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Chapter 6: Q6.1-3PE (page 221)
An automobile with 0.260 m radius tires travels80,000km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
The answer is revolutions.
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A large centrifuge, like the one shown in Figure (a), is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric re-entries. (a) At what angular velocity is the centripetal acceleration \(10g\) if the rider is \(15.0{\rm{ m}}\) from the centre of rotation? (b) The rider’s cage hangs on a pivot at the end of the arm, allowing it to swing outward during rotation as shown in Figure (b). At what angle \(\theta \) below the horizontal will the cage hang when the centripetal acceleration is \(10g\)? (Hint: The arm supplies centripetal force and supports the weight of the cage. Draw a free body diagram of the forces to see what the angle \(\theta \) should be.)
*Figure (a) NASA centrifuge used to subject trainees to accelerations similar to those experienced in rocket launches and re-entries. (Credit: NASA) (b) Rider in cage showing how the cage pivots outward during rotation. This allows the total force exerted on the rider by the cage to be along its axis at all times.
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.
Is there a real force that throws water from clothes during the spin cycle of a washing machine? Explain how the water is removed.
A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for the moon in Table 6.2.
Find the ratio of the mass of Jupiter to that of Earth based on data inTable 6.2.
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