PY CH 7 HW 3:

1)

140 grams of boiling water (temperature 100* C, heat capacity 4.2 J/gram/K) are poured into an aluminum pan whose mass is 950 grams and initial temperature 24" C (the heat capacity of aluminum is 0.9 ]/gram/K). (a) After a short time, what is the temperature of the water? final = (b) What simplifying assumptions did you have to make? Energy transfer between the system (water plus pan) and the surroundings was negligible during this time. o The thermal energy of the water doesn't change. The heat capacities for both water and aluminum hardly change with temperature in this temperature range. O The thermal energy of the aluminum doesn't change. (c) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 27417 J of work, and the temperature of the water and pan increases to 84.2 C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?A certain motor is capable of doing 8000 joules of work in 7 seconds. What is the power output of this motor? Power = watts\fDuring 3 hours one winter afternoon, when the outside temperature was 11' C, a house heated by electricity was kept at 25" C with the expenditure of 59 kwh (kilowatt hours) of electric energy. (a) What was the average energy leakage in joules per second (watts) through the walls of the house to the environment (the outside air and ground)? watts (b) The rate at which energy is transferred between two systems due to a temperature difference is often proportional to their temperature difference. Assuming this to hold in this case, if the house temperature had been kept at 29" C (84.2. F), how many kwh of electricity would have been consumed? kwhEnergy in a spring-mass system A horizontal spring-mass system has low friction, spring stiffness 215 N/m, and mass 0.2 kg. The system is released with an initial compression of the spring of 10 cm and an initial speed of the mass of 3 m/s. (a) What is the maximum stretch during the motion? m (b) What is the maximum speed during the motion? m/s71 = 3 kg, #1 = m/s 2 = 6 kg, #2 = m/s m3 = 2 kg, F3 = m/s (a) What is the total momentum of this system? Ftot = kg . m/s b) What is the velocity of the center of mass of this system? Ucm = m/s (c) What is the total kinetic energy of this system? Ktot = (d) What is the translational Ktrans - energy of this system? () What is the kinetic ene nergy of this system relative to the center of mass? One way to calculate Krel is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the particle's velocity relative to the center of mass, then calculating the corresponding kinetic energy, then adding up the three relative kinetic energies. However, there is a much simpler way to determine the specified quantity, without having to do all those calculations; think about what you know about the relationships among the various kinds of cinetic energy in a multiparticle system. (If you wish, you can check your result by doing the complicated calculation just described.)If an object has a moment of inertia 26 kg.m and rotates with an angular speed of 134 radians/s, what is its rotational kinetic energy? Krot =A barbell spins around a pivot at its center (see figure). The barbell consists of two small balls, each with mass m = 600 grams, at the ends of a very low mass rod whose length is _ = 21 cm. The barbell spins with angular speed a = 60 radians/s. Calculate Krot. Krot =A barbell consists of two massive balls connected by a low-mass rod. The barbell slides across a low-friction icy surface, spinning as it moves, as shown in the diagram. The mass m of each ball is 0.5 kg. The distance d between the centers of the balls is 0.31 m. The speed v of the center of mass of the barbell is 0.61 m/s, and the barbell makes one complete revolution in 3 seconds. What is the translational kinetic energy of the barbell? Ktrans = Considering only the motion of the barbell relative to its center of mass, what is the speed of one ball as it rotates around the center of the barbell? Vrot = m/s What is the rotational kinetic energy of the barbell? (This is the kinetic energy associated with motion relative to the center of mass.) Krot = What is the total kinetic energy of the barbell? *tot =