An object of mass $1\ kg$ traveling in a straight line with a velocity of $10\ ms^{-1}$ collides with, and sticks to, a stationary wooden block of mass $5\ kg$. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
Given: An object of mass $1\ kg$ traveling in a straight line with a velocity of $10\ ms^{-1}$ collides with and sticks to, a stationary wooden block of mass $5\ kg$. Then they both move off together in the same straight line.
To do: To calculate the total momentum just before the impact and just after the impact. Also, to calculate the velocity of the combined object.
Solution:
Mass of the object $m_1=1\ kg.$
Velocity of the object $v_1=10\ ms^{-1}$
Mass of the wooden block $m_2=5\ kg.$
The velocity of the wooden block $v_2=04
As known, Initial momentum$=$Final momentum
Or $m_1v_1+m_2v_2=(m_1+m_2)V$ [Let $V$ be the velocity after collision of the objects]
$1\times10+5\times0=(1+5)V$
Or $10=6V$
Or $V=\frac{10}{6}\ ms^{-1}=\frac{5}{3}\ ms^{-1}$
Thus, the initial momentum$=10\ kg.ms^{-1}$
Final momentum$=10\ kg.ms^{-1}$
The velocity of the combined objects $=\frac{5}{3}\ ms^{-1}$
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