In a ballistic pendulum an object of mass m is fired with an initial speed v 0 a
ID: 1296393 • Letter: I
Question
In a ballistic pendulum an object of mass m is fired with an initial speed v0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement ? as shown (Figure 1) . An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 mm and a .44 caliber. The guns are fired into a10-kg pendulum bob of length L. Assume that the 9.0-mm bullet has a mass of 6.0 g and the .44-caliber bullet has a mass of 12 g . If the 9.0-mmbullet 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 9.0-mm bullet to the speed of the .44-caliber bullet, (v0)9.0/(v0)44.
Explanation / Answer
Vo = (m+M)*V1/m (conservation of momentum)
V1 = ?(2*g*h) where h is the vertical displacement of the bob. (conservation of energy after the impact)
h = L*(1-cos?) where ? is the angular displacement of the bob. (geometry)
Put these together and you have the answer....
Please specify the units of angular displacement