Pascal s Principle. Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid.

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1 Pascal s Principle What happens inside a fluid when pressure is exerted on it? Does pressure have a direction? Does it transmit a force to the walls or bottom of a container? Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid.

2 Boyle s Law Boyle discovered that the volume of a gas is inversely proportional to the pressure. Boyle s Law: PV = constant If the pressure increases, the volume decreases. P 1 V 1 = P 2 V 2 At higher altitude, the air density become smaller, i.e. larger volume, the air pressure become smaller. This is the reason of the balloon inflation.

3 Archimedes Principle The average density of an object compared to a fluid determines whether the object will sink or float in that liquid. The upward force that pushes objects back toward the surface in liquids is called the buoyant force. Archimedes Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.

4 consider a block submerged in water, suspended from a string. The pressure of the water pushes on the block from all sides. Because the pressure increases with depth, the pressure at the bottom of the block is greater than at the top. There is a larger force (F = PA) pushing up at the bottom than there is pushing down at the top. The difference between these two forces is the buoyant force. F = mg = density*volume*g pressure = F/A = density*g*volume/a volume/a =height pressure = density*g*height = ρgh Pascal s principle says: ρgh is the same everywhere and in all directions.

5 Ch 9 CP 4 Wooden boat: 3m x 1.5m x 1m that carries five people. Total mass of boat and people equals 1200 kg. a) What is total weight? b) What is buoyant force required to float? c) What volume of water must be displaced to float? d) How much of the boat underwater? a) W = Mg = 1200 kg (9.8 m/s 2 ) W = N b) F net = F b W = 0 F b = N c) F W b = H2O Vg (see Ch 9 E 12) F b / H2O g = 11760N/(1000 kg/m3)(9.8 m/s2) = V = 1.2 m3 d) V = LWh = (3m)(1.5m)h = 1.2 m 3 h = 0.27 m 3m F b 1m 3/2/2011 Physics 214 Fall

6 2A-03 Vacuum Demos Effects of Vacuum on objects made largely of air or air pockets. Why do the balloons burst in the vacuum? Why do the marshmallows get bigger in vacuum? Do the balloons burst in vacuum differently then they normally burst? What will happen when the marshmallows are returned to normal pressure? Can you guess what happens when Shaving Cream is placed in vacuum? AN AIR-POCKET/BALLOON WILL EXPAND WHEN THE PRESSURE IS REDUCED AND IT WILL DEFLATE WHEN THE PRESSURE IS INCREASED. SO BALLOONS WILL EXPAND AS THEY RISE IN THE ATMOSHPERE AND THE EXPANSION OF A PARTIALLY EVACUATED CAN IS USED IN BAROMETERS. 3/2/2011 Physics 214 Fall

7 2B-04 Liquid Pressure Investigating Pressure in different directions within a liquid in equilibrium. What will happen to the reading on the manometer as the sensor is rotated? The increase in pressure ρgh is measured by the difference in height of the liquid in the U tube. g h A B A B AT ANY GIVEN POINT IN A STATIONARY LIQUID, THE PRESSURE IS THE SAME IN ALL DIRECTIONS. 3/2/2011 Physics 214 Fall

8 2B-05 Pressure Forces in Liquids What happens as the submerged cylinder filled with air is filled with water? An open ended cylinder kept shut by liquid pressure There are two forces acting on the plate. It s weight down and PA up. When PA exceeds the weight the cylinder stays intact Air PA In this situation the plate has to now support the weight of the water and when the weight of the water plus plate exceeds PA the cylinder opens Water PA THE LIQUID PRESSURE DEPENDS ONLY ON DEPTH P = ρgh. THE UPWARD FORCE DEPENDS ON THE AREA F = PA 3/2/2011 Physics 214 Fall

9 2B-08 Buoyant Force Compare the Buoyant Force between two cylinders of equal volume and different mass. Which object experiences the greater buoyant force, the heavier one or lighter one? T F B T Scale reads tension in cord: T = Mg F B Mg = F B + T Mg Mg We find F b to be exactly equal for both masses BUOYANT FORCE DOES NOT DEPEND ON THE MATERIAL OF THE OBJECT DISPLACING THE FLUID. THE BUOYANT FORCE DEPENDS ONLY ON THE VOLUME OF FLUID DISPLACED. 3/2/2011 Physics 214 Fall

10 2B-09 Archimedes I What happens to the reading on the upper scale when the block is lowered into the beaker of water? F B T Mg The fluid exerts a buoyant force on the block, which reduces the tension on the cord. The reading on the scale is lowered. T = Mg F B Should anything happen to the reading on the lower scale? Since the fluid exerts a force on the block, the block exerts an EQUAL and OPPOSITE force on the fluid. EVEN THOUGH THE BLOCK DOES NOT TOUCH THE LOWER SCALE, THE FORCE ON THE FLUID DUE TO THE BLOCK IS TRANSMITTED TO THE SCALE. THE REDUCTION IN READING ON THE UPPER SCALE IS EXACTLY EQUAL TO THE INCREASE IN READING ON THE LOWER SCALE. IF THE CONTAINER WAS FULL SO THAT WHEN THE BLOCK WAS INSERTED THE VOLUME THE BLOCK DISPLACED SPILLS OUT OF THE CONTAINER THEN THE BOTTOM SCALE WOULD NOT CHANGE. 3/2/2011 Physics 214 Fall

11 Quiz: Boat displaces 2.5 m 3 of water. Density of water H2O = 1000 kg/m 3. What is the mass of water displaced? What is the buoyant force? A). Mass = 2500 kg, buoyant force = 24500N B). Mass = 250 kg, buoyant force = 2450N C). Mass = 25 kg, buoyant force = 245N D). Mass = 2500 kg, buoyant force = 2450N E). Mass = 2500 kg, buoyant force = 245N Mass of fluid displaced (m FD ) = volume x density of fluid. M FD = V FD H2O = (2.5 m 3 )(1000 kg/m 3 ) = 2500 kg F b = W FD Buoyant force equals weight of fluid displaced. F b = W FD = m FD g = (2500 kg)(9.8 m/s 2 ) = N 11