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Chapter 1: 15 (page 28)
A useful and easy-to-remember approximate value for the number of seconds in a year is饾洃脳107. Determine the percent error in this approximate value. (There are 365.24 days in one year.)
The percent error in the approximate value is 0.44%.
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Two identical stars with mass orbit around their center of mass. Each orbit is circular and has radius, so that the two stars are always on opposite sides of the circle. (a) Find the gravitational force of one star on the other. (b) Find the orbital speed of each star and the period of the orbit. (c) How much energy would be required to separate the two stars to infinity?
A shower head has 20 circular openings, each with radius 1.0 mm. The shower head is connected to a pipe with radius 0.80 cm. If the speed of water in the pipe is 3.0 m/s, what is its speed as it exits the shower-head openings?
Starting from the front door of a ranch house, you walk 60.0 m due east to a windmill, turn around, and then slowly walk 40.0 m west to a bench, where you sit and watch the sunrise. It takes you 28.0 s to walk from the house to the windmill and then 36.0 s to walk from the windmill to the bench. For the entire trip from the front door to the bench, what are your (a) average velocity and (b) average speed?
Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth鈥檚 surface; at the high point, or apogee, it is 4000 km above the earth鈥檚 surface. (a) What is the period of the spacecraft鈥檚 orbit? (b) Using conservation of angular momentum, find the ratio of the spacecraft鈥檚 speed at perigee to its speed at apogee. (c) Using conservation of energy, find the speed at perigee and the speed at apogee. (d) It is necessary to have the spacecraft escape from the earth completely. If the spacecraft鈥檚 rockets are fired at perigee, by how much would the speed have to be increased to achieve this? What if the rockets were fired at apogee? Which point in the orbit is more efficient to use?.
(a) Write each vector in Fig. E1.39 in terms of the unit vectors and . (b) Use unit vectors to express vector , where (c) Find the magnitude and direction .
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