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標題:
Science
發問:
Take acceleration due to gravity at earth g=10m/s21. On an unknown airless planet an astronaut drops a 4.0 kg ball from a 60 m ledge.The mass hits the bottom with a speed of 12 m/s.a. What is the acceleration of gravity g on this planet?b. The planet has a twin moon with exactly the same acceleration of... 顯示更多 Take acceleration due to gravity at earth g=10m/s2 1. On an unknown airless planet an astronaut drops a 4.0 kg ball from a 60 m ledge. The mass hits the bottom with a speed of 12 m/s. a. What is the acceleration of gravity g on this planet? b. The planet has a twin moon with exactly the same acceleration of gravity. The difference is that this moon has an atmosphere. In this case, when dropped from a ledge with the same height, the 4.0 kg ball hits bottom at the speed of 9 m/s. How much energy is lost to air resistance during the fall? 2. A pendulum has a string with length 1.2 m. You hold it at an angle of 22 degrees to the vertical and release it. The pendulum bob has a mass of 2.0 kg. a. What is the potential energy of the bob before it is released? b. What is its speed when it passes through the midpoint of its swing? c. Now the pendulum is transported to Mars, where the acceleration of gravity g is 2.3 m/s2. Answer parts (a) and (b) again, but this time using the acceleration on Mars. 3. A cube of aluminum with a specific gravity of 2.70 and side length 4.00 cm is put into a beaker of methanol, which has a specific gravity of 0.791. a. Draw a free body diagram for the cube. b. Calculate the buoyant force acting on the cube. c. Calculate the acceleration of the cube toward the bottom when it is released.
最佳解答:
1. Use equation of motion: v^2 = u^2 + 2.a.s with u = 0 m/s, v = 12 m/s, s = 60 m, a = ? hence, 12^2 = 2a(60) i.e. a = 1.2 m/s^2 The acceleration due to gravity on the planet is 1.2 m/s^2 (b) Loss of kinetic energy = (1/2)(40)(12^2) - (1/2)(40)(9^2) J = 1260 J The kinetic energy loss is due to air friction. 2. Height of bob from mean position = [1.2 - 1.2cos(22)] m = 0.0874 m Hence, potential energy = 2g x 0.0874 J = 1.75 J (b) using energy conservation 1.75 = (1/2)(2)v^2 where v is the speed at the lowest point this gives v = 1.32 m/s2 (c) just repeat the above calculation with the new vlaue of g = 2.3 m/s2 instead of 10 m/s2 3. The diagram should show two forces, the weight of the aluminium cube (acting vertically downward) and the upthrust on it (acting vertically upward). (b) volume of cube = 4 x 4 x4 cm^3 = 64 cm^3 volume of methanol displaced = 64 cm^2 weight of methanol displaced = 64 x 0.791 gf = 50.624 gf Hence, buoyance force = 50.624 x10/1000 N = 0.506 N (c) Weight of cube = 64 x 2.7 gf = 172.8 gf = 1.728 N Net force = (1.728 - 0.506) N = 1.222 N hence, acceleration = 1.222/(172.8/1000) m/s^2 = 7 m/s^2
其他解答:C8D74AB62542840B
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