Question

A 1 kg block of wood is attached to a spring, of force constant 200 N/m, which is attached to an immovable support. The block rests on a frictional surface with a coefficient of kinetic friction of 0.2. A 20 g bullet is fired into the block horizontally compressing the spring a maximum distance of 15 cm. Find the original velocity of the bullet before the collision.

Answer 1

`v=15.9499m/s`

Step-by-step explanation:

From the question we are told that:

Mass of wood
`m=1kg`

force constants
`k= 200N-m`

Coefficient of kinetic friction
`\mu= 0.2`

Bullet mass
`m_b= 20 \approx 0.02kg`

Spring compresion
`y=15cm \approx 0.15 m`

Generally the equation for kinetic energy of bullet
`K>E_b` is mathematically given by

Complete Question

`K.E_b=spring potential energy+work done against friction`

`K.E_b=(1)/(2) mbv^2`

`(1)/(2) m_b v^2=(1)/(2) ky^2+\mu my`

`(1)/(2) (0.02)v^2=(1)/(2) (0.2)(0.15)^2+0.2(1)(0.15)`

`v=15.9499m/s`

`v\approx16m/s`