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Chapter 12: Q. 32 (page 331)
A 5.0 kg cat and a 2.0 kg bowl of tuna fish are at opposite ends of the 4.0-m-long seesaw of FIGURE EX12.32. How far to the left of the pivot must a 4.0 kg cat stand to keep the seesaw balanced?
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A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain.
b. What is the satellite’s speed at point b?
c. What is the satellite’s speed at point c?
FIGURE CP12.89 shows a cube of mass m sliding without frictionat speed v0. It undergoes a perfectly elastic collision with the bottom tip of a rod of length d and mass M = 2m. The rod is pivoted about a frictionless axle through its center, and initially it hangs straight down and is at rest. What is the cube’s velocity— both speed and direction—after the collision?
Your engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. You’ve previously determined that the turbine’s moment of inertia is 2.6 kg m2. The next job is to measure the frictional torque of the bearings. Your plan is to run the turbine up to a predetermined rotation speed, cut the power, and time how long it takes the turbine to reduce its rotation speed by 50,. Your data are given in the table. Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the frictional torque.
A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity v, then the end of the axle is placed on a support that allows the gyroscope to precess. a. Find an expression for the precession frequency Ω in terms of M, R, v, and g. b. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?
A solid sphere of radius R is placed at a height of 30 cm on a slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius be released on the same slope in order to equal the sphere's speed at the bottom?
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