In a ballistic pendulum an object of mass m is fired with an initial speed Vo at
ID: 1972009 • Letter: I
Question
In a ballistic pendulum an object of mass m is fired with an initial speed Vo 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 theta as shown .http://session.masteringphysics.com/problemAsset/1010989/30/1010989A.jpg
A) Find an expression for Vo, the initial speed of the fired object.
Express your answer in terms of some or all of the variables m, M, L, and theta and the acceleration due to gravity, g
B)An experiment is done to compare the initial speed of bullets fired from different handguns: a 9 mm and a .44 caliber. The guns are fired into a 10kg pendulum bob of length L. Assume that the 9mm bullet has a mass of 6g and the .44-caliber bullet has a mass of 12 g . If the 9mm bullet causes the pendulum to swing to a maximum angular displacement of 4.3 degrees and the .44-caliber bullet causes a displacement of 10.1 degrees , find the ratio of the initial speed of the 9-{ m mm} bullet to the speed of the .44-caliber bullet, (Vo)9/(Vo)44.
Express numerically
Explanation / Answer
QA) mass of the object = m mass of the bob = M length of the rod = L maximum angular displacement = ? initial speed of the mass = vo Initial Velocity of the combinedmass ( M + m ) just after collision = V From law of conservation of momentum, Total initial momentum beforecollision = Total final momentum after collision m vo = ( M + m ) V V = [ m / ( M + m ) ] vo maximum vertical heightraised, h = L ( 1 - cos ? ) kinetic energy at the lowest point= potential energy at the highest point ( 1/2 ) ( M + m ) V2 = ( M + m ) g h V2 = 2 g h V = v ( 2 g h ) V = v [ 2 g L ( 1- cos ? ) ] [ m / ( M + m ) ] vo = v [ 2 g L ( 1- cos ? )] vo = [ ( M + m ) / m] v [ 2 g L ( 1- cos ? ) ] QB) mass of the 9 mm bullet, m1 = 6 g mass of 0.44 caliber bullet, m2 = 12 g mass of the bob, M = 10 kg maximum angular displacement of 9 mm bullet ,?1 = 4.3o maximum angular displacement of 0.44 bullet, ?2 =10.1o = [ ( M + m1) / m1 ] v [ 2 g L ( 1- cos ?1) ] / [ ( M + m2) / m2] v [ 2 gL ( 1- cos ?2 ) ] = (m2/m1)v [ ( 1- cos 4.3o ) / (1- cos 10.1o ) ][M+m1=M+m2=M] = 2 * v ( 0.00281 / 0.0155 ) = 0.8524