Question

a bullet of mass m moving with velocity v strikes a suspended wooden block of mass M if the block rises to a height h the initial velocity of the block will be

Answer 1

$<b><u>$ Solution

The initial total energy (kinetic + potential) = the final total energy (kinetic + potential)

KE0 + PE0 = KEf + PEf

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=0.

KE0 = PEf

(1/2)(m+M)vf2 = (m+M)gh

We can use this 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*v0,bullet + Mblock*v0,block = (mbullet + Mblock)*vf

Since the block is not moving before the collision, v0,block = 0

mbullet*v0,bullet = (m+M)*vf

Rearranging to solve for in initial velocity of the bullet, "v0":

v0 = (m+M)*vf

                 m

Substituting in the expression for "vf" that we

v0 = (m+M)*√(2gh)

                   m