A satellite is floating in space. Solar wind sweeping past the satellite consists of a stream of particles, mainly hydrogen ions of mass 1.7×10−27 kg. There are about 0.5×105 ions per cubic meter, and their speed is 8.0×105 m/s. An `umbrella' attached to the satellite is slowly opened, such that the radius of the circular cross-section of the umbrella is changing with time as r(t)=bt2, where b=0.1 m/s2 is a constant (see the figure which shows the side and front views). What is the maximum change of momentum of the satellite due to the solar wind hitting this umbrella after a time of 10 seconds? Explain carefully why this is the maximum possible change. You must explain your reasoning every step of the way!

Two particles A and B are connected by a string. Mass m-5kg and mg-2kg. Determine accelerations a4 and as of the two particles. (g-9.81m/s²). 須畫自由體圖與動力圖,否則不計分。 B A G G E E

Problem 18:  A particle of mass 0.61 kg begins at rest and is then subject to a force in the positive x direction that changes with time as given by the following function: F = mg[1-e-3.1t ], where g is the acceleration due to gravity.  Part (a)  Determine the change in the velocity Δv of the particle between t = 0 and t = 2.3 sec. Part (b)  Determine the change in x-coordinate of the particle Δx between t = 0 and t = 2.3.

QUESTION 6 (Gauss's Law for Mass) Journey through the Center of the Earth. COLLAB. A 1024-kg blue ball is dropped from an initial z-position of 3 x 106 m through the center of a planet with radius 7.8 x 10° m. If the mass of the planet is 48.7 x 1015 kg, measure the displacement of the ball at time t = 6 s.

A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ? = 2.67 × 106 g/m3 and volume V =1.71 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 (Nm2)/(kg2).

QUESTION 6 (COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z- position of 2.1 x 10° m through the center of a planet with radius 7.7 x 106 m. If the mass of the planet is 46.5 x 1015 kg, measure the displacement of the ball at time t = 6 s?

The Earth and the Moon form a two-body system interacting through their mutual gravita- tional attraction. In addition, each body is attracted by the gravitational field of the Sun, which here we will treat as an external force to the two-body Earth-Moon system. Take the Sun as the origin and write down the equations of motion for the center of mass X and the relative position x of the Earth-Moon system. Expand the resulting expressions in powers of x/X, the ratio of their magnitudes. Show that to lowest order in x/X the center of mass and relative position are uncoupled, but that in higher orders they are coupled because the Sun's gravitational force is not constant.

QUESTION 6 (COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024.kg blue ball is dropped from an initial z-position of 2.6 x 106 m through the center of a planet with radius 7.7 x 1o6 m. If the mass of the planet is 36.7 x 1015 kg, measure the displacement of the ball at time t = 8 s?

Determine the x- and y-coordinates of the mass center of the plate of uniform thickness t = 0.20 in. The plate has a density that varies accoring to p = Po 10 (1 + 2/6). Answers: x = y = 16.9 x = ky² b=27" in. 17" Thickness t ! in.