Chapter 9: Q2Q (page 376)
Can you give an example of a system that has no atoms located at its center of mass?
Short Answer
A hoop is a system that has no atoms located at its center of mass.
Chapter 9: Q2Q (page 376)
Can you give an example of a system that has no atoms located at its center of mass?
A hoop is a system that has no atoms located at its center of mass.
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Get started for freeThree uniform-density spheres are positioned as follows:
What is the location of the center of mass of this three-sphere system?
A uniform-density disk whose mass is 10 kg and radius is 0.4 m makes one complete rotation every 0.2 s. What is the rotational kinetic energy of the disk?
Consider the acceleration of a car on dry pavement, if there is no slipping. The axle moves at speed v, and the outside of the tire moves at a speed relative to the axle. The instantaneous velocity of the bottom of the tire is zero. How much work is done by the force exerted on the tire by the road? What is the source of the energy that increases the car’s translational kinetic energy?
A runner whose mass is 50 kgaccelerates from a stop to a speed of10 m / s in 3 s. (A good sprinter can run100 m in about 10 s, with an average speed of 10 m / s.) (a) What is the average horizontal component of the force that the ground exerts on the runner’s shoes? (b) How much displacement is there of the force that acts on the sole of the runner’s shoes, assuming that there is no slipping? Therefore, how much work is done on the extended system (the runner) by the force you calculated in the previous exercise? How much work is done on the point particle system by this force? (c) The kinetic energy of the runner increases—what kind of energy decreases? By how much?
Show that moment of inertia of a disk of mass M and radius R is . Divide the disk into narrow rings, each of radius r and width dr. The contribution I of by one of these rings is r2dm, where dm is amount of mass contained in that particular ring. The mass of any ring is the total mass times the fraction of the total area occupied by the area of the ring. The area of this ring is approximately . Use integral calculus to add up all the calculations.
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