A bullet of mass `0.012kg` and horizontal speed `70 ms^(-1)` strikes a block of wood of mass `0.4kg` and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

Explanation

Mass of the bullet m = 0.012 kg
Initial speed of the bullet `u = 70 ms^(-1)`
Final speed of the bullet ` v = 0 ms^(-1)`
Mass of wooden block M = 0.04 kg
Initial speed of the system of the bullet and the block after collision = `V ms^(-1)` (Supposed )
From the law of conservation of momentum ,
` :. ` { momentum of bullet and block before collision } = { momentum of bullet and block after collision}
` :. "mu" +Mu_(1) = (m+M) V`
` :. "mu" =(M+m) V " " [ :. u_(1)=0] `
` :. V = ("mu")/(M+m)`
` =(0.012 xx70)/(0.4 +0.012) =(0.84)/(0.412) = 2.0388 approx 2.04 ms^(-1)`
` = 0.006 xx4900 -(0.412)/2 xx 4.1616`
` = 29.4 - 0.206 xx4.1616 `
` = 29.4 - 0.857`
`H approx 28.543 J `