Review. Why is the following situation impassible? You are in the high-speed package delivers’ business. Your competitor in the next building gains the right-of-way to build an evacuated tunnel just above the ground all the way around the Earth. By firing packages into this tunnel at just the right speed, your competitor is able to send the packages into orbit around the Earth in this tunnel so that they arrive on the exact opposite side of the Earth in a very short time interval. You come up with a competing idea. Figuring that the distance through the Earth is shorter than the distance around the Earth, you obtain permits to build an evacuated tunnel through the center of the Earth (Fig. P15.50). By simply dropping packages into this tunnel, they fall downward and arrive at the other end of your tunnel, which is in a building right next to the other end of your competitor’s tunnel. Because your packages arrive on the other side of the Earth in a shorter time interval, you win the competition and your business flourishes. Note: An object at a distance r from the center of the Earth is pulled toward the center of the Earth only by the mass within the sphere of radius r (the reddish region in Fig. P15.50). Assume the Earth has uniform density. Figure P15.50
Review. Why is the following situation impassible? You are in the high-speed package delivers’ business. Your competitor in the next building gains the right-of-way to build an evacuated tunnel just above the ground all the way around the Earth. By firing packages into this tunnel at just the right speed, your competitor is able to send the packages into orbit around the Earth in this tunnel so that they arrive on the exact opposite side of the Earth in a very short time interval. You come up with a competing idea. Figuring that the distance through the Earth is shorter than the distance around the Earth, you obtain permits to build an evacuated tunnel through the center of the Earth (Fig. P15.50). By simply dropping packages into this tunnel, they fall downward and arrive at the other end of your tunnel, which is in a building right next to the other end of your competitor’s tunnel. Because your packages arrive on the other side of the Earth in a shorter time interval, you win the competition and your business flourishes. Note: An object at a distance r from the center of the Earth is pulled toward the center of the Earth only by the mass within the sphere of radius r (the reddish region in Fig. P15.50). Assume the Earth has uniform density. Figure P15.50
Solution Summary: The author explains Kepler's third law, where the square of the orbital period of Earth is proportional to the cube of its radius. The time period for the competitor’s package to arrive at an arbitrary position
Review.Why is the following situation impassible? You are in the high-speed package delivers’ business. Your competitor in the next building gains the right-of-way to build an evacuated tunnel just above the ground all the way around the Earth. By firing packages into this tunnel at just the right speed, your competitor is able to send the packages into orbit around the Earth in this tunnel so that they arrive on the exact opposite side of the Earth in a very short time interval. You come up with a competing idea. Figuring that the distance through the Earth is shorter than the distance around the Earth, you obtain permits to build an evacuated tunnel through the center of the Earth (Fig. P15.50). By simply dropping packages into this tunnel, they fall downward and arrive at the other end of your tunnel, which is in a building right next to the other end of your competitor’s tunnel. Because your packages arrive on the other side of the Earth in a shorter time interval, you win the competition and your business flourishes. Note: An object at a distance r from the center of the Earth is pulled toward the center of the Earth only by the mass within the sphere of radius r (the reddish region in Fig. P15.50). Assume the Earth has uniform density.
If you were to create a giant tunnel through the middle of the Earth, where would you be so that the force of attraction between you and the earth be the smallest?
A) Center of the earth
B) 10 miles above the surface of the Earth
C) 10 miles below the surface of the Earth
D) Surface of the Earth
After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 145s.
What is the magnitude of the gravitational acceleration on this planet?
gPlanet=(?)m/s^2
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).
Chapter 15 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.