Two rectangular blocks A and B of masses 2 ,k | vedclass

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(C) As the block $A$ moves with velocity $u = 0.15 \,ms^{-1}$, it compresses the spring, which pushes block $B$ towards the right. The spring continue

Vedclass · Accepted Answer

$0.05$

Vedclass · Answer

(C) As the block $A$ moves with velocity $u = 0.15 \,ms^{-1}$, it compresses the spring, which pushes block $B$ towards the right. The spring continues to compress until the velocity of both blocks becomes equal. Let this common velocity be $v$.According to the law of conservation of linear momentum:$m_A u = (m_A + m_B) v$$v = \frac{m_A u}{m_A + m_B} = \frac{2 	imes 0.15}{2 + 3} = \frac{0.3}{5} = 0.06 \,ms^{-1}$According to the law of conservation of energy, the initial kinetic energy of block $A$ is converted into the final kinetic energy of the system and the potential energy stored in the spring at maximum compression $x$:$\frac{1}{2} m_A u^2 = \frac{1}{2} (m_A + m_B) v^2 + \frac{1}{2} k x^2$$\frac{1}{2} 	imes 2 	imes (0.15)^2 = \frac{1}{2} 	imes (2 + 3) 	imes (0.06)^2 + \frac{1}{2} 	imes 10.8 	imes x^2$$0.0225 = 5 	imes 0.0018 + 5.4 x^2$$0.0225 = 0.009 + 5.4 x^2$$5.4 x^2 = 0.0135$$x^2 = \frac{0.0135}{5.4} = 0.0025$$x = \sqrt{0.0025} = 0.05 \,m$

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