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Chapter 5: Q4 (page 206)
Tarzan swings back and forth on a vine. At the microscopic level, why is the tension force on Tarzan by the vine greater than it would be if he were hanging motionless?
As the vine stretches more, that pulls up more Tarzan.
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A rope is attached to a block, as shown in Figure 5.64. The rope pulls on the block with a force of, at an angle ofto the horizontal (this force is equal to the tension in the rope).
(a) What is thecomponent of the force on the block due to the rope?
(b) What is the component of the force on the block due to the rope?
A particle moving at nearly the speed of light passes through a region where it is subjected to a magnetic force of constant magnitude that is always perpendicular to the momentum and has a magnitude of . As a result, the particle moves along a circular arc with a radius of 8m. What is the magnitude of the momentum of this particle?
In outer space a rock of mass 4kgis attached to a long spring and swung at constant speed in a circle of radius 9m. The spring exerts a force of constant magnitude 760N.
(a) What is the speed of the rock?
(b) What is the direction of the spring force?
(c)The relaxed length of the spring is 8.7m. What is the stiffness of this spring?
(a) Many communication satellites are placed in a circular orbit around the Earth at a radius where the period (the time to go around the Earth once) is\(24\;{\rm{h}}\). If the satellite is above some point on the equator, it stays above that point as the Earth rotates, so that as viewed from the rotating Earth the satellite appears to be motionless. That is why you see dish antennas pointing at a fixed point in space. Calculate the radius of the orbit of such a "synchronous" satellite. Explain your calculation in detail.
(b) Electromagnetic radiation including light and radio waves travels at a speed of\(3 \times {10^8}\;{\rm{m}}/{\rm{s}}\). If a phone call is routed through a synchronous satellite to someone not very far from you on the ground, what is the minimum delay between saying something and getting a response? Explain. Include in your explanation a diagram of the situation.
(c) Some human-made satellites are placed in "near-Earth" orbit, just high enough to be above almost all of the atmosphere. Calculate how long it takes for such a satellite to go around the Earth once, and explain any approximations you make.
(d) Calculate the orbital speed for a near-Earth orbit, which must be provided by the launch rocket. (The advantages of near-Earth communications satellites include making the signal delay unnoticeable, but with the disadvantage of having to track the satellites actively and having to use many satellites to ensure that at least one is always visible over a particular region.)
(e) When the first two astronauts landed on the Moon, a third astronaut remained in an orbiter in circular orbit near the Moon's surface. During half of every complete orbit, the orbiter was behind the Moon and out of radio contact with the Earth. On each orbit, how long was the time when radio contact was lost?
A child rides on a playground merry-go-round, from the center. The merry-go-round makes one complete revolution every 5 s. How large is the net force on the child? In what direction does the net force act?
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