Conservation Laws - Real-life applications
C ONSERVATION OF L INEAR M OMENTUM : R IFLES AND R OCKETS
FIRING A RIFLE.
The conservation of linear momentum is reflected in operations as simple as the recoil of a rifle when it is fired, and in those as complex as the propulsion of a rocket through space. In accordance with the conservation of momentum, the momentum of a system must be the same after it undergoes an operation as it was before the process began. Before firing, the momentum of a rifle and bullet is zero, and therefore, the rifle-bullet system must return to that same zero-level of momentum after it is fired. Thus, the momentum of the bullet must be matched—and "cancelled" within the system under study—by a corresponding backward momentum.
When a person shooting a gun pulls the trigger, it releases the bullet, which flies out of the barrel toward the target. The bullet has mass and velocity, and it clearly has momentum; but this is only half of the story. At the same time it is fired, the rifle produces a "kick," or sharp jolt, against the shoulder of the person who fired it. This backward kick, with a velocity in the opposite direction of the bullet's trajectory, has a momentum exactly the same as that of the bullet itself: hence, momentum is conserved.
But how can the rearward kick have the same momentum as that of the bullet? After all, the bullet can kill a person, whereas, if one holds the rifle correctly, the kick will not even cause any injury. The answer lies in several properties of linear momentum. First of all, as noted earlier, momentum is equal to mass multiplied by velocity; the actual proportions of mass and velocity, however, are not important as long as the backward momentum is the same as the forward momentum. The bullet is an object of relatively small mass and high velocity, whereas the rifle is much larger in mass, and hence, its rearward velocity is correspondingly small.
In addition, there is the element of impulse, or change in momentum. Impulse is the product of force multiplied by change or interval in time. Again, the proportions of force and time interval do not matter, as long as they are equal to the momentum change—that is, the difference in momentum that occurs when the rifle is fired. To avoid injury to one's shoulder, clearly force must be minimized, and for this to happen, time interval must be extended.
If one were to fire the rifle with the stock (the rear end of the rifle) held at some distance from one's shoulder, it would kick back and could very well produce a serious injury. This is because the force was delivered over a very short time interval—in other words, force was maximized and time interval minimized. However, if one holds the rifle stock firmly against one's shoulder, this slows down the delivery of the kick, thus maximizing time interval and minimizing force.
ROCKETING THROUGH SPACE.
Contrary to popular belief, rockets do not move by pushing against a surface such as a launchpad. If that were the case, then a rocket would have nothing to propel it once it had been launched, and certainly there would be no way for a rocket to move through the vacuum of outer space. Instead, what propels a rocket is the conservation of momentum.
Upon ignition, the rocket sends exhaust gases shooting downward at a high rate of velocity. The gases themselves have mass, and thus, they have momentum. To balance this downward momentum, the rocket moves upward—though, because its mass is greater than that of the gases it expels, it will not move at a velocity as high as that of the gases. Once again, the upward or forward momentum is exactly the same as the downward or backward momentum, and linear momentum is conserved.
Rather than needing something to push against, a rocket in fact performs best in outer space, where there is nothing—neither launch-pad nor even air—against which to push. Not only is "pushing" irrelevant to the operation of the rocket, but the rocket moves much more efficiently without the presence of air resistance. In the same way, on the relatively frictionless surface of an ice-skating rink, conservation of linear momentum (and hence, the process that makes possible the flight of a rocket through space) is easy to demonstrate.
If, while standing on the ice, one throws an object in one direction, one will be pushed in the opposite direction with a corresponding level of momentum. However, since a person's mass is presumably greater than that of the object thrown, the rearward velocity (and, therefore, distance) will be smaller.
Friction, as noted earlier, is not the only force that counters conservation of linear momentum on Earth: so too does gravity, and thus, once again, a rocket operates much better in space than it does when under the influence of Earth's gravitational field. If a bullet is fired at a bottle thrown into the air, the linear momentum of the spent bullet and the shattered pieces of glass in the infinitesimal moment just after the collision will be the same as that of the bullet and the bottle a moment before impact. An instant later, however, gravity will accelerate the bullet and the pieces downward, thus leading to a change in total momentum.
C ONSERVATION OF A NGULAR M OMENTUM : S KATERS AND O THER S PINNERS
As noted earlier, angular momentum is equal to mr 2 ω, where m is mass, r is the radius of rotation, and ω stands for angular velocity. In fact, the first two quantities, mr 2 , are together known as moment of inertia. For an object in rotation, moment of inertia is the property whereby objects further from the axis of rotation move faster, and thus, contribute a greater share to the overall kinetic energy of the body.
One of the most oft-cited examples of angular momentum—and of its conservation—involves a skater or ballet dancer executing a spin. As the skater begins the spin, she has one leg planted on the ice, with the other stretched behind her. Likewise, her arms are outstretched, thus creating a large moment of inertia. But when she goes into the spin, she draws in her arms and leg, reducing the moment of inertia. In accordance with conservation of angular momentum, mr 2 ω will remain constant, and therefore, her angular velocity will increase, meaning that she will spin much faster.
The motion of a spinning top and a Frisbee in flight also illustrate the conservation of angular momentum. Particularly interesting is the tendency of such an object to maintain a constant orientation. Thus, a top remains perfectly vertical while it spins, and only loses its orientation once friction from the floor dissipates its velocity and brings it to a stop. On a frictionless surface, however, it would remain spinning—and therefore upright—forever.
A Frisbee thrown without spin does not provide much entertainment; it will simply fall to the ground like any other object. But if it is tossed with the proper spin, delivered from the wrist, conservation of angular momentum will keep it in a horizontal position as it flies through the air. Once again, the Frisbee will eventually be brought to ground by the forces of air resistance and gravity, but a Frisbee hurled through empty space would keep spinning for eternity.
WHERE TO LEARN MORE
Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.
"Conservation Laws: An Online Physics Textbook" (Web site). <http://www.lightandmatter.com/area1book2.html> (March 12, 2001).
"Conservation Laws: The Most Powerful Laws of Physics" (Web site). <http://webug.physics.uiuc.edu/courses/phys150/fall 99/slides/lect07/> (March 12, 2001).
"Conservation of Energy." NASA (Web site). <http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.html e; (March 12, 2001).
Elkana, Yehuda. The Discovery of the Conservation of Energy. With a foreword by I. Bernard Cohen. Cambridge, MA: Harvard University Press, 1974.
"Momentum and Its Conservation" (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/mo toc.html> (March 12, 2001).
Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981.
Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.