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Chapter 13: Q69P (page 384)
Question: In Fig. 13-18b, the scale on which thephysicist stand reads . How long will the cantaloupe take to reach the floor if the physicist drops it (from rest relative to himself) at a height ofabove the floor?
Answer:
Time taken by cantaloupe to reach the floor ist =1.1s
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Mile-high building.In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth’s rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh, to the top of the building.
Question: In a shuttle craft of mass m = 3.00 kg , Captain Janeway orbits a planet of mass , in a circular orbit of radius .What are (a) the period of the orbit and (b) the speed of the shuttle craft? Janeway briefly fires a forward pointing thruster, reducing her speeds by 2.00%. Just then, what are (c) the speed, (d) the kinetic energy, (e) the gravitational potential energy, and (f) the mechanical energy of the shuttle craft? (g) What is the semi major axis of the elliptical orbit now taken by the craft? (h)What is the difference between the period of the original circular orbit and that of the new elliptical orbit? (i) Which orbit has the smaller period?
A satellite has a circular orbit with a period ofand a radius of around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is , what is the radius of the planet?
We watch two identical astronomical bodies Aand B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation isRi. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this two body system. Use the principle of conservation of mechanical energy (Kf+ Uf=Ki +Ui ) to find the following when the center-to-center separation is 0.5Ri:
(a) the total kinetic energy of the system,
(b) the kinetic energy of each body,
(c) the speed of each body relative to us, and
(d) the speed of body Brelative to body A. Next assume that we are in a reference frame attached to body A(we ride on the body). Now we see body Bfall from rest toward us. From this reference frame, again useto find the following when the center-to-center separation is:
(e) the kinetic energy of body Band
(f) the speed of body Brelative to body A.
(g) Why are the answers to (d) and (f) different? Which answer is correct?
z Assume a planet is a uniform sphere of radiusRthat (somehow) has a narrow radial tunnel through its center. Also assume we can position an apple any where a long the tunnel or outside the sphere. Letbe the magnitude of the gravitational force on the apple when it is located at the planet’s surface. How far from the surface is there a point where the magnitude isrole="math" localid="1657195577959" if we move the apple (a) away from the planet and (b) into the tunnel?
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