Answer to Question #101650 in Mechanics | Relativity for Titomi

Question

Class Work A bullet is shot into a wooden block suspended by strings and lodges in the block, losing energy in its penetration, and the increase in the height of the swinging block and bullet is measured. If the masses of the bullet and block are 19 gram and 50 gram respectively, and the swing rises 0.1m, determine the velocity of the penetrating bullet and the fraction of its energy lost during the penetration.

Answer 1

Let,

m=Mass of the bullet

M= Mass of the wooden block

Considering the energy conservation of the swing, where V is the initial velocity of the wooden block with the bullet included,

$(m+M)gh=\frac{1}{2}(m+M)v^2 \\ v=\sqrt{2gh}\\ v=1.400ms^{-1} \to(1)$

Considering the conservation of linear momentum,

where u is the speed of the bullet,

$mu=(m+M)v\\ u=\frac{(50+19)}{19}*1.4 \\ u=5.08ms^{-1}\\$

Considering the conservation of energy at the bullet impact,

Energy of the bullet = Energy gained by the wooden block with the bullet+ Energy LOSS(E)

$\frac{1}{2}mu^2 =(m+M)gh+E \\ E= 0.177J$