The ballistic pendulum is a device used to measure the speed of a fast - moving projectile such as a bullet. The bullet is fired into a large block of wood suspended from some light wires. The bullet embeds in the block, and the entire system swings up to a height h. A Walther PPK, the gun used by James Bond, has an average muzzle velocity of 950 m/s. In a ballistic pendulum, how high would we expect the block to travel when shot by a Walther PPK, given the mass of a 0.32 ACP is 5 grams, a the mass of the block is 2kg

 h =

Explanation:

To solve this problem, let's work in parts, let's start with the conservation of the moment, for this we define a system formed by the block and the bullet, in such a way that the forces during the collision have been internal and the moment is conserved.

initial instant. Before the crash

         p₀ = m v₀

final instant. Right after the crash, but before the pendulum started to climb

         m_f = (m + M) v

the moment is preserved

        p₀ = p_f

        m v₀ = (m + M) v

        v =  

Now we work the pendulum system with embedded block, we use the concept of conservation of energy

starting point. Lower

        Em₀ = K = ½ (m + M) v²

final point. higher, when it stops

         Em_f = U = (m + M) g h

as there is no friction, energy is conserved

        Em₀ = Em_f

        ½ (m + M) v² = (m + M) g h

         h =

we substitute the speed value of the block plus bullet set

        h =

        h =

this could be newton#'s law of cooling. the cooling curve is exponential