Question

Problem 3 A "ballistic pendulum" is a device (now largely obsolete, but very useful in its day) to measure the speed of a bullet as it hits a target. Let the target be a block of wood suspended from a string, as in the figure below. When the bullet hits, it is embedded in the wood, and together they swing, like a pendulum, to some maximum height h. The question is, how do you find the initial speed of the bullet (v) if you know the mass of the bullet (mi), the mass of the block (m2), and the height h? Ballistic pendulum. (a) Before the bullet hits. (b) After the bullet hits and is embedded in the block, at the maximum height of the swing.

Answer 1

During collision Momentum is Conserved therefore mv = (m + M) V rightdoublearrow v = (m + M/m) v (1) when pendulum swings and goes at height 'h' , i.e Maximum height energy (Potential & Kinetic) is conserved therefore 1/2 (m + M) V^2 = (m + M) gh rightdoublearrow v = squareroot 2gh (II) therefore from (I) & (II) V = m + M/m times squareroot 2gh