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Professional Application
A 30,000-kg freight car is coasting at 0.850 m/s with negligible friction under a hopper that dumps 110,000 kg of scrap metal into it. (a) What is the final velocity of the loaded freight car? (b) How much kinetic energy is lost?
Professional Application
Space probes may be separated from their launchers by exploding bolts. (They bolt away from one another.) Suppose a 4800-kg satellite uses this method to separate from the 1500-kg remains of its launcher, and that 5000 J of kinetic energy is supplied to the two parts. What are their subsequent velocities using the frame of reference in which they were at rest before separation?
0.704 m/s
–2.25 m/s
A 0.0250-kg bullet is accelerated from rest to a speed of 550 m/s in a 3.00-kg rifle. The pain of the rifle’s kick is much worse if you hold the gun loosely a few centimeters from your shoulder rather than holding it tightly against your shoulder. (a) Calculate the recoil velocity of the rifle if it is held loosely away from the shoulder. (b) How much kinetic energy does the rifle gain? (c) What is the recoil velocity if the rifle is held tightly against the shoulder, making the effective mass 28.0 kg? (d) How much kinetic energy is transferred to the rifle-shoulder combination? The pain is related to the amount of kinetic energy, which is significantly less in this latter situation. (e) Calculate the momentum of a 110-kg football player running at 8.00 m/s. Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s. Discuss its relationship to this problem.
(a) 4.58 m/s away from the bullet
(b) 31.5 J
(c) –0.491 m/s
(d) 3.38 J
Professional Application
One of the waste products of a nuclear reactor is plutonium-239 $\left({}^{\text{239}}\text{Pu}\right)$ . This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus $({}^{4}{\text{He}}^{}+{}^{\text{235}}\mathrm{U})$ , the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is $\text{8.40}\times {\text{10}}^{\u2013\text{13}}\phantom{\rule{0.25em}{0ex}}\mathrm{J}$ and is entirely converted to kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is $\text{6.68}\times {\text{10}}^{\u2013\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ , while that of the uranium is $3\text{.}\text{92}\times {\text{10}}^{\u2013\text{25}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ (note that the ratio of the masses is 4 to 235). (a) Calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest. (b) How much kinetic energy does each nucleus carry away? Note that the data given here are accurate to three digits only.
Professional Application
The Moon’s craters are remnants of meteorite collisions. Suppose a fairly large asteroid that has a mass of $5\text{.}\text{00}\times {10}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ (about a kilometer across) strikes the Moon at a speed of 15.0 km/s. (a) At what speed does the Moon recoil after the perfectly inelastic collision (the mass of the Moon is $7\text{.}\text{36}\times {10}^{\text{22}}\phantom{\rule{0.25em}{0ex}}\text{kg}$ ) ? (b) How much kinetic energy is lost in the collision? Such an event may have been observed by medieval English monks who reported observing a red glow and subsequent haze about the Moon. (c) In October 2009, NASA crashed a rocket into the Moon, and analyzed the plume produced by the impact. (Significant amounts of water were detected.) Answer part (a) and (b) for this real-life experiment. The mass of the rocket was 2000 kg and its speed upon impact was 9000 km/h. How does the plume produced alter these results?
(a) $1\text{.}\text{02}\times {\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$
(b) $5\text{.}\text{63}\times {\text{10}}^{\text{20}}\phantom{\rule{0.25em}{0ex}}\mathrm{J}$ (almost all KE lost)
(c) Recoil speed is $6\text{.}\text{79}\times {\text{10}}^{-\text{17}}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ , energy lost is $6\text{.}\text{25}\times {\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\mathrm{J}$ . The plume will not affect the momentum result because the plume is still part of the Moon system. The plume may affect the kinetic energy result because a significant part of the initial kinetic energy may be transferred to the kinetic energy of the plume particles.
Professional Application
Two football players collide head-on in midair while trying to catch a thrown football. The first player is 95.0 kg and has an initial velocity of 6.00 m/s, while the second player is 115 kg and has an initial velocity of –3.50 m/s. What is their velocity just after impact if they cling together?
What is the speed of a garbage truck that is $1\text{.}\text{20}\times {\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{kg}$ and is initially moving at 25.0 m/s just after it hits and adheres to a trash can that is 80.0 kg and is initially at rest?
24.8 m/s
During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of 10.0 kg and the horizontal component of its velocity is 8.00 m/s when the 65.0-kg performer catches it. If the performer is on nearly frictionless roller skates, what is his recoil velocity?
(a) During an ice skating performance, an initially motionless 80.0-kg clown throws a fake barbell away. The clown’s ice skates allow her to recoil frictionlessly. If the clown recoils with a velocity of 0.500 m/s and the barbell is thrown with a velocity of 10.0 m/s, what is the mass of the barbell? (b) How much kinetic energy is gained by this maneuver? (c) Where does the kinetic energy come from?
(a) 4.00 kg
(b) 210 J
(c) The clown does work to throw the barbell, so the kinetic energy comes from the muscles of the clown. The muscles convert the chemical potential energy of ATP into kinetic energy.
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