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

Answer:

$v=15.9499m/s$

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

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

$K.E_b=\frac{1}{2} mbv^2$

$\frac{1}{2} m_b v^2=\frac{1}{2} ky^2+\mu my$

$\frac{1}{2} (0.02)v^2=\frac{1}{2} (0.2)(0.15)^2+0.2(1)(0.15)$

$v=15.9499m/s$

$v\approx16m/s$