A ballistic pendulum is a device that can be used in police labs to measure the

Question

A ballistic pendulum is a device that can be used in police labs to measure the muzzle velocity of a particular firearm. In this example, we're given the velocity of the bullet, and we're going to use that to find other things The ballistic pendulum is a simple device-the pendulum part consists of a wooden block, which has a mass of 840. grams, hanging from a string. The block is initially at rest. However, a bullet with a mass of 15.0 grams is fired at the block. The bullet embeds itself in the block, and the bullet and block then oscillate back and forth on the string, pendulum style, after the collision. Just before impact with the block, the bullet's velocity is 160. m/s, directed entirely horizontally. Use g 9.80 m/s (a) Determine the speed of the block bullet system immediately after the collision m/s (b) Determine the maximum height, measured from the level where the block starts, that the block bullet rise to after the collision.

Explanation / Answer

Given

   mass of bullet m = 15 g = 0.015 kg

   mass of wooden block M = 840 g = 0.84 kg

velocity of the bullet before the collision is vb = 160 m/s and of wooden block is vw = 0 m/s

a)
the law of conservation of momentum

   m*vb +M vW = (m+M)V

   V = m*vb /(m+M)
  
   v = 0.015*160 /(0.015+0.84) m/s

   V = 2.81 m/s

b)

by using this kinetic energy the bullet and wooden block system will reach to a height h

   given by conservation of energy

   0.5*(m+M)v^2 = (m+M)gh

   h = 0.5*v^2/g

   h = 0.5*2.81^2/9.8 m

   h = 0.4029 m/s

so the height reached by the system is 0.4029 m

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