The ballistic pendulum Fig 811 is an apparatus used to measu

The ballistic pendulum (Fig. 8.11) is an apparatus used to measure the speed of a fast-moving projectile such as a bullet. A projectile of mass m\\ is fired into a large block of wood of mass m1 suspended from some light wires. The projectile embeds is the block, and the entire system swings through a height h. How can we determine the speed of the projectile from a measurement of h?

Solution

Let the speed of the bullet before collision be u

So, conserving momentum before and after collision:

m1*u = (m1+m2)*v

where v = speed of the bullet just after the collision

So, v = m1*u/(m1+m2)

Now, the KE of the combined mass = 0.5*(m1+m2)*v^2

After swinging to the highest position,

the PE gained = (m1+m2)*g*h

Now, by Work energy principle,

KE = PE

So, 0.5*(m1+m2)*v^2 = (m1+m2)*g*h

So, v = sqrt(2gh)

Now, v = m1*u/(m1+m2) = sqrt(2gh)

So, u = (m1+m2)*sqrt(2gh)/m1 <------answer