The model was built on the knowledge of the particle nature of matter and the analysis of the motion of the par ticles.
The phenomena we analyzed were influenced by the temperature of the gas and the pressure it exerts on surfaces.
We didn't pay attention to the effect of the Earth's gravity on the gas particles.
In most of the processes we analyzed the gases had little mass and occupied a relatively small region of space.
The force that Earth exerts is an important part of phenomena in this chapter.
The discussion will be limited to fluids that are static.
The concept of density is familiar to us.
Measure the density of an object or substance to determine its mass and volume.
Determine its mass using a scale.
The iron nail's density is 7800 kilogrammes, which is relatively large.
The pul Volume sar, a rapidly spinning neutron star, has a density of 1018 kilogrammes.
The plastic shell of the ball has less mass than an equal volume.
The volume of water is the mass of either filled ball.
The ball is made of soil from the Earth's surface.
Unless otherwise stated, densities of liquids are at 0 oC.
Unless noted, the densities of gases are at 0 oC and 1 atm.
Understanding density allows us to pose questions about phenomena we observe.
The layer of oil on top of the water is independent of which fluid is poured first.
The density of water is larger than that of oil.
The density of corn syrup is greater than the pressure of the water in the container.
There are similar phenomena with gases.
The mass of he lium atoms is less than that of any other molecule in the air.
The air must be denser than the bal oon.
The water skin of a balloon is denser than air.
Liquid water and solid ice are not usually denser than the liq uid form of the substance.
We can assume that the density of ice is less than water because it floats on liquid water.
The density of water varies with temperature and is the highest at 4 C. The ice has a density of 917 kilogrammes.
In forming the crystal struc ture of ice, water atoms spread apart.
Life on Earth is dependent on the fact that water expands when ice forms.
The fish and plants live in lakes under a shield of ice and snow.
Water is absorbed in the cracks of rocks and expands in the winter.
Over the years, this process of liquid water absorption, freezing, and cracking eventu al y converts the rock into soil.
We can investigate whether pressure explains why a nail sinks in water or why a hot air bal oon rises.
As gas particles collide with the walls of the container in which they reside, they exert pressure.
There are holes in the container.
The bottle is open.
Let's conduct an experiment.
Take a plastic water bot tle and poke several small holes at the same height along its perimeter.
The holes in the bottle of water shoot out of them.
The behavior of the water when the tacks are at the same level surface is similar to a person leaning on a door that is suddenly opened.
The water inside must push out from the wal of the bottle in the same way gas pushes out from the wall of a balloon.
Liquids and gases are often studied together and referred to as fluids.
The pressure at al points at the same depth in the fluid since the four streams are identically shaped.
Practical applications involve situations in which an external object is present.
Water comes out of all of the holes when we push the apparatus with water.
We get the same result when we fil the apparatus with smoke.
The gas and liquid behave the same.
The pressure in the fluid close to the piston was increased when the piston was pushed in one direction.
This is what comes out of the holes.
Similarly, pushing the cylinder.
The above experiment describes the first law.
We can explain the first law at a macro level.
The first law of Pascal can help us understand a common eye problem.
New fluid is released into the eye's intraocular pressure when there is a blockage of the chambers.
The ducts drain humor from the eye.
The eye pressure of a person with glau Optic coma is 3000 N>m2 above atmospheric pressure.
Pressure goes up.
If the normal drainage and barbers use them to raise and lower their clients' chairs, then automobile mechanics, dentists, and barbers use hydraulic presses to lift and lower their cars.
There are canals that are blocked.
A liquid is compressed in the lift.
The pistons should be at the same el evation.
The liquid exerts a force on the upward force on piston 2 that is greater than the downward force on piston 1...
2 on L has a small piston with a surface area of less than 20 m2 and a larger pis.
1 on L is equivalent to 180 N.
The force equal to lifting an object of mass 18 kg, constant velocity is what the levels of the two pistons are.
The force diagram can be used for the car.
The units are similar to the first law and the second one.
2 supports the car.
You should specify the assumptions you made.
The small piston has to push farther than the large one.
If you poke a lot of holes in a closed toothpaste tube and squeeze it, the paste will come out the same.
According to the first law of static fluids, an increase in the pressure in one part of an en closed fluid results in an increase in the pressure in other parts of the fluid.
Consider an experiment with a water bottle.
Go along one side of the bottle and poke holes.
Put tacks in the holes and fill the bottle with water.
The cap should be left off.
Water seems to be pushed harder from deeper in the water.
From lo wer holes, the w ater streams ater streams.
Scientists don't throw out the principle immediately, but first look at the assumptions used to make the prediction.
We did not consider the impact of poking holes at different heights in our first experiment with the water bottle.
This may have been an important factor in the experiment.
The stream from the lower holes shoots farther when water comes out on the left and right.
We can conclude that the distance above the top tack mass of the water is the same as the distance above the big bottle with the ger bottle.
Is the same in different directions.
The amount of liquid above the hole does not affect the height of the water above the hole.
It doesn't depend on the amount or depth of the water below the hole.
Pressure goes up with depth.
Air pushing down from above causes pressure on the top surface of the book.
The air exerts pressure on the top book.
If the top surface of each book in the stack behaves differently, the pressure on the side of a bottle will increase.
On the top layer, air pushes down.
The air is pushed down on the top layer by a closed bottle.
The fluid has the lowest pressure at the top and the greatest at the bottom.
The pressure is the same at each layer.
If we could place a pressure sensor inside a container of water, the readings of the sensor would be the same regardless of the orientation of the sensor.
The plane descends from a higher elevation to a lower one.
In a pressurized cabin, the air pressure at the lower elevation is slightly higher than at the higher elevation, which causes the bottle to crush.
Some water is leaking.
The air outside pushes in the force of the inside.
Some water is leaking.
Some water is leaking.
There are bubbles of air coming in when a on S W goes inward.
The air above the water is trapped by the bottle closing.
There is additional pressure from the water pressing downward when there is a leak.
The water should accelerate if you remove that tack.
The air volume at the top of the bottle increases when water comes out of the hole.
Air cannot enter the bottle because it is closed.
When the cap on is reduced, the pressure at the top is reduced.
When water leaks out through the water leaks out through the bottom hole, the model predicts that the cap on will be reduced.
This is what happens when we do an experiment.
You should try to predict the outcome.
The second tack pushed in.
The water in the bottle exerts on that portion.
Air flows into the bottle when the top hole is removed.
When we remo tack, the top ater pressure inside ater pressure inside ter pressure increases and more water squirts out of the lower hole, reducing tack, the water pressure inside near the top is less.
The upper hole has more air than the outside pressure.
The bottle has air in it.
The bottle is leaking.
The bottle has air in it.
Does the pressure depend on the depth of the fluid?
The mass of fluid is below the liquid in the cylinder.
The three forces add to zero because the liquid is not speeding up.
Pascal has a second law.
Pressure varies with depth.
direction is moving in a different direction.
When using the second law.
The axis has a defined origin or zero point.
The positions are relative to the axis.
You can relate the pressures at those two points.
In order to see if the pressure of a fluid depends on the depth and not on the mass of the fluid, a long, narrow tube was inserted into the water from above.
The barrel burst, supporting the idea that the height of the liquid above, not the amount of water above, determines the pressure.
Air pressure is higher at the bottom of a mountain than it is at the top.
Consider the water at positions 1 and 2, that's what Blaise Pascal came up with.
If the columns of water in the apparatus are the same height as above points 1 and 2, the pressures can be equal.
You can use your understanding of pressure to explain why our ears pop.
The outside air pushing in on the eardrum is the same as the inside air.
Venting air from the middle ear can equalize the pressures.
The popping sensation is what it is.
You are in an airplane.
Consider the horizontal por tion of water along the bottom of the apparatus.
The air is at sea level.
The eardrum is 0.50 cm2.
Rolin Graphics sity of air at sea level is 1.3 kg.
The air density should be constant during the hike.
Below is a drawing of 1000 m.
The net force is less when you are at the surface.
The density of Earth's force on an apple.
There is no water.
A cyl inder that is pulled up causes water to rise to a maximum in pressure in a part of the liquid that is not open.
We can use the second law to develop a method for measuring atmo spheric air pressure.
During Galileo's time, pumps were used to remove water from flooded mines and lift drinking water from wells.
The pump was long.
The limit to how far water could be lifted could be explained by the pressure of the air in the atmosphere.
It was published in the year that Torricelli died.
At point 1 there is atmospheric pressure.
The pressure at point 3 is assumed to be zero.
We will use Eq.
The value of the atmospheric pressure that we discussed in Chapter 9 is exactly this number.
If there is a vacuum above the water in the tube, the atmospheric pres can push water up the tube a maximum of 10.3 m.
The huge number that came out of this analysis surprised Torricel i because the value of normal atmospheric pressure was not known at that time.
He tested it using a different liquid.
In an evacuated tube, mercury should rise 1/14 times as high.
Torricel came up with a method that would guarantee that the pressure at the top of the column was zero.
Testing Torricelli's hypothesis with mercury.
Torricelli filled a long Mercury should start leaking from the tube.
It leaves mercury leaking from the end when it leaks.
The height of the mer will stop the leak.
There is a dish filled with mercury.
Predicting what he observed was based on the hypothesis that atmospheric pressure limits the height of the liquid.
The height of the mercury column should be lower in the mountains if the atmospheric pressure is lower.
Experiments have shown that the level decreases at higher altitudes.
The explanation that atmospheric air pushes the liquids upward was supported by these experiments.
The mercury tube became a useful device for measuring atmospheric pressure.
The Torricelli device has been replaced by the aneroid ba rometer.
We now know why pressure is measured in millimetres Hg and atmospheric pressure is 760 millimetres Hg.
Mercury can be pushed up a column by the atmospheric pressure.
Simple experiments that lead to important practical applications can be explained with our understanding of atmospheric pressure.
As the in verted container is pushed deeper into the water, more water enters the con tainer.
A diving bell is a large bottomless chamber lowered under water with people and equipment inside.
Divers use the diving bel to take a break.
The bel has a height of the water inside it.
We don't know the depth underwater.
The pressure of the air inside the sult can be used to determine how far the bell is from the water.
We sketched the situation.
The positive direction will point upward, with 3 being the origin.
The diving bell's air volume is half what it was before it entered the water.
2.0 m is the submerged amount.
If the air pressure in the bell is 12.02, then 105 Pa is 1.01 and 105 Pa2 is 3.0 atm.
Pressure changes in one part of a fluid result in pressure changes in other parts.
The pressure in a fluid depends on the depth of the fluid.
There is a steel block suspended in water.
Translating to 7.8 N, the number is 11.0 kg219.8 N.
The reading of the scale does not change when W is on B water level.
As more of the block is submerged in the water, the level of the water in the container increases.
As more of the block is submerged, the scale reading decreases.
A fluid exerts force on the block.
The fluid pushing up on the bottom exerts more force than the fluid pushing down on the top of the block.
The fluid on the block exerts F on O.
Its height is 12.
The results of the experiments can now be understood.
The scale reading decreased when the block was further into the water.
After the block was under the water, the scale reading stopped.
The submerged volume did not change even after it was completely submerged.
The equation is called the Archimedes' principle.
If the object floats, the volume in the equation is equal to the space taken up by the object below the fluid's surface.
We adapt our problem-solving strategy to analyze processes in static fluids.
You have a mass of 70.0 kg and a density of 970 kg.
The system object is you.
When in a vacuum, the scale reads 686 N.
The air density should be uniform.
There are other forces included in the diagram.
If the upward direction is positive, the component form ofNewton's second law in component acceleration is.
The expression for the force and the definitions of pressure and density can be used.
The force the scale exerts on you is equal to Y on S.
Air's force can be neglected.
The air pushes up on objects.
The scale will not push upward on you because you are less dense than water.
These strategies will be used to analyze more situations in the chap ter.
It might not be obvious how to arrive at the answer to the question in the next example.
You can help arrive at a solution by following the suggested routine.
You need to determine if a crown is made from pure strategy and see what happens.
First, we have gold or something less valuable.
You can draw force diagrams for the crown hanging in the air and know that it has a density of 19,300 grams of gold.
You find it when hanging in water.
When the crown hangs in to the spring scale, the upward force that a string attached to the air exerts on the crown is 25.0 N, and the downward force that a string attached to the air exerts on the crown is 22.6 N. We don't pay attention to the force of air and water.
We label the givens by drawing a sketch of the situation.
If you could exert force on the crown.
It should be force that the water exerts on the crown combine.
The mass of the crown can be determined from the measurement of the balance of the Earth's gravity.
How can you affect the crown?
When the crown is suspended in air, the 25.0-N string tension force exerts 11000 kg>m3219.8 N>kg2 on the crown.
The crown is not made of law when it hangs in water because it is the upward pure gold.
The gold direction must have been combined with some less expensive metal by the goldsmith.
The density of the fluid affects whether an object floats or sinks.
The object interacts with the fluid and Earth.
The forces are in opposite directions.
What happens to the object when placed in the fluid is determined by the relative magnitudes of the forces and densities.
The object sinks until it reaches the bottom of the container.
The density of the object can be changed to make it float or sink in the same fluid.
This phenomenon and its many practical applications are investigated in this section.
When water fills its compartments, the submarine's density increases.
The density of the submarine is greater than that of the water outside, and it sinks if there isn't enough water in the compartments.
The density of the submarine decreases when the water is pumped out.
The density of the submarine is less than that of the outside water because it has less air in it.
For a long time ships were made of wood.
People decided to build metal ships in the 17th century.
Iron is denser than water and an iron boat would sink.
The first iron ship that did not sink was built in 1787.
Since the middle of the 19th century, large ships have mostly been made of steel, which is denser than water.
The age density of the ships can be reduced by filling part of the ship's volume with air.