A block of wood of mass 0.5 kg is suspended by means of a thin wire. A bullet of mass 0.020 kg is fired horizontally in the plane of the block with a velocity of `100ms^(-1)`. If the bullet gets stuck inside the block, then calculate the height by which the system rises `(g=9.8ms^(-2))`. Calculate the amount of heat produced in the block.

Explanation

Mass of wooden block = 0.5 kg (M)
Mass of bullet (m) = 0.020 kg
Velocity of bullet = `100ms^(-1)(v_(2i))`
From the law of conservation of linear momentum
`Mv_(1i)+mv_(2i)=(M+m)v`
`0+0.02xx100=(0.5+0.02)v`
Velocity of the system of block & bullet
Velocity of the system of block & bullet
`v=(2)/(0.52)=3.85ms^(-1)`
Also K.E. of the system = P.E. of the system
`(1)/(2)(M+m)v^(2)=(M+m)gh`
`therefore h=(v^(2))/(2g)=(3.85xx3.85)/(2xx9.8)`
i.e. `h=0.756m`
Heat produced = `(1)/(2)mv_(1i)^(2)-(1)/(2)(M+m)v^(2)`
`=((1)/(2)xx0.02xx100xx100)-((1)/(2)(0.5+0.2)3.85xx3.85)`
`=100-3.854=96.15J`