A bullet of mass 9 g moving with an initial speed 400 m/s is fired into and pass

Question

A bullet of mass 9 g moving with an initial speed 400 m/s is fired into and passes through a block of mass 2 kg, as shown in the figure. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring of force constant 439 N/m. If the block moves a distance 3.6 cm to the right after the bullet passed through it, find the speed v at which the bullet emerges from the block.
Answer in units of m/s. Find the magnitude of the energy lost in the collision. Answer in units of J

Explanation / Answer

Let velocity of bullet after is v Let velocity of 2 kg mass be v' so 2*v'^2 = 439*(.036^2) v'^2 = 439*(.036^2)/2 v' = 0.533359 m/s center of mass of the system will remain same so 400*.009/(2.009) = (.009*v+ 2* 0.533359 )/2.009 v =( 400*.009 - 2* 0.533359 )/.009 v =281.475 m/s Energy lost in during the process is .5*.009*(400^2) = .5*.009*(281.475^2) + .5*439*(.039^2) + Energy Energy = .5*.009*(400^2) - .5*.009*(281.475^2) - .5*439*(.039^2) Energy = 720 - 356.52679 - 0.3338595 Energy = 363.139J

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