Answer to Question #141510 in Mechanics | Relativity for Sandra

Question

Projectiles containing delicate electronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not from guns with short barrels. (a) State 2 factors that affect the range of a projectile fired from a gun (b) Explain why a projectile fired from a long-barrelled gun is subject to less acceleration than a projectile fired from a short-barrelled gun if the range is the same in both cases. © Draw a free-body force diagram for a projectile just after it has left the barrel of a gun (L)

Answer 1

A) Force of powder charges and barrel length.

B) Since the work is equal to the change in kinetic energy, $F\times L =\frac {m\times v ^ 2} {2}$ , where F is the force of powder charges, L is the length of the barrel, m is the mass of the projectile, v is the velocity of the projectile. Since acceleration $a =\frac {F} {m}$ , therefore:

$a =\frac {v ^ 2} {2\times L}$ , since the flight length $l =\frac {v ^ 2\times\sin {2\alpha}} {g}$ , then

$a =\frac {g\times l} {2\times L\times\sin {2\alpha}}$ , therefore the smaller the barrel length the greater the acceleration.