Question

A bullet with a mass of 45 g is fired into a 8.3-kg block of wood resting on a floor against a spring. This ideal spring (k = 76 N/m) has a maximum compression of 28 cm. What was the initial speed of the bullet?

Answer 1

The law of conservation of energy says

$$\frac{mv^2}{2}=\frac{kx^2}{2}$$

Hence, the initial velocity of a system "bullet+block"

$$v=\sqrt{\frac{k}{m_1+m_2}}x=\sqrt{\frac{76}{8.3+0.045}}\times 0.28=0.84\:\rm m/s.$$

The initial velocity of a bullet

$$v_0=\frac{m_1+m_2}{m_1}v=\frac{8.3+0.045}{0.045}\times 0.84=157\:\rm m/s$$