96上普物期中考 æ±&or

96上普物期中考 æ±&or

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Student ID Number: General Physics Midterm Examination (Fall Term) Write down the steps that lead to your answers. If your answers are represented by numbers, write the numbers scientific notation with two significant digits. For examples, 1478.5 should be written as 1 . 5 × 10 3 and 0.008327 should be written as 8 . 3 × 10 - 3 . Note that 454.5 should be written as 4 . 5 × 10 2 . Some people may carry the last digit to make it 4 . 55 × 10 2 first, then carry the last digit again to make it 4 . 6 × 10 2 . This is not right. Do not forget to include the units in your answers. Carry out your derivation and calculation on the scratch pad, then copy to the answer sheet neatly. Gravitational constant G = 6 . 67259 × 10 - 11 N · m 2 / kg 2 Mass of the Earth M = 5 . 976 × 10 24 kg Radius of the Earth at the equator R = 6 . 378 × 10 6 m Boltzmann’s constant k = 1 . 38065 × 10 - 23 J/ K Avogadro’s number N A = 6 . 02214 × 10 23 Vacuum permittivity ² 0 = 8 . 85418781762 × 10 - 12 C 2 / (N · m 2 ) Vacuum permeability μ 0 = 4 π × 10 - 7 T · m / A Planck’s constant h = 6 . 62607 × 10 - 34 J · s Electron mass m e = 9 . 10939 × 10 - 31 kg Proton mass m p = 1 . 6726 × 10 - 27 kg Neutron mass m n = 1 . 6749 × 10 - 27 kg Mass of the Sun: 1 . 9891 × 10 30 kg Distance between the Earth and the Sun: 1 . 50 × 10 11 m Do not read the hints until you are desperate, or you will lose all the fun. You can register at the proctor to get the hint for each specific problem, then the maximum score you can get for that problem will be 8 points. Without hint the maximum score is 10 points. There are no hints for problems 1 and 2, and the hints for problems 3 and 4 are already included for free. In the following problems, a ¿ b means a/b is arbitrarily small but not zero. 1. A solid ball of mass m and radius r is rotating around a horizontal shaft parallel to the x -axis. The angular velocity is ω ˆ x where ω > 0. The shaft is supported by two vertical poles that are parallel to the z -axis and separated by a distance d . The ball is at an equal distance d/ 2 from the poles. If the shaft is tilted by a small angle θ ¿ 1 as shown in Fig. 1, what is the impulse acted on each pole? Note that impulse is an vector, so you should include the direction of the impulse in your answer. 2. If the form of gravitational force is changed from
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96上普物期中考 æ±&or

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