The velocity of both the objects after the collision is [tex]\frac{25}{11} m/s[/tex].
(a) the relative velocity of the masses is zero.
(b) the compression of the spring is 0.185m.
The given case is an example of an inelastic collision in which two objects after the collision move together. The momentum of the system is conserved, therefore,
[tex]m_1u_1+m_2u_2=(m_1+m_2)v[/tex]
here, mâ = 5kg , mâ = 6kg
uâ = 5 m/s , initial velocity of mass mâ, and
uâ= 0, initial speed of the mass mâ
[tex]5\times5+0=(5+6)v\\\\v=\frac{25}{11}m/s[/tex]
(a) When the spring is fully compressed both the masses move with the same velocity, therefore the relative speed of the masses is zero.
(b) from the law of conservation of energy:
the initial kinetic energy of the masses is converted into final kinetic energies and the potential energy of the spring:
[tex]\frac{1}{2} m_1u_1^2+\frac{1}{2} m_2u^2_2=\frac{1}{2} (m_1+m_2)v^2+\frac{1}{2}kx^2[/tex]
where x is the compression of the spring
[tex]\frac{1}{2}\times5\times5^2+0=\frac{1}{2}(5+6)\times(\frac{25}{11})^2=\frac{1}{2}\times2000x^2\\\\x=0.185m[/tex]
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