Final Exam Spring 2000

Do any FIVE of the following SIX questions. X-OUT the question you OMIT.

1. A 160 kg satellite orbits the Earth (M E = 5.974x10 24kg, R E = 6378 km) with a total mechanical energy of –3.75 GJ and eccentricity of .220.

(A) What is the semimajor axis of the satellite’s orbit about the Earth?
Ans:{8500 km}
(B) How close does this satellite come to the Earth’s surface?
Ans:{255 km}
(C) What is the gravitational force that this satellite exerts on the Earth when it is furthest from the Earth?
Ans:{596 N}
2. A 7.20 kg block, setting at rest on a frictionless horizontal surface, is attached to an unstretched, horizontal spring with a spring constant of 5.90 N/cm. The block is set into motion by pushing it to the to right using 24.0 J of work and then releasing the block.
(A) How many times does the block oscillate in 1.60 minutes?
Ans:{138 times}
(B) What is the equation of motion of the position of the block relative starting location as a function of time, x(t)?
Ans:{x(t) = 28.5 cm sin(9.05 rad/s t+_/2) or x(t) = 28.5 cm cos(9.05 rad/s t)}
(C) How fast is the block moving when it is 4.6 cm from its starting position?
Ans:{2.55 m/s}
3. A tank with cross-sectional area of 2.70 m 2 and a height of 4.50 m, is filled to a depth of 4.00 m with gasoline whose density is 710 kg/m 3. There are 150 moles of air in the tank above the gasoline at the same temperature as the gasoline, 23.0 oC. A small hole with a cross-sectional area of 52.0 mm 2 is located 3.20 m above the bottom of the tank.
(A) What is the pressure of the air in the tank?
Ans:{274 kPa}
(B) What is the pressure on the bottom of the tank if no gasoline is escaping from the tank?
Ans:{301 kPa}
(C) How many liters of gasoline are escaping from hole each second?
Ans:{1.16l/s}
4. A solid, 3.20 kg cube of Aluminum has a density of 2700 kg/m 3 at 20.0 oC. The cube is heated until it has absorbed 330 kcal of heat energy. Aluminum has a coefficient of linear expansion a = 24.0x10 -6/oC and heat capacity C = 910 J/kg/ oC.
(A) What is the final volume of the cube in liters?
Ans:{1.23 l}
(B) How much work does the cube do against the surrounding air as it expands if the pressure of the air is 101 kPa?
Ans:{4.08 J}
(C) What is the change in entropy of the cube?
Ans:{2800 J/K}

5. An ideal monatomic gas ( cp = 5/2 R) containing 4.90x10 21 molecules is heated from 30.0 oC to 420 oC. If the initial volume of the gas is 37.0 liters and the gas is heated at a constant pressure:

(A) How much work is done on or by the gas during this process?
Ans:{26.4 J}
(B) What is the change gas’s internal energy?
Ans:{39.6 J}
(C) What is the change in entropy of the gas during this process?
Ans:{.140 J/K}
6. A power plant operating from a heat reservoir at 120 oC, produces 890 MW of power. The exhaust heat is dumped into a stream with a flow rate of 8.50x10 6 kg/sec at an initial temperature of 18.0 oC. If the thermal efficiency of the heat engine is 32.0%:
(A) What is the change in temperature of the stream?
Ans:{.0531 0C}
(B) What is the change in entropy of the power plant's heat source per second? Be sure and indicate if the reservoir gains or loses entropy.
Ans:{+7.07 MJ/K, gain}
(C) Does this plant violate the second law of thermodynamics? Explain why?
Ans:{Yes, e th = 32.0% > e max = 25.9%}

Final Exam W2000

Do any FIVE of the following SIX questions. X-OUT the question you OMIT.

1. A 320 gram object oscillates 175 times a minute with a maximum speed of 32.0 cm/s. If the oscillations can be approximated by simple harmonic motion, x(t) = A sin(w t + f), with an initial phase angle of -38.0 o,

2. A 180 kg solid wooden sphere with a radius of 46.0 cm floats half submerged in oil. (The surface area of a sphere is 4π r2 and its volume is 4/3 π r3.)

3. Gasoline with a density of 790 kg/m 3 flows through the lower tube with a velocity of 110 cm/s. The gasoline flows into a smaller tube with a cross-sectional area of 14.0 mm 2 and out the end of the smaller tube at 260 cm/s into the atmosphere at a pressure of 105 kPa.

4. One end of an insulated - 46.0cm long - aluminum rod (a = 24x10 -6 / oC, k = 55.0 cal/ oC/m, c = .215 cal/g/ oC, Lf = 94.5 cal/g) is placed in a large insulated container of ice-water at 0 oC. The other end of the rod is placed in an insulated container of molten lead (a = 51x10 -6 / oC, k = 8.40 cal/ oC/m, c = .0310 cal/g/ oC, Lf = 5.90 cal/g) at its melting point, 327 oC. If 24.0 grams of lead freeze per minute:

5. A cold aluminum rod ( C = .215 cal/gm/ oC, a = 24.0x10 -6 1/ oC, k =230 W/m/ oC, Lf = 94.5 cal/gm) with a mass of 2.30 kg is placed in a large vat that contains a mixture of ice and water at 0.00 oC. Before the rod is placed in the vat it has a length of 198.00 cm and cross-sectional area of 4.30 cm 2; after it is placed in the vat it has a length of 198.69 cm.

6. A reversible heat engine use a 45.0 kg block of copper ( C = 29.4 cal/kg/ oC) at 590 oC as a heat source and dumps its exhaust heat into a large vat of ice and water at 0 oC. The heat pump operates until the temperature of the cooper block drops to that of the ice-water mixture.