The ballistic pendulum was used to measure the speeds of bullets before electronic timing devices were developed. The version shown in Fig. 10-11 consists of a large block of wood of mass M = 5.4 kg, hanging from two long cords. A bullet of mass m = 9.5 g is fired into the block, coming quickly to rest. The block + bullet then swing upward, their center of mass rising a vertical distance” = 6.3 cm before the pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the collision?
SOLUTION; We can see that the bullet’s speed v must determine the rise height h. However, a Key Idea is that we cannot use the conservation of mechanical energy to relate these two quantities because surely energy is transferred from mechanical energy to other forms (such as thermal energy and energy to break apart the wood) as the bullet penetrates the block. Another Key Idea helps-we can split this complicated motion into two steps )hat we can separately analyze: (I) the buller block collision and (2) the bullet block rise, during which mechanical energy is conserved.
Step 1. Because the collision within the bullet-block system is so brief, we can make two important assumptions: (I) During the collision, the gravitational force on the block and the force on the block from the cords are still balanced. Thus, during the collision, the net external impulse on the bullet-block system is zero.
Step 2. As the bullet and block now swing up together, the mechanical energy of the bullet block Earth system is conserved. (This mechanical energy is not changed by the force of the cords on the block.