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Chapter 1: Q26E (page 461)
A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.250 m and the period is 3.20 s. What are the speed and acceleration of the block when x = 0.160 m?
The speed and acceleration of the block is and .
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Planet Vulcan.Suppose that a planet were discovered between the sun and Mercury, with a circular orbit of radius equal to of the average orbit radius of Mercury. What would be the orbital period of such a planet? (Such a planet was once postulated, in part to explain the precession of Mercury鈥檚 orbit. It was even given the name Vulcan, although we now have no evidence that it actually exists. Mercury鈥檚 precession has been explained by general relativity.)
A driver in Massachusetts was sent to traffic court for speeding. The evidence against the driver was that a policewoman observed the driver鈥檚 car alongside a second car at a certain moment, and the policewoman had already clocked the second car going faster than the speed limit. The driver argued, 鈥淭he second car was passing me. I was not speeding.鈥� The judge ruled against the driver because, in the judge鈥檚 words, 鈥淚f two cars were side by side, both of you were speeding.鈥� If you were a lawyer representing the accused driver, how would you argue this case?
The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (a) Compute the acceleration due to gravity on the surface of Venus from these data. (b) If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?
A closed and elevated vertical cylindrical tank with diameter 2.00 m contains water to a depth of 0.800 m. A worker accidently pokes a circular hole with diameter 0.0200 m in the bottom of the tank. As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure of 5 X 103Pa at the surface of the water. Ignore any effects of viscosity. (a) Just after the hole is made, what is the speed of the water as it emerges from the hole? What is the ratio of this speed to the efflux speed if the top of the tank is open to the air? (b) How much time does it take for all the water to drain from the tank? What is the ratio of this time to the time it takes for the tank to drain if the top of the tank is open to the air?
A Simple Reaction-Time Test.A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. When you see the meter stick released, you grab it with those two fingers. You can calculate your reaction time from the distance the meter stick falls, read directly from the point where your fingers grabbed it. (a) Derive a relationship for your reaction time in terms of this measured distance, d. (b) If the measured distance is 17.6 cm, what is your reaction time?
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