Physics - OAK PARK USD



AP Physics 12: Fluids Name __________________________

A. Static Fluids

1. states of matter

a. solid

1. shape and size unchanged by pressure

2. useful properties are mass and force

b. fluid

1. flows under pressure

2. two phases

a. liquid—incompressible

b. gas—compressible

3. useful properties are density and pressure

a. density, ρ = m/V (kg/m3)

b. pressure, P = F/A (Pa—Pascal)

c. plasma—ionized atoms at high temperature

2. Pascal's principle

a. pressure applied to a confined fluid is equal to the pressure throughout the fluid

b. Pin = Pout ∴ Fin/Ain = Fout/Aout

c. Win = Wout ∴ Findin = Foutdout

3. pressure in a liquid, P = ρgh

|Steps |Algebra |

|start with |P = Fg/A |

|substitute mg for Fg |P = mg/A |

|substitute ρV for m |P = ρVg/A |

|substitute Ah for V |P = ρAhg/A |

|simplify |P = ρgh |

a. equal in all directions and ⊥ to object surface

b. not used with gases because density isn't constant

c. absolute pressure

1. absolute = fluid pressure + air pressure

2. P = ρgh + Po (Po = 1 x 105 Pa = 100 kPa)

4. Archimedes' principle, Fb = ρfVog

a. the buoyant force (weight loss when an object is submerged)

1. ρf = fluid density

2. Vo = object's submerged volume

|Steps |Algebra |

|start with |Fb = F2 – F1 = (P2 – P1)A |

|substitute ρgh for P |Fb = (ρgh2 – ρgh1)A |

|regroup |Fb = ρg(h2 – h1)A |

|substitute h for h2 – h1 |Fb = ρghA |

|substitute V for hA |Fb = ρfVog |

b. Fb = "weight of the displaced fluid"

Fb = (ρfVo)g = ρf(mo/ρo)g = mog(ρf/ρo)

5. specific gravity, s.g. = ρobject/ρfluid

a. because of buoyancy:

ρobject/ρfluid = mair/(mair – mfluid)

b. used to determine density: ρoject = (s.g.)ρfluid

c. ρH2O = 1 g/cm3 = 1 kg/L = 1000 kg/m3

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B. Fluid flow

1. streamline—fluid layers slide by each other

2. turbulent—eddy currents (increase viscosity)

3. volume flow rate

[pic]

a. ΔV/t = AΔl/Δt = Av (m3/s)

b. assume constant volume when water moves through closed system, then V/t = A1v1 = A2v2

4. Bernoulli's equation, P + ρgh + ½ρv2 = C

a. based on conservation of energy

|Steps |Algebra |

|start with |WP = FPd |

|substitute PA for Fp |Wp = PAd |

|Δl for d |Wp = PAΔl |

|substitute V for AΔl |Wp = PV |

|start with |Ug = mgh |

|substitute ρV for m |Ug = ρVgh |

|start with |K = ½mv2 |

|substitute ρV for m |K = ½ρVv2 |

|total energy is constant |PV + ρVgh + ½ρVv2 = constant |

|divide both sides by V |P + ρgh + ½ρv2 = C |

b. three types of problems

1. plumbing system:

[pic]

P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22

2. leaking tank (P1 = P2, y2 = 0 and v1 = 0):

ρgy1 = ½ρv22 ∴ v22 = 2gy1

(same for an object that falls y1 meters!)

3. lift caused by moving air (y1 = y2):

P1 – P2 = ½ρv22 - ½ρv22

(F1 – F2)/A = ½ρ(v22 – v12)

Flift = ½ρ(vtop2 – vbottom2)A

C. Kinetic theory—Gases

1. temperature scales

a. 2 relative scales (oF, oC)

b. 1 absolute scale (K) = oC + 273

2. molecular kinetic energy

a. K = 3/2RT = 3/2kBT

b. vrms = (3RT/M)½ = (3kBT/μ)½

R = 8.31 J/mol•K

kB = 1.38 x 10-23 J/K (kB = R/6.02 x1023)

M = mass per mole in kg

μ = mass per molecule (μ = M/6.02 x 1023)

3. ideal gas

a. no cohesive force or appreciable volume

b. PV = nRT = NkBT

P = pressure in Pa (100 kPa = 1 atm)

V = volume in m3 (1 m3 = 1000 L)

n = moles of molecules

N = number of molecules (N = n x 6.02 x 1023)

T = temperature in K

c. sample of gas: P1V1/T1 = P2V2/T2

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Experiments

1. Specific Gravity Lab: mass a weight in air and water and calculate the specific gravity and density.

a. Collect the following data.

|mair (g) |mH2O (g) |

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b. Calculate the following from the data.

| |Formula |Calculation |

|s.g. |s.g. = mair/(mair – mH2O) | |

|ρ |ρ = s.g.(ρH2O) | |

2. Bernoulli Lab: mark the spot where the splash from the leak hits the bottom of the sink and calculate the velocity using kinematics and Bernoulli's equation.

a. Collect the following data.

|Horizontal Distance (dx) |Vertical Distance (dy) |Height of Water in |

| | |bottle (h) |

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b. Calculate the following from the data.

| |Formula |Calculation |

|kinematics |

|t |dy = ½gt2 | |

|vx |vx = dx/t | |

|Bernoulli's equation |

|vx |gy1 = ½v22 | |

c. What is the percent difference between the vx values?

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3. Gas Law Constant Lab: measure the temperature, pressure and volume of the gas generated when a known mass of magnesium reacts with HCl, calculate R and compare the value to the known constant.

a. Collect the following data.

|mMg |V (mL) |T |P (Pa) |

|(g) | |(oC) | |

| |Vo |Vf | |Plab |PH2O |

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b. Calculate the following from the data.

| |Formula |Calculation |

|n |n = mMg/24.3 | |

|Vm3 |Vm3 = (Vf – Vo)10-6 | |

|TK |TK = ToC + 273 | |

|PPa |PPa = Plab – PH2O | |

|R |R = PPaVm3/nTK | |

c. What is the percent difference between the calculate R and 8.31?

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Practice Problems

A. Static Fluid

Questions 1-22 Briefly explain your answer.

1. If one material has a higher density than another, does this mean that the molecules of the first material must be more massive than those of the second?

(A) yes (B) no

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2. Consider what happens when you push both a pin and a blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?

(A) the pressure on your skin

(B) the net applied force on your skin

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3. You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?

(A) stand absolutely still and don't move a muscle

(B) slide your feet (with lifting them) to move towards shore

(C) try to leap in one bound to the bank of the lake

(D) lie down flat on the ice and crawl toward shore

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4. While swimming near the bottom of a swimming pool, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter?

(A) decreases (B) same (C) increases

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5. Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each. Which container has the greatest total force acting on the base?

(A) (B) (C) (D) tie

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6. When a hole is made in the side of a water bottle, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will

(A) diminish (B) stop

(C) go in a straight line (D) curve upward

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7. When you drink liquid through a straw, which below is primarily responsible for this to work?

(A) water pressure (B) gravity

(C) inertia (D) atmospheric pressure

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8. You put a straw into a glass of water, place your finger over the top so no air can get in our out, and then lift the straw from the liquid. You find that the straw retains some liquid. How does the air pressure P inside the straw compare to atmospheric pressure PA?

(A) P > PA (B) P = PA (C) P < PA

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9. In a mercury barometer at room pressure, the height of the mercury column in a glass tube is 760 mm. If another mercury barometer is used that has a larger diameter tube, how high will the column of mercury be in this case?

(A) greater (B) same (C) less

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10. Thermometers often use mercury or alcohol in a thin glass tube, but barometers never use alcohol. Why?

(A) mercury is less flammable

(B) mercury's color is easier to see

(C) mercury is less toxic than alcohol

(D) mercury is more dense than alcohol

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11. Imagine holding two identical bricks in place under water. Brick A is just beneath the surface of the water, while brick B is held about two feet down. The force needed to hold brick B in place is

(A) greater (B) same (C) less

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Questions 12-13 A beaker filled completely with water is placed on a scale and weighs 29 N. A block is carefully placed in the beaker at the same time water overflows out of the beaker.

12. The block is made of wood and floats in the water. When placed on the scale the beaker and floating block will weigh

(A) < 29 N (B) = 29 N (C) > 29 N

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13. The block is made of aluminum and sinks. When placed on the scale the beaker and sunk block will weigh

(A) < 29 N (B) = 29 N (C) > 29 N

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14. A raft carrying a large tank is floating in a pool. The tank is then thrown overboard and sinks. What happens to the water level in the pool with respect to the pool side?

(A) rise (B) same (C) drop

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Questions 15-19 Object A floats in pail of water with ¾ of its volume submerged.

15. What is the ratio of the density of object A to that of water?

(A) ¼ (B) ¾ (C) 4/3 (D) 4

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16. Object A is now placed in oil with a density half that of water. What fraction of object A is above the fluid line?

(A) 0 (B) ¼ (C) ½ (D) ¾

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17. Water is added to the pail to a level above the top of object A, the object will

(A) move up slightly (B) stay at the same place

(C) move down slightly (D) float to the top

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18. Oil is added to the pail to a level above the top of object A, the object will

(A) move up slightly (B) stay at the same place

(C) move down slightly (D) float to the top

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19. Object A, in a pail of water, is observed on the moon. What fraction of its volume is submerged?

(A) < ¾ (B) = ¾ (C) > ¾

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Questions 20-21 A helium balloon is placed in an inverted air-filled jar, which rests on a table. The balloon floats to the top of the jar.

20. If the air is replaced with helium, where will the balloon be?

(A) at the top (B) in the middle (C) at the bottom

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21. If the jar if lifted off the table, but the helium remains in the jar, where will the balloon end up?

(A) top (B) middle (C) bottom (D) ground

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22. A small rubber balloon is filled with water and just enough trapped air so that it floats. The balloon is placed in a large glass cylinder also filled with water and is sealed with a flexible cap. When you push down on the flexible cap, the balloon

(A) sinks down (B) stays put (C) rises up

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23. How does a liquid differ from a solid or gas?

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24. What is the mass of a piece of gold (ρ = 1.93 x 104 kg/m3) that has a volume of 22 cm3?

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25. Why is the formula P = ρgh useful for liquids but not gases?

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26. At what depth in water is the added pressure equal to 1 atm (1.0 x 105 Pa)?

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27. What is the absolute air pressure, in Pa, in a tire that has a gauge pressure reading of 30 lbs/in2? (1 atm = 14.7 lbs/in2)

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28. a. 1,000 N of force is used to raise a 10,000 N car. What is the ratio of the cross-sectional area of the lift piston to the force piston (A2/A1)?

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b. How far does the force piston move to lift the car 2 m?

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29. How much mass (M) must be added to a diver (85-kg, 0.090-m3) to allow him to float under water?

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30. What percentage of the volume of a floating iceberg is above sea water? (ρice = 920 kg/m3, ρsea water = 1030 kg/m3)

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31. What volume of helium is needed to lift a load of 800 kg? (ρair = 1.29 kg/m3, ρHe = 0.18 kg/m3)

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32. What is the specific gravity of a piece of metal that has a mass of 125 g in air and 78.7 g in water?

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34. A crown's "weight" in air is 14.7 kg. What is its "weight" under water if it is made of

|gold (s.g. = 19.3) | |

|lead (s.g. = 11.3) | |

35. The weight of a 300 N piston compresses gas in a tank.

a. What is the pressure on the gas generated by the piston, which has a radius of 0.050 m?

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b. What is the total pressure in the tank if the atmospheric pressure is 1 x 105 Pa?

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36. What is the water pressure in a pipe that is 45 m below the water level in the city's water storage tank?

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37. In a hydraulic system, cylinder A with a 100 cm2 cross section is connected by fluid to cylinder B with a 10 cm2 cross section. 2000 N of force push on the cylinder A's piston. Determine

a. the force generated on cylinder B's piston?

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b. the distance piston B moves if piston A moves 5 cm.

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38. What is the density of a log when 65% of the volume is submerged in water (ρ = 1000 kg/m3)?

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39. An aluminum (ρ = 2700 kg/m3) object has a mass of 27 kg. The object is attached to a string and immersed in a tank of water. Determine

a. the volume of the object.

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b. the tension in the string.

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40. What volume of helium will support a load of 1000 kg?

(ρair = 1.29 kg/m3, ρHe = 0.18 kg/m3)

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B. Fluid Flow

Questions 41-44 Briefly explain your answer.

41. Water flows through a 1-cm diameter pipe connected to a ½-cm diameter pipe. Compared to the speed of the water in the 1-cm pipe, the speed in the ½-cm pipe is

(A) ¼ (B) ½ (C) 2 (D) 4

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42. A blood platelet drifts along with the flow of blood through an artery that is partially blocked. As the platelet moves from the wide region into the narrow region, the blood pressure

(A) increases (B) same (C) decreases

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43. A person's blood pressure is generally measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person's leg instead?

(A) higher (B) same (C) lower (D)

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44. Smoke is drawn up a chimney on a windy day. The draw on a windy day compared to a calm day is

(A) faster (B) same (C) slower

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45. Consider the diagram in your notes (B3).

a. How many times bigger is A1 compared to A2 if the diameter, d1, is two times the diameter, d2?

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b. How many times faster is v2 compared to v1?

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46. Consider the water pipe in your notes (B4). What is P2 when P1 = 3 x 105 Pa, v1 = 2 m/s, v2 = 5 m/s, y1 = 0 m, y2 = 4 m?

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47. A water leaks out of a hole 5 m below the surface in a tank.

a. What is the velocity of water that leaks out of the tank?

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b. What is the radius of the whole in the water tank if the volume rate flow out of the leak is 3 x 10-3 m3/s?

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48. a. Air flows past the upper surface of an airplane wing at 250 m/s and past the lower surface of the wing at 200 m/s. The density of air is 1.0 kg/m3 and the area of the wing is 20 m2. What is the net lift on the wing?

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b. Racing cars have a rear spoiler, which is able to keep the car from lifting up at high speeds. Describe the design of the spoiler.

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49. When a truck passes you on the left, your car initially is pushed right then pulled left. Why?

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50. Water flows at a rate of 0.5 m/s through a 4-cm diameter pipe on the first floor of a house.

a. What is the cross-sectional area of the pipe?

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b. What is the volume flow rate in the 4-cm pipe?

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c. What is the velocity of the water in a 2.6-cm diameter pipe on the second floor of the house.

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d, The pressure in the 4-cm pipe is 3 atm. What is the pressure in the 2.6 cm section that is elevated 3 m?

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51. Air (ρ = 1 kg/m3) passes over a roof at 60 m/s. Determine

a. the pressure difference between the attic air and the air passing over the roof.

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b. the upward force exerted on the roof (area = 300 m2).

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C. Kinetic Theory—Gases

Questions 52-60 Briefly explain your answer.

52. Which is the largest unit, 1oC, 1 K or 1oF?

(A) 1oC (B) 1 K (C) 1oF (D) 1oC and 1 K

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53. It turns out -40oC is the same temperature as -40oC. Is there a temperature where the Kelvin and Celsius scales agree?

(A) yes 0oC (B) yes, -273oC

(C) yes, 0 K (D) no

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54. Which has more molecules, one mole of N2 or one mole of O2?

(A) N2 (B) O2 (C) tie

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55. Which weighs more, one mole of N2 or one mole of O2?

(A) N2 (B) O2 (C) tie

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56. Two identical cylinders at the same temperature contain the same gas. If A contains three times as much gas as B, which cylinder has the higher pressure?

(A) A (B) B (C) tie

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57. Two identical cylinders at the same pressure contain the same gas. If A contains three times as much gas as B, which cylinder has the higher temperature?

(A) A (B) B (C) tie

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58. Two cylinders at the same temperature contain the same gas. If A has twice the volume and half the number of moles as B, how does the pressure of A compare with the pressure of B?

(A) PA = ¼PB (B) PA = ½PB (C) PA = 2PB

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59. A partially filled, sealed plastic water bottle sits out in the sun, heating the air inside. What happens to the bottle?

(A) it expands (B) nothing (C) it shrinks

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60. What happens to the volume of a balloon if you put it in the refrigerator?

(A) it expands (B) nothing (C) it shrinks

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61. In the formulas K = 3/2RT and PV = nRT

a. The value of R is (__________).

b. Why must you use the Kelvin temperature scale for these calculations?

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c. What is the Kelvin temperature for 25oC?

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62. Consider oxygen gas (O2) at 22oC.

a. What is the temperature in Kelvin?

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b. What is the mass of one mole in kg?

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c. What is the mass of one molecule in kg?

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d. What is the average kinetic energy of a molecule?

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e. What is the kinetic energy of a mole?

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f. What is the average speed?

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63. Consider one mole of helium gas at room temperature (22oC) and pressure (1.0 x 105 Pa).

a. What is the volume (in m3)?

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b. What is the volume (in m3) of one helium atom with an atomic radius is 5 x 10-11 m?

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c. What is the volume (in m3) of one mole of helium atoms?

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d. What percentage of the total volume (part a) is taken up by the helium atoms (part c)?

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e. What is the volume when the pressure is increased to 2.0 x 105 Pa and the temperature is raised to 44oC?

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64. A 0.01 m3 vessel contains 0.02 kg of an ideal gas at 50oC and a pressure of 3 x 105 Pa. Determine the

a. kinetic energy per molecule

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b. moles of gas are in the vessel (R = 8.31).

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c. molar mass of the gas.

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Practice Multiple Choice

Briefly explain why the answer is correct in the space provided.

Questions 1-2 The spring scale reads 0.45 kg when the rock is suspended in air and 0.36 kg when the rock is fully submerged in water.

1. The buoyant force that the fluid exerts on the object is

(A) 1.3 N (B) 0.9 N

(C) 0.75 N (D) 0.33 N

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2. The density (in kg/m3) of the rock is

(A) 200 (B) 800 (C) 1,250 (D) 5,000

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3. An object weighs 15,000 N. When it is submerged in a liquid that has a density of 1500 kg/m3, its apparent weight is 7500 N. What is the density (in kg/m3) of the object?

(A) 1,500 (B) 2,000 (C) 3,000 (D) 6,000

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4. Two dams are alike in every respect (i.e. height, width and thickness of dam) except the length of the lake behind the dam. The first lake extends 1 km away from its dam; the second 5 km. The force exerted on the first dam is:

(A) equal to the force on the second dam

(B) greater than the force on the second dam

(C) less than the force on the second dam

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5. Each beaker is filled to the same depth with the same liquid and the area of the flat bottom is the same for each.

[pic]

Which ranks the beakers from greatest to least force exerted by the liquid on the flat bottom?

(A) I > III > II > IV (B) I > IV > III > II

(C) II > III > IV > I (D) force on each is the same

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6. What is the force exerted by a wind, which generates a pressure difference of 3 x 104 Pa, on the 3 m by 20 m side of a house trailer?

(A) 0.5 N (B) 500 N (C) 1800 N (D) 1.8 x 106 N

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7. What is the absolute pressure (in Pa) 3 m down in a swimming pool, when atmospheric pressure is 1 x 105 Pa?

(A) 3 x 104 (B) 7 x 104 (C) 1.1 x 105 (D) 1.3 x 105

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8. A rock is thrown into a swimming pool filled with water that is at a uniform temperature. While the rock sinks, the buoyant force

(A) is zero (B) increases

(C) decreases (D) is constant

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Questions 9-11 Two pistons are connected in a hydraulic lift. The diameter of the large piston is ten times that of the small.

9. How many times larger is the cross-sectional area of the larger piston compared to the smaller?

(A) 10 (B) 20 (C) 50 (D) 100

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10. A 500 N force is applied to the smaller piston. What load can be lifted by the larger piston?

(A) 5,000 N (B) 50,000 N

(C) 500,000 N (D) 5,000,000 N

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11. If the load is lifted 2 m, how far is the smaller piston moved?

(A) 0.2 m (B) 2 m (C) 20 m (D) 200 m

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Questions 12-13 A 1500-kg stone of volume 0.5 m3 is lowered to the bottom of a lake on the end of a rope.

12. What buoyant force acts on the stone?

(A) 5 N (B) 50 N (C) 500 N (D) 5,000 N

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13. What is the tension when the stone is submerged?

(A) 3,500 N (B) 5,000 N

(C) 10,000 N (D) 15,000 N

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14. Water is flowing through a pipe with a cross-sectional area of 30 cm2 at a velocity of 4 m/s. What is the velocity of the water in a section of the pipe where the cross-sectional area is 50 cm2?

(A) 1.2 m/s (B) 3.6 m/s (C) 2.4 m/s (D) 4.8 m/s

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15. Water is pumped into one end of a long pipe at a rate of 50 liters per minute. The water is emerges from the other end of the pipe at a rate of 20 liters per minute. The reason for this decrease in volume flow rate is

(A) the water is being pumped uphill

(B) the pipe diameter is not the same at the two ends

(C) there is friction in the pipe

(D) there is a leak in the pipe

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16. An ideal gas confined in a box initially has pressure P. If the absolute temperature of the gas is doubled and the volume of the box is quadrupled, the pressure is

(A) ⅛ P (B) ¼ P (C) ½ P (D) P

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17. The absolute temperature of a sample of monatomic ideal gas is doubled at constant volume. What effect, if any, does this have on the pressure and density of the sample of gas?

Pressure Density

(A) Remains the same Remains the same

(B) Remains the same Doubles

(C) Doubles Remains the same

(D) Doubles Is 4 times greater

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Questions 18-19 An ideal gas molecule at absolute temperature, T, has kinetic energy, K, and velocity, v.

18. What is the kinetic energy at 4T?

(A) ¼K (B) ½K (C) 2K (D) 4K

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19. What is the velocity at 4T?

(A) ¼v (B) ½v (C) 2v (D) 4v

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20. A pitched baseball, which rotates counterclockwise about a vertical axis as seen from above, will curve:

(A) to the pitcher's right (B) to the pitcher's left

(C) upward (D) downward

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21. If wind blows at 30 m/s over your house, the net force on the roof (area = 400 m2) is

(A) 100,000 N (B) 150,000 N

(C) 180,000 N (D) 200,000 N

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22. Water flows out of a hole at 4 m/s. What is the height of the water above the hole inside the bucket?

(A) 0.8 m (B) 1.25 m (C) 2.5 m (D) 1.5 m

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23. A T-shaped tube with a constriction is inserted in a vessel containing a liquid, as shown.

[pic]

What happens if air is blown through the tube from the left?

(A) The liquid level in the tube rises up into the tube.

(B) The liquid level in the tube falls below the level of the surrounding liquid.

(C) The liquid level in the tube remains where it is.

(D) The air bubbles out at the bottom of the tube.

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24. The area of an airplane wing is 100 m2. What is the lift force on the wing when the speed of air below and above the wing 200 m/s and 250 m/s respectively?

(A) 2,500 N (B) 11,250 N

(C) 4.2 x l05 N (D) 1.125 x l06 N

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25. At best, a person can reduce the pressure in the lungs about 1 x 104 Pa below atmospheric pressure. How high can a person suck water up a straw?

(A) 0.1 m (B) 0.3 m (C) 1.0 m (D) 3.0 m

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26. If a crown of density 14,000 kg/m3 weights 140 N in air, the force needed to support it when submerged in water is:

(A) 100 N (B) 130 N (C) 140 N (D) 150 N

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27. A rowboat has a volume of 1.5 m3 and a mass of 40 kg. How many people, of mass 70 kg each, can the boat support without sinking?

(A) 15 (B) 19 (C) 20 (D) 21

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28. An object floats in water and displaces 150 cm3 of water. The same object floats in oil, displacing 375 cm3 of that oil. The density (in kg/m3) of the oil is:

(A) 1,500 (B) 1,100 (C) 600 (D) 400

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29. Water is flowing through a horizontal pipe with a constriction. At one end of the pipe we have A1 = 10 cm2, v1 = 4 m/s, and P1 = 500 kPa. In the constriction of the pipe we have

A2 = 2 cm2. The pressure (in kPa) in the constriction is:

(A) 120 (B) 308 (C) 480 (D) 690

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30. A sample of an ideal gas is in a tank of constant volume. The sample absorbs heat energy so that its temperature changes from 300 K to 600 K. If v1 is the average speed of the gas molecules before the absorption of heat and v2 is their average speed after the absorption of heat, what is the ratio v2/v1?

(A) ½ (B) 1 (C) √2 (D) 2

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Practice Free Response

1. A large rectangular raft (density 650 kg/m3) is floating on a lake. The surface area of the top of the raft is 8.2 m2 and its volume is 1.80 m3. The density of water is 1000 kg/m3.

A = 8.2 m2

h

water line

a. Calculate the height h of the portion of the raft that is above the surrounding water.

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b. Calculate the maximum number of 75-kg people that can be on the raft without the top of the raft sinking.

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2. The large container is filled with water (ρ = 1000 kg/m3). A small hole of area 2.5 x 10-6 m2 is opened in the side of the container a distance h below the water surface, which allows a stream of water to flow through the hole and into a beaker. At the same time, water is also added to the container so that h remains constant. The amount of water collected in the beaker in 2.0 minutes is 7.2 x 10-4 m3.

a. Calculate the volume rate of flow of water from the hole in m3/s.

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b. Calculate the speed of the water as it exits from the hole.

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c. Calculate the height h of water needed above the hole to cause the speed you determined in part (b).

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d. Calculate the distance, d, from the small hole to the table top, which would produce a value of x = 0.50 m.

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e. Suppose that there is now less water in the container so that the height h is reduced to h/2. Where will the water hit the tabletop?

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3. Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown.

[pic]

a. Must all three strings have the same tension?

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The tension in the string supporting A (V = 1.0 x 10-5 m3 and ρ = 1300 kg/m3) is 0.0098 N.

b. Calculate the buoyant force on object A.

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c. Calculate the density of the liquid.

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d. Some of the liquid is now drained until only half of A is submerged. Would the tension increase, decrease, or remain the same? Justify your answer.

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