Approaching the ISS A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of 7500 kg. The International Space Station (ISS) has a mass of 420,000 kg. When Soyuz docks at the ISS, the two centers of mass are separated by 9.5 m. (a) Find the average of the gravitational force of attraction between the two spacecraft when Soyuz is docked and when it is 110 m from the ISS. (b) If Soyuz approached the ISS from rest at a distance of 110 m, a thruster would have to counteract the average force of gravitational attraction between it and the ISS. If this thruster has an exhaust velocity of 590 m/s, at what average rate must it burn fuel (in kg/s) to counteract the pull of the ISS? (See Section 9-8 for a discussion of thrust.) (c) If the approach requires 330 s, how much fuel will the thruster burn in order to counteract the gravitational attraction?
Approaching the ISS A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of 7500 kg. The International Space Station (ISS) has a mass of 420,000 kg. When Soyuz docks at the ISS, the two centers of mass are separated by 9.5 m. (a) Find the average of the gravitational force of attraction between the two spacecraft when Soyuz is docked and when it is 110 m from the ISS. (b) If Soyuz approached the ISS from rest at a distance of 110 m, a thruster would have to counteract the average force of gravitational attraction between it and the ISS. If this thruster has an exhaust velocity of 590 m/s, at what average rate must it burn fuel (in kg/s) to counteract the pull of the ISS? (See Section 9-8 for a discussion of thrust.) (c) If the approach requires 330 s, how much fuel will the thruster burn in order to counteract the gravitational attraction?
Approaching the ISS A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of 7500 kg. The International Space Station (ISS) has a mass of 420,000 kg. When Soyuz docks at the ISS, the two centers of mass are separated by 9.5 m. (a) Find the average of the gravitational force of attraction between the two spacecraft when Soyuz is docked and when it is 110 m from the ISS. (b) If Soyuz approached the ISS from rest at a distance of 110 m, a thruster would have to counteract the average force of gravitational attraction between it and the ISS. If this thruster has an exhaust velocity of 590 m/s, at what average rate must it burn fuel (in kg/s) to counteract the pull of the ISS? (See Section 9-8 for a discussion of thrust.) (c) If the approach requires 330 s, how much fuel will the thruster burn in order to counteract the gravitational attraction?
Figure 8.14 shows a cube at rest and a small object heading toward it. (a) Describe the directions (angle 1) at which the small object can emerge after colliding elastically with the cube. How does 1 depend on b, the so-called impact parameter? Ignore any effects that might be due to rotation after the collision, and assume that the cube is much more massive than the small object. (b) Answer the same questions if the small object instead collides with a massive sphere.
2. A projectile is shot from a launcher at an angle 0,, with an initial velocity
magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a
child's noggin (see Figure 1). The apple is a height y above the tabletop, and a
horizontal distance x from the launcher. Set this up as a formal problem, and solve
for x. That is, determine an expression for x in terms of only v₁, 0, y and g.
Actually, this is quite a long expression. So, if you want, you can determine an
expression for x in terms of v., 0., and time t, and determine another expression for
timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of
t into the expression for x. Your final equation(s) will be called Equation 3 (and
Equation 4).
Draw a phase portrait for an oscillating, damped spring.
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