a block of mass 4m rest on a frictionless surface and is attached to a spring(wi

Question

a block of mass 4m rest on a frictionless surface and is attached to a spring(with constant k)that is attached to the wall.A bullet of mass m and initial speed v initial hits the block and passes through it exiting with a final speed equal to (2/3)v initial.If x is the maximum compression of the spring,then what is the final speed of the bullet in terms of m,x and k?If the energy difference between the final and initial state is Q,then find Q in terms of the initial kinetic energy of the bullet.

Explanation / Answer

initial kinetic energy of bullet = 0.5mv2

final kinetic energy of bullet = 0.5m(2v/3)2

applying energy conservation we get ;

0.5kx2 = 0.5m(v2 - (2v/3)2)

x = v(5m/9k)1/2 (maximum compression)

Q = 0.5m*(5v2/9)

Q = (5/9)*KE

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