Question

1. An object of mass 3kg moving with an initial velocity of 5i m/s² collides with and sticks to an object of mass 2kg with an initial velocity of -3j m/s². What is the velocity of the composite object
2. A 30kg hammer strikes a steel spike of 2.3cm in diameter while moving with a speed of 20m/s². The hammer rebounds with a speed of 10m/s² after 0.11s. What is the average strain in the spike during this impact.

Answer 1

1)

$u=\frac{m_1v_1+m_2v_2}{m_1+m_2}=\frac{3\cdot 5-2\cdot 3}{3+2}=1.8i~\frac ms.$

2)

$F=\frac{m\Delta v}{\Delta t}=\frac{30\cdot(20-(-10))}{0.11}=8.18~kN,$

$p=\frac FA=\frac{4F}{\pi d^2}=\frac{4\cdot 8180}{3.14\cdot 0.023^2}=19.7\cdot 10^6~\frac {N}{m^2},$

$S=\frac pY=\frac{19.7\cdot 10^6}{2\cdot 10^{11}}=10^{-4}.$