A rifle is a long gun whose barrel has been grooved or \"rifled\" on the inside

Question

A rifle is a long gun whose barrel has been grooved or "rifled" on the inside with spiral channels. (For comparison, a long gun with a smooth bore is called a musket.) Bullets fired from a rifled barrel spin. This gives them greater stability in flight and thus greater accuracy when fired. Since 1964, the standard infantry weapon in the US Army has been the.22 caliber M16 rifle. Due to rifling, a bullet fired from an M16 rotates two and a half times on its journey from the breech to the muzzle. Given a barrel length of 510 mm and a muzzle velocity of 950 m/s, determine the average translational acceleration, the average rotational acceleration (in radians per second squared), and the final angular velocity (in rotations per second)

Explanation / Answer

Part a)

the average translational acceleration

We use the kinematic relations

V2 = Vo2 + 2 a X

Vo=0 leaves the rest

V2= 2 a X

a = V2/2X

X = 510 mm = 0.510 m

a= 9502/ (2 0.510)

a= 8.84 10-5m/s

Part b)

W2= Wo2+ 2

Data

Wo = 0 leaves the rest

= 2.5 rev (2 rad/1rev)

= 5 rad

W2 = 2

= W2 /2

To find the angular acceleration need the final angular velocity

as there is no data to calculate directly, we will assume that you can get from the relationship between the linear and rotational movement, if we had the energy of the bullet to the exit we could calculate the angular velocity through the kinetic energy

V = R W

R = 510 mm

W = V/R

W = 950 /0.510

W = 1862 rad/s

= 18622/ (2 5)

= 1.10 105 rad/s2

Part c)

W = 1862 rad/s

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