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Chapter 6: Q6.1-2PE (page 221)
Microwave ovens rotate at a rate of about . What is this in revolutions per second? What is the angular velocity in radians per second?
It is 0.1 revolutions per second (rps).
The angular velocity is .
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On February 14, 2000 the NEAR spacecraft was successfully inserted into orbit around Eros, becoming the first artificial satellite of an asteroid. Construct a problem in which you determine the orbital speed for a satellite near Eros. You will need to find the mass of the asteroid and consider such things as a safe distance for the orbit. Although Eros is not spherical, calculate the acceleration due to gravity on its surface at a point an average distance from its center of mass. Your instructor may also wish to have you calculate the escape velocity from this point on Eros.
If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a \(100{\rm{ m}}\) radius curve banked at \(15.0^\circ \). (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at \(20.0{\rm{ km}}/{\rm{h}}\)?
What is the ideal banking angle for a gentle turn of \(1.20{\rm{ km}}\) radius on a highway with a \(105{\rm{ km}}/{\rm{h}}\) speed limit (about \(65{\rm{ mi}}/{\rm{h}}\)), assuming everyone travels at the limit?
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about solar masses. A star orbiting on the galaxy鈥檚 periphery is about light-years from its center.
(a) What should the orbital period of that star be?
(b) If its period is instead, what is the mass of the galaxy? Such calculations are used to imply the existence of 鈥渄ark matter鈥� in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
A mother pushes her child on a swing so that his speed is at the lowest point of this path. The swing is suspended 2.00 mabove the child鈥檚 center of mass.
(a) What is the magnitude of the centripetal acceleration of the child at the low point?
(b) What is the magnitude of the force the child exerts on the seat if his mass is 18.0 kg?
(c) What is unreasonable about these results?
(d) Which premises are unreasonable or inconsistent?
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