Chapter 13: Q9 CQ (page 409)
A satellite in low-Earth orbit is not truly travelling through a vacuum. Rather, it moves through very thin air. Does the resulting air friction cause the satellite to slow down?
The air friction helps the satellite speed up the air resistance.
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An object is released from rest at an altitude h above the surface of the Earth. (a) Show that its speed at a distance r from the Earth’s center, where , is
(b) Assume the release altitude is. Perform the integral
to find the time of fall as the object moves from the release point to the Earth’s surface. The negative sign appears because the object is moving opposite to the radial direction, so its speed is. Perform the integral numerically.
Work done on a system puts energy into it. Work done by a system removes energy from it. Give an example for each statement.
(a) If a hole could be dug to the center of the Earth, would the force on an object of mass m still obey Equation 13.1 there? (b) What do you think the force on m would be at the center of the Earth?
Two spheres having masses Mand 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. (a) What two isolated system models are appropriate for this system? (b) Write an equation from one of the models and solve it for , the velocity of the sphere of mass M at any time after release in terms of , the velocity of 2M. (c) Write an equation from the other model and solve it for speed in terms of speed when the spheres collide. (d) Combine the two equations to find the two speeds and when the spheres collide.
The maximum distance from the Earth to the Sun (at aphelion) is , and the distance of closest approach (at perihelion) is . The Earth’s orbital speed at perihelion is . Determine (a) the Earth’s orbital speed at aphelion and the kinetic and potential energies of the Earth–Sun system (b) at perihelion and (c) at aphelion. (d) Is the total energy of the system constant? Explain. Ignore the effect of the Moon and other planets.
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