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Question

# A bullet of mass m kg and horizontal speed u ms−1 strikes a block of wood of mass M kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

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Solution

## The initial total energy (kinetic + potential) = the final total energy (kinetic + potential)KE0+PE0=KEf+PEfRight after the bullet hits the block, the initial height is 0, so PE0=0. When the bullet/block reaches its maximum height, it is at rest, so KEf=0KE0=PEf12(m+M)×vf2=(m+M)×gh Equation to solve for "vf, the velocity of the bullet/block after the collision: vf=√2gh For an inelastic collision (where the objects become stuck together), the initial momentum = final momentum. p0=pf mbullet×v0bullet+Mblock×v0block=(mbullet+Mblock)×vfSince the block is not moving before the collision,v0block=0mbullet×v0,bullet=(m+M)×vf Rearranging to solve for in initial velocity of the bullet, "v0": v0=(m+M)×vfm Substituting in the expression for "vf" solved for: v0=(m+M)×√2ghm

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