Q08. Gravity

Which is the most efficient way to launch a satellite? 那一個發射衛星的方法效率最高？ Westward at low latitudes. 在低緯度朝西。 Eastward at low latitudes. 在低緯度朝東。 Westward at high latitudes. 在高緯度朝西。 Eastward at high latitudes. 在高緯度朝東。 <PowerClick><Answer>2</Answer><Option>4</Option></PowerClick>

Earth turns from west to east. A stationary object on earth has a tangential velocity vT pointing to the east. vT is largest at the equator. W E

Consider a planet in an elliptical orbit around the sun. 考慮一個在橢圓形繞日軌道上的行星。 Let WT be the work done by the gravitational force of the sun on the planet over a short period of time T, and W be the work done over a complete orbit of the planet. 設 WT 為太陽施於行星的重力在一短時間 T 內所作的功，W 則為完成整個軌道一次後所作的功。 Which of the following statement is true? 下面那一個論述是對的？ WT  0 , W  0. WT  0 , W ¹ 0 WT ¹ 0 , W  0 WT ¹ 0 , W ¹ 0 <PowerClick><Answer>3</Answer><Option>4</Option></PowerClick>

Elliptical orbit  F  dr ≠ 0  WT ≠ 0 Gravity is conservative  W = 0

Which point in the orbit has the lowest orbital velocity? 軌道上那一點的軌道速度最低？ A B C D <PowerClick><Answer>4</Answer><Option>4</Option></PowerClick>

 v is smallest when r is largest.

Suppose the paths in the figure are the paths of four projectiles. 假設圖中的路徑是四個拋射體的路徑。 All four projectiles were launched from a common point at the top of the figure. 四個拋射體都從圖頂的共同點發射。 Which projectile had the second-highest initial speed? 那一個拋射體的初速是第二大？ The projectile with the closed circular path. 走圓形路徑的拋射體。 The projectile with the hyperbolic path. 走雙曲線路徑的拋射體。 The projectile with the parabolic path. 走拋物線路徑的拋射體。 The projectile with the elliptical path. 走橢圓形路徑的拋射體。 <PowerClick><Answer>3</Answer><Option>4</Option></PowerClick>

E & K ordering from smallest to largest. 3 1 2 1

假設航空器 A 和 B 都在繞地球的圓形軌道上，且 B 比較高。 Suppose Spacecraft A and Spacecraft B are in circular orbits around the Earth, with Spacecraft B at a higher altitude. 假設航空器 A 和 B 都在繞地球的圓形軌道上，且 B 比較高。 Which one of the following statements is true? 下面的論述那一個是對的？ Spacecraft B has greater kinetic energy K. 航空器 B 有較大的動能 K。 A larger proportion of spacecraft B's total energy is kinetic. 航空器 B 的總能量中，動能佔的比重較大。 Spacecraft B has greater total energy, E. 航空器 B 有較大的總能量 E。 None of the above statements are true. 上述皆非。 <PowerClick><Answer>3</Answer><Option>4</Option></PowerClick>

Spacecraft B has greater kinetic energy K. 航空器 B 有較大的動能 K。 A larger proportion of spacecraft B's total energy is kinetic. 航空器 B 的總能量中，動能佔的比重較大。 Spacecraft B has greater total energy, E. 航空器 B 有較大的總能量 E。 None of the above statements are true. 上述皆非。 

如果地球的質量忽然增大四倍，它繞太陽運行的週期與原來的週期比較會 If the mass of the Earth were suddenly increased four times, its new period around the Sun compared to the original period would be 如果地球的質量忽然增大四倍，它繞太陽運行的週期與原來的週期比較會 four times greater. 變大四倍。 two times greater. 變大兩倍。 four times smaller. 變小四倍。 two times smaller. 變小兩倍。 unchanged. 不變。 <PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

 New orbit :    

以下有關繞著地球的人造衛星的論述中，那一個是對的？ Which of the following is true about artificial satellites in Earth's orbit? 以下有關繞著地球的人造衛星的論述中，那一個是對的？ The speed required to keep a satellite in a given orbit is proportional to the mass of the satellite. 維持衛星在軌道上所需的速率與衛星的質量成正比。 The satellite's period of revolution about the Earth is independent of its orbital radius. 衛星繞地球的週期與它的軌道半徑無關。 The speed of a satellite in a circular orbit can vary. 在圓形軌道上的衛星，其速率可以變動。 All the orbits for artificial satellites are circular. 人造衛星的軌道都是圓的。 A satellite in a larger circular orbit always has a longer orbital period than a satellite in a smaller circular orbit. 在較大圓形軌道上的衛星，週期一定比在較小圓形軌道上的衛星長。 <PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

The speed required to keep a satellite in a given orbit is proportional to the mass of the satellite. 維持衛星在軌道上所需的速率與衛星的質量成正比。 The satellite's period of revolution about the Earth is independent of its orbital radius. 衛星繞地球的週期與它的軌道半徑無關。 The speed of a satellite in a circular orbit can vary. 在圓形軌道上的衛星，其速率可以變動。 All the orbits for artificial satellites are circular. 人造衛星的軌道都是圓的。 A satellite in a larger circular orbit always has a longer orbital period than a satellite in a smaller circular orbit. 在較大圓形軌道上的衛星，週期一定比在較小圓形軌道上的衛星長 is indep of m. Elliptical in general.

Each of the four corners of a square with edge a is occupied by a point mass m. There is a fifth mass, also m, at the center of the square. To remove the mass from the center to a point far away the work that must be done by an external agent is given by : 4Gm2/a –4Gm2/a (42) Gm2/a –(42) Gm2/a 4Gm2/a2 <PowerClick><Answer>3</Answer><Option>5</Option></PowerClick>

Potential energy of m at center of square is : To bring it to infinity, where requires work

A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is R/4 R/3 R/2 R 2R <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

By definition: Maximum height H is given by: ( Energy conservation ) 

An object is dropped from an altitude of one Earth radius above Earth's surface. If M is the mass of Earth and R is its radius the speed of the object just before it hits Earth is given by : <PowerClick><Answer>1</Answer><Option>5</Option></PowerClick>

Energy conservation :