PROBLEM ONE Pete meets Eileen for the first time and is immediately attracted to her. If Pete has a mass of 86 kg and Eileen has a mass of 59 kg and they are separated by a distance of 2 m, is their attraction purely physical? PROBLEM TWO What is the value of g at a distance from the earth (Me = 5.98 x 10 24 kg) of two (2) earth radii? PROBLEM THREE Three 5.0-kg masses are located at points in the xy plane, as shown. What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0, y = 0.30 m? PROBLEM FOUR What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 x 10 6 m around the Earth? (Mass of Earth = 6.0 x 10 24 kg.) PROBLEM FIVE An object is released from rest at a distance h above the surface of a planet (mass = M, radius = R < h). With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet. PROBLEM SIX What is the escape speed from a planet of mass M and radius R if M = 3.2 x 10 23 kg and R = 2.4 x 10 6 m? Please be sure to show all your work. Once complete, you should scan your homework and submit the file as an attachment here. If you do not have access to a scanner, please contact your instructorBEFORE THE DUE DATE to make arrangements for another method of submission. PROBLEM SEVEN In a few billion years, the sun will start undergoing changes that will eventually result in its puffing up into a red giant star. (Near the beginning of this process, the earth’s oceans will boil off, and by the end, the sun will probably swallow the earth completely.) As the sun’s surface starts to get closer and close to the earth, how will the earth’s orbit be affected? Complete the following problems: 1. Two kilograms of water at 100°C is converted to steam at 1 atm. Find the work done (in J). (The density of steam at 100°C is 0.598 kg/m3 .) 2. How much heat, in joules, is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (Lice = 333 J/g; Lsteam = 2.26 ´ 103 J/g.) 3. Assume 3.0 moles of a diatomic gas has an internal kinetic energy of 10 kJ. Determine the temperature of the gas after it has reached equilibrium. 4. One mole of helium gas expands adiabatically from 2 atm pressure to 1 atm pressure. If the original temperature of the gas is 20°C, what is the final temperature of the gas? (g = 1.67) 5. A refrigerator has a coefficient of performance of 4. If the refrigerator absorbs 30 cal of heat from the cold reservoir in each cycle, how much heat is expelled (in cal) into the heat reservoir? 6. An 800-MW electric power plant has an efficiency of 30%. It loses its waste heat in large cooling towers. Approximately how much waste heat (in MJ) is discharged to the atmosphere per second? 7. Exactly 500 grams of ice are melted at a temperature of 32°F. (Lice = 333 J/g.) What is the change in entropy (in J/K) ? 8. Answer any two (2) of the following questions in as much detail as possible. Once you have completed your post, respond to the post of at least 2 of your classmates. 1. Why will a refrigerator with a fixed amount of food consume more energy in a warm room than in a cold room? 2. Water put into a freezer compartment in the same refrigerator goes into a state of less molecular disorder when it freezes. Is this an exception to theentropy principle? 3. Comment on the following statement: The second law of thermodynamics is one of the most fundamental laws of nature, yet it is not an exact law at all. PROBLEM ONE An object of mass 0.03 kg is displaced from its equilibrium position at x = 0 to a distance x = 40 cm and is then released. The restoring force acting on the object is proportional to its displacement and acts in the opposite direction of the displacement. The period of an oscillating particle is 2.0 sec. Write equations for (a) the position x versus t, (b) the velocity v versus t, (c) the acceleration a versus t, and find (d) the maximum velocity of the particle, (e) the maximum acceleration of the particle and (f) its total energy. PROBLEM TWO A simple pendulum 2.50 m long swings with a maximum angular displacement of 16°. Find its (a) period of vibrations, (b) frequency of vibrations, (c) linear speed at its lowest point of vibration, and (d) linear acceleration at the end of its path. PROBLEM THREE A spherical ornament of mass 0.01 kg and radius 0.20 m is doing simple harmonic motion about an axis passing through its surface. It swings back and forth as a physical pendulum. Find its period of oscillation. PROBLEM FOUR A 0.540 kg mass is attached to the end of a spring with force constant k = 300 N/m. The object is displaced and released. A damping force F = −b v acts on the object where b = 7.5 kg/s. (a) Find the frequency of the oscillation of the mass. (b) For what value of b will the motion be critically damped? PROBLEM FIVE The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s) is the potential energy equal to the kinetic energy? PROBLEM SIX An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow? PROBLEM SEVEN For the wave described by , determine the first positive x coordinate where y is a maximum when t = 0. PROBLEM EIGHT Answer the following questions in as much detail as possible. Once you have completed your post, respond to the post of at least 2 of your classmates. 1. Nikola Tesla, one of the inventors of radio and an archetypal mad scientist, told a credulous reporter in 1912 the following story about an application of resonance. He built an electric vibrator that fit in his pocket, and attached it to one of the steel beams of a building that was under construction in New York. Although the article in which he was quoted didn’t say so, he presumably claimed to have tuned it to the resonant frequency of the building. “In a few minutes, I could feel the beam trembling. Gradually the trembling increased in intensity and extended throughout the whole great mass of steel. Finally, the structure began to creak and weave, and the steelworkers came to the ground panic-stricken, believing that there had been an earthquake. … [If] I had kept on ten minutes more, I could have laid that building flat in the street.” Is this physically plausible? 2. A sound wave that underwent a pressure-inverting reflection would have its compressions converted to expansions and vice versa. How would its energy and frequency compare with those of the original sound? Would it sound any different? What happens if you swap the two wires where they connect to a stereo speaker, resulting in waves that vibrate in the opposite way?