In a ballistic pendulum an object of mass is fired with an initial speed at a pe
ID: 1702013 • Letter: I
Question
In a ballistic pendulum an object of mass is fired with an initial speed at a pendulum bob. The bob has a mass , which is suspended by a rod of length and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement as shown .a) Find an expression for , the initial speed of the fired object.
b) An experiment is done to compare the initial speed of bullets fired from different handguns: a 9 and a .44 caliber. The guns are fired into a 10- pendulum bob of length . Assume that the 9- bullet has a mass of 6 and the .44-caliber bullet has a mass of 12 . If the 9- bullet causes the pendulum to swing to a maximum angular displacement of 4.3 and the .44-caliber bullet causes a displacement of 10.1 , find the ratio of the initial speed of the 9- bullet to the speed of the .44-caliber bullet, (vo)9/ (vo)44.
Explanation / Answer
Part A:
Vo = ((m+M)/m)(sqrt(2gL(1-cos(?))))
Part B:
First: 9mm
v0,9 = ((m+M)/m)((m+M)/m)(sqrt(2gL(1-cos(?))))
v0,9 = ((0.006+10)/0.006)(sqrt(2(9.8)L(1-cos(4.3))))
v0,9 = 1667.67(sqrt(19.6L(0.0028)))
v0,9 = 1667.67(sqrt(0.05488L))
v0,9 = 1667.67(0.2343)(sqrt(L))
v0,9 = 390.74sqrt(L)
Second: 0.44 caliber
0.44 caliber
v0,44 = ((m+M)/m)((m+M)/m)(sqrt(2gL(1-cos(?))))
v0,44 = ((0.012+10)/0.012)(sqrt(2(9.8)L(1-cos(10.1))))
v0,44 = 834.33(sqrt(19.6L(0.0155)))
v0,44 = 834.33(sqrt(0.3038L))
v0,44 = 834.33(0.55)(sqrt(L))
v0,44 = 458.88sqrt(L)
9mm / 0.44 caliber
v0,9 / v0,44 = 390.74sqrt(L) / 458.88sqrt(L) (The sqrt(L) cancel each other out)
v0,9 / v0,44 = 0.8515080195
v0,9 / v0,44 = 0.852