Athletes competing in the 50-m rifle three positions event use a 0.22-caliber (5.6 mm) small-bore, single-loader rifle. They shoot in prone, kneeling, and standing positions. Rifle barrels are grooved (called "rifling") so that bullets emerge from the barrel with spin along their longitudinal axis. Why? Conservation of angular momentum -- again! Bullets, like people on moving bicycles, are more stable because of rotation. Changing a large angular momentum requires a large torque. That is why it is easier to stay on a moving bicycle than on a stationary one. It's also how American football quarterbacks reduce air drag on their passes, by spinning the ball along its longitudinal axis, exactly analogous to the fired bullet.
Bullets emerge from the rifles at speeds around 331 m/s (740 mph), which isn't too far from sound speed. Air drag slows them so that they enter the target with a speed around 302 m/s (676 mph). I modeled the flight of the bullet with air drag and found that the bullet takes about one-sixth of a second to reach the target. Gee, where has that time of one-sixth of a second come up in the recent past? In my table-tennis post (click here)! A smashed table-tennis ball (initial speed of 20 m/s or 45 mph) with lots of topspin (120 rev/s or 7200 rpm) traverses a horizontal distance equivalent to the length of the table-tennis table (2.74 m or 9 feet) in a time of about one-sixth of a second. If you want to visualize the bullet's time of flight in "slow motion" on a "reduced scale," watch a table-tennis smash.
So, do you think you could hit the competition target from a distance of 50 m? Consider the image of the target given below (click on image for larger view).
The outermost circle, which defines the target's size, is 154.4 mm (6.08 in) in diameter. Just hitting the target means shooting inside an angle of 1/6 degree, which is 10' arc. Not much room for error, is there?!? Well, if you want to hit the bullseye, which is defined by the penultimate interior circle, which has a diameter of 10.4 mm (0.409 in), you must fire within an angle of 1/84 degree, which is 43" arc.
In the US, swimmers and gymnasts get all the press during the first week of the Summer Olympics; track and field takes center stage in the second week. Think about how difficult it is to win gold in a shooting event, and then remember the name Jamie Gray!
The concept of conservation of momentum works when we shoot something with a bullet.The bullet stores momentum before we shoot it then suddenly it looses its all momentum.
ReplyDeleteConservation of Angular Momentum
The bullet loses its linear and angular momenta after hitting the target and embedding itself into what lies behind the target. The bullet does not, however, lose its angular momenta "suddenly" after being shot -- if that is what your comment implies. Also, "before we shoot it," the bullet has essentially no linear momentum (with respect to the target's frame) because its speed is essentially zero and no angular momentum (with respect to its longitudinal axis) because its angular speed is zero. The bullet, therefore, "stores" no momenta before we shot it.
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That is why it is easier to stay on a moving bicycle than on a stationary one. It's also how American football quarterbacks reduce air drag on their passes, by spinning the ball along its longitudinal axis, exactly analogous to the fired bullet.ShootingTargets7
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