Welcome back to Physics 211

1. Welcome back to Physics 211 Today’s agenda: Pressure Pressure as a function of depth Forces exerted on and by liquids Buoyancy

2. Reminder • Exam 3 solutions posted. • Homework 10 due Wednesday (Nov. 30) • problems from textbook: 10.22, 10.41, 12.51, 12.53

3. Fluid mechanics • Fluid = substance which is unable to support a shear stress • liquids, gases • Apply Newton’s laws to study statics of fluids...

4. Definition of pressure: where |N| is the magnitude of the (normal) force exerted on one object by another and A is the area of the surface at which the two objects are in contact. also, 1 atm = 1.01 x 105 Pa

5. Pressure in liquids (and gases): • Pressure is not a vector; (does not have a direction). • Normal force (N) is between two “objects” which can be adjacent regions of water in the same container. • Pressure in liquids is associated with a geometric point, not with an object or pair of objects.

6. Demo Pressure probe Vary depth

7. Pressure as a function of depth in a liquid The pressure in a liquid increases linearly with depth from its value P0 at the surface that is open to the atmosphere or from some other reference point. The increase in pressure for every one meter increase in depth is proportional to the density of the liquid.

8. Comparing pressures at different points The difference in pressure between two points in a liquid depends on the difference of their depths below the open surface (i.e., below the points where P = P0.)

9. Rank the pressures at the three points 1. PA < PB = PC 2. PA < PB < PC 3. PA < PC < PB 4. PC < PA < PB

10. Demo Pressure probe two beakers with different diameters

11. Demo Communicating tubes or“Pascal’s Vases”

12. Three containers of different shape but with bases of equal area (or equal “footprints”) are filled with water to the same height. The weight of the water is the greatest in container… 1. A 2. B 3. C 4. The weight of the water is the same in all three containers.

13. Three containers of different shape but with bases of equal area (or equal “footprints”) are filled with water to the same height. The pressure at the bottom of the container is the greatest in container… 1. A 2. B 3. C 4. The pressure at the bottom is the same in all three containers.

14. For differently shaped containers that have the same bottom surface and are filled with the same liquid up to the same height • the weights of the contents are different • the pressures at the bottom are the same

15. Free-body diagrams for liquids

16. Pascal’s principle A change in pressure applied to a fluid at rest is transmitted undiminished to every point of the fluid and to the walls of the container. Pascal’s principle does not state that the pressure is the same at every point in the fluid.

17. Principle of hydraulic lift

18. Mercury barometer

19. Another barometer is placed next to the one discussed previously. The second barometer uses a wider glass tube but is otherwise the same. The top of the column in the second barometer is the height in the narrow barometer. 1. higher than 2. lower than 3. at the same height as 4. “Don’t know.”

20. Mercury has a density that is about 14 times greater than that of water. If you were to build a barometer that uses water instead of mercury, how would the height of the column of water needed compare to that of the mercury? 1. higher than 2. lower than 3. equal to 4. Can’t tell.

21. How big is atmospheric pressure? Two disks that make a tight seal contain a small space that is initially filled with air. The space is then evacuated, so that atmospheric pressure holds the two disks together. 1. A one-kilogram mass 2. Two physics text books 3. A three-gallon bucket of water 4. Two (physics) students Atmospheric pressure is about 15 psi (pounds per square inch), or 100 000 N/m2. The radius of the disks is about 6 inches, or 15 cm. If the evacuated disks are hung from the ceiling, what objects can they support?

22. A glass beaker is filled with water and placed on a balance. A person holds a finger into the water. The reading on the balance will 1. go up 2. go down 3. stay the same 4. Can’t tell.

23. Archimedes’ principle The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object. The buoyant force is the total upward force exerted on an object by the surrounding fluid.

24. Demo: Submerged object on scale; Weighing displaced water

25. A cubical block made of a certain type of plastic has a density of 0.75 g/cm3. The density of water is 1.0 g/cm3. If the block is allowed to float in water, what fraction of the volume of the block would be below the water level? 1. one quarter 2. one half 3. three quarters 4. some other fraction

26. The density of aluminum is about 2.7 times greater than that of water, so a block of aluminum will sink when placed in water. How is it possible to build a boat using only aluminum?

27. How do boats float? • If the density of an object is less than that of water, an object floats in water. • If the density of an object is greater than that of water, an object sinks in water. • …but boats can be made of metal…