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Figure 1 1-2 The kinetic energy after throwing or catching a ball is equal to the kinetic energy before plus the input work
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11 Energy and Its Conservation
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Catching a ball What happens when you catch a ball Before hitting your hands or glove, the ball is moving, so it has kineticc energy In catching it, you exert a force on the ball in the direction opposite to its motion Therefore, you do negative work on it, causing it to stop Now that the ball is not moving, it has no kinetic energy This process and the bar graph that represents it are shown in Figure 11-2b Kinetic energy is always positive, so the initial kinetic energy of the ball is positive The work done on the ball is negative and the final kinetic energy is zero Again, the kinetic energy after the ball has stopped is equal to the sum of the initial kinetic energy plus the work done on the ball
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Kinetic Energy
Recall that kinetic energy, KE 1 mv2, where m is the mass of the object 2 and v is the magnitude of its velocity The kinetic energy is proportional to the object s mass A 726-kg shot put thrown through the air has much more kinetic energy than a 0148-kg baseball with the same velocity, because the shot put has a greater mass The kinetic energy of an object is also proportional to the square of the object s velocity A car speeding at 20 m/s has four times the kinetic energy of the same car moving at 10 m/s Kinetic energy also can be due to rotational motion If you spin a toy top in one spot, does it have kinetic energy You might say that it does not because the top is not moving anywhere However, to make the top rotate, someone had to do work on it Therefore, the top has rotational kinetic energy This is one of the several varieties of energy Rotational kinetic 1 2 energy can be calculated using KErot I , where I is the object s 2 moment of inertia and is the object s angular velocity The diver, shown in Figure 11-3a, does work as she pushes off of the diving board This work produces both linear and rotational kinetic energies When the diver s center of mass moves as she leaps, linear kinetic energy is produced When she rotates about her center of mass, as shown in Figure 11-3b, rotational kinetic energy is produced Because she is moving toward the water and rotating at the same time while in the tuck position, she has both linear and rotational kinetic energy When she slices into the water, as shown in Figure 11-3c, she has linear kinetic energy
1 A skater with a mass of 520 kg moving at 25 m/s glides to a stop over a distance of 240 m How much work did the friction of the ice do to bring the skater to a stop How much work would the skater have to do to speed up to 25 m/s again 2 An 8750-kg compact car speeds up from 220 m/s to 440 m/s while passing another car What are its initial and final energies, and how much work is done on the car to increase its speed 3 A comet with a mass of 785 1011 kg strikes Earth at a speed of 250 km/s Find the kinetic energy of the comet in joules, and compare the work that is done by Earth in stopping the comet to the 42 1015 J of energy that was released by the largest nuclear weapon ever built
Figure 1 1-3 The diver does work as she pushes off of the diving board (a) This work produces rotational kinetic energy as she rotates about her center of mass (b) and she has linear kinetic energy when she slices into the water (c)
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