Bernoulli’s Principle states states

that:that:• if the velocity of a fluid if the velocity of a fluid is high, the pressure in it is high, the pressure in it is low.is low.

•If the velocity of fluid is If the velocity of fluid is low, the pressure is high.low, the pressure is high.

Q1:Q1: Explain why blowing Explain why blowing aa piece of paper piece of paper causes itcauses it to rise. to rise.Q2:Q2: You are told to avoid You are told to avoid standing too close to a standing too close to a rapidly moving light rail rapidly moving light rail transit (LRT) because you transit (LRT) because you might get sucked under it. might get sucked under it. Is this possible? Explain.Is this possible? Explain.

Properties of Properties of fluids:fluids:•The forces that a fluid The forces that a fluid exerts on the walls of exerts on the walls of the container, and the container, and those that the walls those that the walls exert on the fluid, exert on the fluid, always act always act perpendicular to the perpendicular to the walls.walls.

Properties of fluids:Properties of fluids:•The force exerted by the The force exerted by the pressure in a fluid is the pressure in a fluid is the same in all directions at same in all directions at a given depth.a given depth.

•An external pressure An external pressure exerted on a fluid is exerted on a fluid is transmitted uniformly transmitted uniformly through out the fluid.through out the fluid.