Question

A ballistic pendulum is a device for the finding the speed of the bullets. A bullet of mass 10.7g is shot into a block of mass 5.60kg. After collision, the center of the mass of the block swings to a height of 50.0mm. Find the speed of the bullet.

Answer 1

Given that,

Mass of bullet = 10.7 g

Mass of block = 5.60 Kg

Height = 50.0 mm

We need to calculate the speed of block after collision

Using conservation of energy

$(m+M)gh=\dfrac{1}{2}(m+M)v^2$

Put the value into the formula

$9.8\times50.0\times10^{-3}=\dfrac{1}{2}v^2$

$v^2=0.49\times2$

$v=\sqrt{0.49\times2}$

$v=0.98\ m/s$

We need to calculate the initial velocity of bullet

Using conservation of momentum

$mu=(m+M)v$

Put the value into the formula

$10.7\times10^{-3}\times u=(10.7\times10^{-3}+5.60)\times0.98$

$u=\dfrac{(10.7\times10^{-3}+5.60)\times0.98}{10.7\times10^{-3}}$

$u=513.8\ m/s$

Hence, The initial speed of the bullet is 513.8 m/s.