What is the initial speed of the bullet?

Question

A 30-g bullet is shot horizontally into a 650-g wooden block attached to a spring (k=800 N/m). If the block compresses by 20 cm what is the initial speed of the bullet? (Assume frictionless surface)

Answer 1

Given

Mass of the bullet, m_b = 30 g = 0.03 kg

Mass of the wooden block, m_w = 650 g =0.65 kg

Spring constant, k = 800 N/m

Compressed length of the spring, x = 20 cm = 0.2 m

Calculate the initial speed of the bullet by using the conservation of the energy.

T₁ + V₁ = T₂ +V₂ 

(1/2) m_bv₁² + 0 = (1/2) m_wv₂² + 0 +(1/2) k x²

(1/2) (0.03)v₁²  = (1/2) (0.65) (0) ² + 0 +(1/2)(800)(0.2)²

(0.03)v₁²  =(800)(0.2)²

v₁²  =1066.667

v₁=32.66 m/s

Therefore, the initial speed of the bullet is 32.66 m/s