Without benefit of modern instrumentation, you are required to determine the spe

Question

Without benefit of modern instrumentation, you are required to determine the speed of a bullet. You do this using a ballistic mass your bullet is m_b = 0.050 kg. The mass of the target block is M = 8.0 kg. You measure the height reached by the bullet/block after the inelastic collision ash = 0.72 meters. a) Find the mechanical energy of the bullet block. b) Use conservation of energy to determine the initial speed of the bullet/block right after the collision. c) Then use conservation of linear momentum to determine the speed of the bullet before the collision. (Show all your work!)

Explanation / Answer

a) Mechanical energy of the bullet block system = potetial energy at height h

So, Mecahanical energy = (m+M)*g*h = (0.050+8)*9.8*0.72 = 56.8 J

b) As from the given condition

Kinetic energyof bullet-block system = potential energy of bullet-block system (by using conservation of energy)

(1/2)(m+M)V2 = 56.8

V = sqrt (2*56.8/(0.050+8)) = 3.756 m/s

c) bullet of mass m (initial speed v) embeds in pendulum (M) at rest, momentum conservation
before = after
m*v +0 = (M+m) V

v = (M+m) V /m

= (8+0.050)*3.756 / 0.050

= 604.7 m/s

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