| Assignment #8 |
Sections 13-1 & 13-2 |
Due: Tue. Jan. 29 |
8. The same volume of two different liquids is poured into two identical beakers that each weigh 4.70 N and have a bottom radius of 9.00 cm. In to one beaker 44.0 cm
3 {1.50 liters} of Ethanol (
rE = 790 kg/m
3) is poured, and in to the other beaker a 44.0 cm
3 {1.50 liters} of Glycerol (
rG = 1.26 g/cm
3) is added.
(A) If placed on separate scales, which beaker would weigh the most ? State the values.
(B) In which beaker is the pressure on the bottom (due to the liquid it contains) the greatest? State the values.
(C) In which beaker will the height of the fluid level be the highest ? State the height of both liquids.
(D) How many grams of Ethanol would have to be added to the beaker containing Ethanol in order that the pressure on the bottom of both beakers would be the same ?
BONUS:
(E) If the same mass of Glycerol and Ethanol are mixed together, what is the density of the resulting mixture assuming that the total volume of the mixture is the same the sum of the volumes of the two liquids before they are mixed ?
| {ANS:} #8 |
(A)
Glycerol = 23.2 N, Ethanol = 16.3 N |
(B)
Glycerol = 728 Pa, Ethanol = 456 Pa |
(C)
? |
(D)
705 g |
(E)
971 kg/m 3 |
| Assignment #9 |
Sections 13-2 & 13-3 |
Due: Wed. Jan. 30 |
9. A solid copper (
rCu = 8,960 kg/m
3) cylinder has length of 26.0 cm {17.5 cm} and a radius of 14.8 cm {42.2 mm}.
(A) What pressure will the cylinder exert on a surface if it is stood on end ?
(B) The copper is stood on end in a container of water. The water is 11.0 cm {20.0 cm} deep, what buoyant force will the water exert on the copper cylinder ?
(C) What force would it take to just lift the cylinder off the bottom of the container if the water is 11.0 cm {20.0 cm} deep ?
(D) What pressure does the copper cylinder exert on the bottom of the container if the water is 11.0 cm {20.0 cm} deep ?
BONUS:
(E) If the copper cylinder is placed in a container of mercury ( rHg =13.6 g/cm 3) and water, to what depth will the cylinder float in the mercury if cylinder's top is completely submerged in the water ?
| {ANS:} #9 |
(A)
15.4 kPa |
(B)
9.59 N |
(C)
76.4 N |
(D)
13.7 kPa |
(E)
d = 11.1 cm |
| Assignment #10 |
Section 13-4 |
Due: Fri. Feb. 1 |
10. Water escapes from the end of a garden hose at a speed of 16.3 m/s {12.5 m/s}. The area of the nozzle is 25.0 mm 2 {23.0 mm 2} and the inside radius of the hose is 5.30 mm {.750 cm}. Assume frictionless fluid flow and that the pressure of the escaping water is equal to atmosphere, 101 kPa.
(A) How long will it take to fill a 12.0 liter jug if none of the water is spilled ?
(B) How long will it take for 5.30 kg of water to escape out the end of the hose ?
(C) What is the speed of the water inside the hose ?
(D) What is the volume flow rate inside the hose in liter/min ?
BONUS:
(E) What is the pressure of the water in the hose just before it exit the nozzle ?
| {ANS:} #10 |
(A)
41.7 s |
(B)
18.4 s |
(C)
1.63 m/s |
(D)
17.3 l/min |
(E)
178 kPa |
| Assignment #11 |
Section 13-4 |
Due: Mon. Feb. 4 |
11. A cylindrical tank with a radius of 3.80 m is filled with gasoline (
r = 730 kg/m
3) to a depth of 9.60 m {8.50 m}. The pressure of the air in the tank above the gasoline is 310 kPa. There is a cavity on the side of the tank 2.70 m above the bottom of the tank with a circular opening that has a radius of 11.0 cm. A pipe with a radius of 4.10 cm is attached to the side of the cavity and drops 1.50 m {2.90 m} below the bottom of the tank where before is rises to the level of the bottom of the tank where it exits to the atmosphere, 101 kPa. Assume frictionless flow.
(A) Neglecting the motion of the surface of the gasoline in the tank, calculate the initial velocity which the gasoline flows through and out the end of the pipe.
(B) Using the answer you found in (A), determine the rate at which the surface of the gasoline is dropping initially. Does this justify neglecting the surface speed in part (A) ?
(C) What is the pressure in the pipe at its lowest point, 1.50 m {2.90 m} below the bottom of the tank ?
(D) What is the pressure in the gasoline flowing through the opening of the cavity that is 2.70 m above the bottom of the tank ?
BONUS:
(E) Not neglecting the speed of the surface of the gasoline, calculate the velocity at which the gasoline exits. Since this is the same answer as you found in (A) to 3 sig. figs. calculate the change between the two answers.
| {ANS:} #11 |
(A)
27.2 m/s |
(B)
3.17 mm/s |
(C)
122 kPa |
(D)
346 kPa |
(E)
Dv = 1.87x10-7 m/s |
| Assignment #12 |
Section 18-4 |
Due: Tue. Feb. 5 |
12-1. A container of nitrogen has a temperature of 15.0
oC {21.4
oC}, a pressure of 3.75x10
5 Pa {1.50 atm}, and a volume of 451 liters initially.
(A) Find the pressure of the nitrogen when the temperature is increased to 45.0 oC and the volume remains fixed.
(B) Find the pressure of the nitrogen when the volume is compressed to a volume of 275 liters and the nitrogen's temperature returns to its original value of 15.0 oC {21.4 oC}.
(C) Find the pressure of the nitrogen when the volume is expanded to 722 liters and the temperature is lowered to -10.5 oC.
12-2. A large volume of oxygen O 2 contains 182 grams {44.7 kg} at a pressure of 1.50x10 5 Pa {3.66x10 5 Pa} and a temperature of 318 K.
(A) How many molecules of oxygen are there in the volume ?
(B) What is the volume of oxygen in this problem ?
| {ANS:} #12 |
12-1.
(A) 1.62 atm
(B) 2.46 atm
(C) .837 atm
|
12-2.
(A) 8.41x1026 molecules
(B) 10.1 m 3 |
| Assignment #13 |
Section 18-5 |
Due: Wed. Feb. 6 |
13. A 3.60 m
3 {6.90 m
3} tank contains 5.70 mg {4.70 mg} of the rigid diatomic molecule N
2 (diameter = .180 nm, M = 28.0 gm/mole) at a temperature of 88.0
oC { 52.0
oC}.
(A) How many molecules of nitrogen are there in the tank and what is the mass of each molecule?
(B) What is the average kinetic energy of a N 2 molecule ?
(C) What is the internal energy of the nitrogen in the tank ?
(D) What is the root-mean-square speed, the average speed, and the most probable speed of a N 2 molecule ?
(E) What is the mean free path distance a nitrogen molecule travels between collisions ? Using the average speed, determine the average number of collisions per second in the nitrogen gas under these conditions.
BONUS:
(F) If 2.60 mg of Nitrogen at the same temperature are injected into the tank,and the gas is allowed to return to its original temperature, which of the above quantities you calculated will change ? If they change, state the direction of change.
| {ANS:} #13 |
(A)
1.01x10 20 molecules, 4.65x10 -26 kg |
(B)
6.73x10 -21 J |
(C)
1.13 J |
(D)
v rms = 538 m/s, v av = 496 m/s, v prob = 439 m/s |
(E)
47.4 cm, 1050 collisions/s |
(F)
? |
