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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

User Melpomene
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1 Answer

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Answer:

h =
((m)/(m+M) )^2 \ (v_o^2)/(2g)

Step-by-step 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 =
(m)/(m+M) \ v_o

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 =
(v^2)/(2g)

we substitute the speed value of the block plus bullet set

h =
( (m)/( m+M) \ v_o )^2 \ (1)/(2g)

h =
((m)/(m+M) )^2 \ (v_o^2)/(2g)

User Dier
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